[{"data":1,"prerenderedAt":4841},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse":4829},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":441,"checks":4747,"conditions":4779,"conditionsHtml":4780,"deprecated":4781,"description":4741,"extension":4782,"figure":4781,"figureCaption":4781,"figureHtml":4781,"formulaId":4783,"latex":4784,"latexHtml":4785,"level":4786,"meta":4787,"navigation":4788,"path":4789,"redirectFrom":4790,"related":4791,"seo":4796,"stem":4797,"subject":577,"summary":4798,"tags":4799,"variables":4805,"__hash__":4828},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse.md","Varianz einer Zufallsgröße",[550,551,552,553,554],"Varianz Zufallsvariable","V(X) berechnen","Var(X)","Varianz Wahrscheinlichkeitsverteilung","Sigma Zufallsgröße",{"type":556,"value":557,"toc":4740},"minimark",[558,563,936,939,1114,1121,1630,1634,1732,2249,2862,3294,3746,4294,4298],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,666,667,671,672,718,719,748,749,839,840,935],"p",{},"Der Erwartungswert ",[568,569,572,612],"span",{"className":570},[571],"katex",[568,573,576],{"className":574},[575],"katex-mathml",[577,578,580],"math",{"xmlns":579},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[581,582,583,607],"semantics",{},[584,585,586,590,594,597,601,604],"mrow",{},[587,588,589],"mi",{},"μ",[591,592,593],"mo",{},"=",[587,595,596],{},"E",[591,598,600],{"stretchy":599},"false","(",[587,602,603],{},"X",[591,605,606],{"stretchy":599},")",[608,609,611],"annotation",{"encoding":610},"application\u002Fx-tex","\\mu = E(X)",[568,613,617,643],{"className":614,"ariaHidden":616},[615],"katex-html","true",[568,618,621,626,631,636,640],{"className":619},[620],"base",[568,622],{"className":623,"style":625},[624],"strut","height:0.625em;vertical-align:-0.1944em;",[568,627,589],{"className":628},[629,630],"mord","mathnormal",[568,632],{"className":633,"style":635},[634],"mspace","margin-right:0.2778em;",[568,637,593],{"className":638},[639],"mrel",[568,641],{"className":642,"style":635},[634],[568,644,646,650,654,658,662],{"className":645},[620],[568,647],{"className":648,"style":649},[624],"height:1em;vertical-align:-0.25em;",[568,651,596],{"className":652,"style":653},[629,630],"margin-right:0.0576em;",[568,655,600],{"className":656},[657],"mopen",[568,659,603],{"className":660,"style":661},[629,630],"margin-right:0.0785em;",[568,663,606],{"className":664},[665],"mclose"," sagt, wo eine Zufallsgröße im Mittel liegt. Die ",[668,669,670],"strong",{},"Varianz"," ",[568,673,675,696],{"className":674},[571],[568,676,678],{"className":677},[575],[577,679,680],{"xmlns":579},[581,681,682,693],{},[584,683,684,687,689,691],{},[587,685,686],{},"V",[591,688,600],{"stretchy":599},[587,690,603],{},[591,692,606],{"stretchy":599},[608,694,695],{"encoding":610},"V(X)",[568,697,699],{"className":698,"ariaHidden":616},[615],[568,700,702,705,709,712,715],{"className":701},[620],[568,703],{"className":704,"style":649},[624],[568,706,686],{"className":707,"style":708},[629,630],"margin-right:0.2222em;",[568,710,600],{"className":711},[657],[568,713,603],{"className":714,"style":661},[629,630],[568,716,606],{"className":717},[665]," misst, wie stark die Werte um ",[568,720,722,736],{"className":721},[571],[568,723,725],{"className":724},[575],[577,726,727],{"xmlns":579},[581,728,729,733],{},[584,730,731],{},[587,732,589],{},[608,734,735],{"encoding":610},"\\mu",[568,737,739],{"className":738,"ariaHidden":616},[615],[568,740,742,745],{"className":741},[620],[568,743],{"className":744,"style":625},[624],[568,746,589],{"className":747},[629,630]," streuen. Für jeden Wert ",[568,750,752,773],{"className":751},[571],[568,753,755],{"className":754},[575],[577,756,757],{"xmlns":579},[581,758,759,770],{},[584,760,761],{},[762,763,764,767],"msub",{},[587,765,766],{},"x",[587,768,769],{},"i",[608,771,772],{"encoding":610},"x_i",[568,774,776],{"className":775,"ariaHidden":616},[615],[568,777,779,783],{"className":778},[620],[568,780],{"className":781,"style":782},[624],"height:0.5806em;vertical-align:-0.15em;",[568,784,786,789],{"className":785},[629],[568,787,766],{"className":788},[629,630],[568,790,793],{"className":791},[792],"msupsub",[568,794,798,830],{"className":795},[796,797],"vlist-t","vlist-t2",[568,799,802,825],{"className":800},[801],"vlist-r",[568,803,807],{"className":804,"style":806},[805],"vlist","height:0.3117em;",[568,808,810,815],{"style":809},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[568,811],{"className":812,"style":814},[813],"pstrut","height:2.7em;",[568,816,822],{"className":817},[818,819,820,821],"sizing","reset-size6","size3","mtight",[568,823,769],{"className":824},[629,630,821],[568,826,829],{"className":827},[828],"vlist-s","​",[568,831,833],{"className":832},[801],[568,834,837],{"className":835,"style":836},[805],"height:0.15em;",[568,838],{}," quadriert man die Abweichung ",[568,841,843,866],{"className":842},[571],[568,844,846],{"className":845},[575],[577,847,848],{"xmlns":579},[581,849,850,863],{},[584,851,852,858,861],{},[762,853,854,856],{},[587,855,766],{},[587,857,769],{},[591,859,860],{},"−",[587,862,589],{},[608,864,865],{"encoding":610},"x_i - \\mu",[568,867,869,926],{"className":868,"ariaHidden":616},[615],[568,870,872,876,916,919,923],{"className":871},[620],[568,873],{"className":874,"style":875},[624],"height:0.7333em;vertical-align:-0.15em;",[568,877,879,882],{"className":878},[629],[568,880,766],{"className":881},[629,630],[568,883,885],{"className":884},[792],[568,886,888,908],{"className":887},[796,797],[568,889,891,905],{"className":890},[801],[568,892,894],{"className":893,"style":806},[805],[568,895,896,899],{"style":809},[568,897],{"className":898,"style":814},[813],[568,900,902],{"className":901},[818,819,820,821],[568,903,769],{"className":904},[629,630,821],[568,906,829],{"className":907},[828],[568,909,911],{"className":910},[801],[568,912,914],{"className":913,"style":836},[805],[568,915],{},[568,917],{"className":918,"style":708},[634],[568,920,860],{"className":921},[922],"mbin",[568,924],{"className":925,"style":708},[634],[568,927,929,932],{"className":928},[620],[568,930],{"className":931,"style":625},[624],[568,933,589],{"className":934},[629,630]," und gewichtet sie mit ihrer Wahrscheinlichkeit.",[564,937,938],{},"Sie ist das Gegenstück zur empirischen Varianz von Messdaten: Statt relativer Häufigkeiten stehen hier Wahrscheinlichkeiten.",[564,940,941,942,945,946,1083,1084,1113],{},"Die ",[668,943,944],{},"Standardabweichung"," ist ",[568,947,949,979],{"className":948},[571],[568,950,952],{"className":951},[575],[577,953,954],{"xmlns":579},[581,955,956,976],{},[584,957,958,961,963],{},[587,959,960],{},"σ",[591,962,593],{},[964,965,966],"msqrt",{},[584,967,968,970,972,974],{},[587,969,686],{},[591,971,600],{"stretchy":599},[587,973,603],{},[591,975,606],{"stretchy":599},[608,977,978],{"encoding":610},"\\sigma = \\sqrt{V(X)}",[568,980,982,1002],{"className":981,"ariaHidden":616},[615],[568,983,985,989,993,996,999],{"className":984},[620],[568,986],{"className":987,"style":988},[624],"height:0.4306em;",[568,990,960],{"className":991,"style":992},[629,630],"margin-right:0.0359em;",[568,994],{"className":995,"style":635},[634],[568,997,593],{"className":998},[639],[568,1000],{"className":1001,"style":635},[634],[568,1003,1005,1009],{"className":1004},[620],[568,1006],{"className":1007,"style":1008},[624],"height:1.24em;vertical-align:-0.305em;",[568,1010,1013],{"className":1011},[629,1012],"sqrt",[568,1014,1016,1074],{"className":1015},[796,797],[568,1017,1019,1071],{"className":1018},[801],[568,1020,1023,1048],{"className":1021,"style":1022},[805],"height:0.935em;",[568,1024,1028,1032],{"className":1025,"style":1027},[1026],"svg-align","top:-3.2em;",[568,1029],{"className":1030,"style":1031},[813],"height:3.2em;",[568,1033,1036,1039,1042,1045],{"className":1034,"style":1035},[629],"padding-left:1em;",[568,1037,686],{"className":1038,"style":708},[629,630],[568,1040,600],{"className":1041},[657],[568,1043,603],{"className":1044,"style":661},[629,630],[568,1046,606],{"className":1047},[665],[568,1049,1051,1054],{"style":1050},"top:-2.895em;",[568,1052],{"className":1053,"style":1031},[813],[568,1055,1059],{"className":1056,"style":1058},[1057],"hide-tail","min-width:1.02em;height:1.28em;",[1060,1061,1067],"svg",{"xmlns":1062,"width":1063,"height":1064,"viewBox":1065,"preserveAspectRatio":1066},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[1068,1069],"path",{"d":1070},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[568,1072,829],{"className":1073},[828],[568,1075,1077],{"className":1076},[801],[568,1078,1081],{"className":1079,"style":1080},[805],"height:0.305em;",[568,1082],{},". Sie hat dieselbe Einheit wie ",[568,1085,1087,1100],{"className":1086},[571],[568,1088,1090],{"className":1089},[575],[577,1091,1092],{"xmlns":579},[581,1093,1094,1098],{},[584,1095,1096],{},[587,1097,603],{},[608,1099,603],{"encoding":610},[568,1101,1103],{"className":1102,"ariaHidden":616},[615],[568,1104,1106,1110],{"className":1105},[620],[568,1107],{"className":1108,"style":1109},[624],"height:0.6833em;",[568,1111,603],{"className":1112,"style":661},[629,630]," und ist deshalb anschaulicher.",[564,1115,1116,1117,1120],{},"Oft schneller ist der ",[668,1118,1119],{},"Verschiebungssatz",":",[568,1122,1125],{"className":1123},[1124],"katex-display",[568,1126,1128,1231],{"className":1127},[571],[568,1129,1131],{"className":1130},[575],[577,1132,1134],{"xmlns":579,"display":1133},"block",[581,1135,1136,1228],{},[584,1137,1138,1140,1142,1144,1146,1148,1150,1152,1161,1163,1165,1171,1173,1191,1200,1203,1206,1208,1210,1212,1218,1220,1222],{},[587,1139,686],{},[591,1141,600],{"stretchy":599},[587,1143,603],{},[591,1145,606],{"stretchy":599},[591,1147,593],{},[587,1149,596],{},[591,1151,600],{"stretchy":599},[1153,1154,1155,1157],"msup",{},[587,1156,603],{},[1158,1159,1160],"mn",{},"2",[591,1162,606],{"stretchy":599},[591,1164,860],{},[1153,1166,1167,1169],{},[587,1168,589],{},[1158,1170,1160],{},[591,1172,593],{},[1174,1175,1176,1179,1188],"munderover",{},[591,1177,1178],{},"∑",[584,1180,1181,1183,1185],{},[587,1182,769],{},[591,1184,593],{},[1158,1186,1187],{},"1",[587,1189,1190],{},"n",[1192,1193,1194,1196,1198],"msubsup",{},[587,1195,766],{},[587,1197,769],{},[1158,1199,1160],{},[591,1201,1202],{},"⋅",[587,1204,1205],{},"P",[591,1207,600],{"stretchy":599},[587,1209,603],{},[591,1211,593],{},[762,1213,1214,1216],{},[587,1215,766],{},[587,1217,769],{},[591,1219,606],{"stretchy":599},[591,1221,860],{},[1153,1223,1224,1226],{},[587,1225,589],{},[1158,1227,1160],{},[608,1229,1230],{"encoding":610},"V(X) = E(X^2) - \\mu^2 = \\sum_{i=1}^{n} x_i^2 \\cdot P(X = x_i) - \\mu^2",[568,1232,1234,1261,1317,1362,1512,1537,1595],{"className":1233,"ariaHidden":616},[615],[568,1235,1237,1240,1243,1246,1249,1252,1255,1258],{"className":1236},[620],[568,1238],{"className":1239,"style":649},[624],[568,1241,686],{"className":1242,"style":708},[629,630],[568,1244,600],{"className":1245},[657],[568,1247,603],{"className":1248,"style":661},[629,630],[568,1250,606],{"className":1251},[665],[568,1253],{"className":1254,"style":635},[634],[568,1256,593],{"className":1257},[639],[568,1259],{"className":1260,"style":635},[634],[568,1262,1264,1268,1271,1274,1305,1308,1311,1314],{"className":1263},[620],[568,1265],{"className":1266,"style":1267},[624],"height:1.1141em;vertical-align:-0.25em;",[568,1269,596],{"className":1270,"style":653},[629,630],[568,1272,600],{"className":1273},[657],[568,1275,1277,1280],{"className":1276},[629],[568,1278,603],{"className":1279,"style":661},[629,630],[568,1281,1283],{"className":1282},[792],[568,1284,1286],{"className":1285},[796],[568,1287,1289],{"className":1288},[801],[568,1290,1293],{"className":1291,"style":1292},[805],"height:0.8641em;",[568,1294,1296,1299],{"style":1295},"top:-3.113em;margin-right:0.05em;",[568,1297],{"className":1298,"style":814},[813],[568,1300,1302],{"className":1301},[818,819,820,821],[568,1303,1160],{"className":1304},[629,821],[568,1306,606],{"className":1307},[665],[568,1309],{"className":1310,"style":708},[634],[568,1312,860],{"className":1313},[922],[568,1315],{"className":1316,"style":708},[634],[568,1318,1320,1324,1353,1356,1359],{"className":1319},[620],[568,1321],{"className":1322,"style":1323},[624],"height:1.0585em;vertical-align:-0.1944em;",[568,1325,1327,1330],{"className":1326},[629],[568,1328,589],{"className":1329},[629,630],[568,1331,1333],{"className":1332},[792],[568,1334,1336],{"className":1335},[796],[568,1337,1339],{"className":1338},[801],[568,1340,1342],{"className":1341,"style":1292},[805],[568,1343,1344,1347],{"style":1295},[568,1345],{"className":1346,"style":814},[813],[568,1348,1350],{"className":1349},[818,819,820,821],[568,1351,1160],{"className":1352},[629,821],[568,1354],{"className":1355,"style":635},[634],[568,1357,593],{"className":1358},[639],[568,1360],{"className":1361,"style":635},[634],[568,1363,1365,1369,1446,1450,1503,1506,1509],{"className":1364},[620],[568,1366],{"className":1367,"style":1368},[624],"height:2.9291em;vertical-align:-1.2777em;",[568,1370,1374],{"className":1371},[1372,1373],"mop","op-limits",[568,1375,1377,1437],{"className":1376},[796,797],[568,1378,1380,1434],{"className":1379},[801],[568,1381,1384,1406,1419],{"className":1382,"style":1383},[805],"height:1.6514em;",[568,1385,1387,1391],{"style":1386},"top:-1.8723em;margin-left:0em;",[568,1388],{"className":1389,"style":1390},[813],"height:3.05em;",[568,1392,1394],{"className":1393},[818,819,820,821],[568,1395,1397,1400,1403],{"className":1396},[629,821],[568,1398,769],{"className":1399},[629,630,821],[568,1401,593],{"className":1402},[639,821],[568,1404,1187],{"className":1405},[629,821],[568,1407,1409,1412],{"style":1408},"top:-3.05em;",[568,1410],{"className":1411,"style":1390},[813],[568,1413,1414],{},[568,1415,1178],{"className":1416},[1372,1417,1418],"op-symbol","large-op",[568,1420,1422,1425],{"style":1421},"top:-4.3em;margin-left:0em;",[568,1423],{"className":1424,"style":1390},[813],[568,1426,1428],{"className":1427},[818,819,820,821],[568,1429,1431],{"className":1430},[629,821],[568,1432,1190],{"className":1433},[629,630,821],[568,1435,829],{"className":1436},[828],[568,1438,1440],{"className":1439},[801],[568,1441,1444],{"className":1442,"style":1443},[805],"height:1.2777em;",[568,1445],{},[568,1447],{"className":1448,"style":1449},[634],"margin-right:0.1667em;",[568,1451,1453,1456],{"className":1452},[629],[568,1454,766],{"className":1455},[629,630],[568,1457,1459],{"className":1458},[792],[568,1460,1462,1494],{"className":1461},[796,797],[568,1463,1465,1491],{"className":1464},[801],[568,1466,1468,1480],{"className":1467,"style":1292},[805],[568,1469,1471,1474],{"style":1470},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[568,1472],{"className":1473,"style":814},[813],[568,1475,1477],{"className":1476},[818,819,820,821],[568,1478,769],{"className":1479},[629,630,821],[568,1481,1482,1485],{"style":1295},[568,1483],{"className":1484,"style":814},[813],[568,1486,1488],{"className":1487},[818,819,820,821],[568,1489,1160],{"className":1490},[629,821],[568,1492,829],{"className":1493},[828],[568,1495,1497],{"className":1496},[801],[568,1498,1501],{"className":1499,"style":1500},[805],"height:0.247em;",[568,1502],{},[568,1504],{"className":1505,"style":708},[634],[568,1507,1202],{"className":1508},[922],[568,1510],{"className":1511,"style":708},[634],[568,1513,1515,1518,1522,1525,1528,1531,1534],{"className":1514},[620],[568,1516],{"className":1517,"style":649},[624],[568,1519,1205],{"className":1520,"style":1521},[629,630],"margin-right:0.1389em;",[568,1523,600],{"className":1524},[657],[568,1526,603],{"className":1527,"style":661},[629,630],[568,1529],{"className":1530,"style":635},[634],[568,1532,593],{"className":1533},[639],[568,1535],{"className":1536,"style":635},[634],[568,1538,1540,1543,1583,1586,1589,1592],{"className":1539},[620],[568,1541],{"className":1542,"style":649},[624],[568,1544,1546,1549],{"className":1545},[629],[568,1547,766],{"className":1548},[629,630],[568,1550,1552],{"className":1551},[792],[568,1553,1555,1575],{"className":1554},[796,797],[568,1556,1558,1572],{"className":1557},[801],[568,1559,1561],{"className":1560,"style":806},[805],[568,1562,1563,1566],{"style":809},[568,1564],{"className":1565,"style":814},[813],[568,1567,1569],{"className":1568},[818,819,820,821],[568,1570,769],{"className":1571},[629,630,821],[568,1573,829],{"className":1574},[828],[568,1576,1578],{"className":1577},[801],[568,1579,1581],{"className":1580,"style":836},[805],[568,1582],{},[568,1584,606],{"className":1585},[665],[568,1587],{"className":1588,"style":708},[634],[568,1590,860],{"className":1591},[922],[568,1593],{"className":1594,"style":708},[634],[568,1596,1598,1601],{"className":1597},[620],[568,1599],{"className":1600,"style":1323},[624],[568,1602,1604,1607],{"className":1603},[629],[568,1605,589],{"className":1606},[629,630],[568,1608,1610],{"className":1609},[792],[568,1611,1613],{"className":1612},[796],[568,1614,1616],{"className":1615},[801],[568,1617,1619],{"className":1618,"style":1292},[805],[568,1620,1621,1624],{"style":1295},[568,1622],{"className":1623,"style":814},[813],[568,1625,1627],{"className":1626},[818,819,820,821],[568,1628,1160],{"className":1629},[629,821],[559,1631,1633],{"id":1632},"beispiele","Beispiele",[564,1635,1636,1637,1665,1666,1120],{},"Augenzahl ",[568,1638,1640,1653],{"className":1639},[571],[568,1641,1643],{"className":1642},[575],[577,1644,1645],{"xmlns":579},[581,1646,1647,1651],{},[584,1648,1649],{},[587,1650,603],{},[608,1652,603],{"encoding":610},[568,1654,1656],{"className":1655,"ariaHidden":616},[615],[568,1657,1659,1662],{"className":1658},[620],[568,1660],{"className":1661,"style":1109},[624],[568,1663,603],{"className":1664,"style":661},[629,630]," eines fairen Würfels, ",[568,1667,1669,1688],{"className":1668},[571],[568,1670,1672],{"className":1671},[575],[577,1673,1674],{"xmlns":579},[581,1675,1676,1685],{},[584,1677,1678,1680,1682],{},[587,1679,589],{},[591,1681,593],{},[1158,1683,1684],{},"3,5",[608,1686,1687],{"encoding":610},"\\mu = 3{,}5",[568,1689,1691,1709],{"className":1690,"ariaHidden":616},[615],[568,1692,1694,1697,1700,1703,1706],{"className":1693},[620],[568,1695],{"className":1696,"style":625},[624],[568,1698,589],{"className":1699},[629,630],[568,1701],{"className":1702,"style":635},[634],[568,1704,593],{"className":1705},[639],[568,1707],{"className":1708,"style":635},[634],[568,1710,1712,1716,1720,1728],{"className":1711},[620],[568,1713],{"className":1714,"style":1715},[624],"height:0.8389em;vertical-align:-0.1944em;",[568,1717,1719],{"className":1718},[629],"3",[568,1721,1723],{"className":1722},[629],[568,1724,1727],{"className":1725},[1726],"mpunct",",",[568,1729,1731],{"className":1730},[629],"5",[568,1733,1735],{"className":1734},[1124],[568,1736,1738,1836],{"className":1737},[571],[568,1739,1741],{"className":1740},[575],[577,1742,1743],{"xmlns":579,"display":1133},[581,1744,1745,1833],{},[584,1746,1747,1749,1751,1753,1755,1757,1817,1819,1827,1830],{},[587,1748,686],{},[591,1750,600],{"stretchy":599},[587,1752,603],{},[591,1754,606],{"stretchy":599},[591,1756,593],{},[1758,1759,1760,1815],"mfrac",{},[584,1761,1762,1764,1766,1768,1770,1776,1779,1781,1783,1785,1787,1793,1795,1798,1800,1802,1805,1807,1809],{},[591,1763,600],{"stretchy":599},[1158,1765,1187],{},[591,1767,860],{},[1158,1769,1684],{},[1153,1771,1772,1774],{},[591,1773,606],{"stretchy":599},[1158,1775,1160],{},[591,1777,1778],{},"+",[591,1780,600],{"stretchy":599},[1158,1782,1160],{},[591,1784,860],{},[1158,1786,1684],{},[1153,1788,1789,1791],{},[591,1790,606],{"stretchy":599},[1158,1792,1160],{},[591,1794,1778],{},[591,1796,1797],{},"…",[591,1799,1778],{},[591,1801,600],{"stretchy":599},[1158,1803,1804],{},"6",[591,1806,860],{},[1158,1808,1684],{},[1153,1810,1811,1813],{},[591,1812,606],{"stretchy":599},[1158,1814,1160],{},[1158,1816,1804],{},[591,1818,593],{},[1758,1820,1821,1824],{},[1158,1822,1823],{},"35",[1158,1825,1826],{},"12",[591,1828,1829],{},"≈",[1158,1831,1832],{},"2,92",[608,1834,1835],{"encoding":610},"V(X) = \\frac{(1 - 3{,}5)^2 + (2 - 3{,}5)^2 + \\ldots + (6 - 3{,}5)^2}{6} = \\frac{35}{12} \\approx 2{,}92",[568,1837,1839,1866,2151,2230],{"className":1838,"ariaHidden":616},[615],[568,1840,1842,1845,1848,1851,1854,1857,1860,1863],{"className":1841},[620],[568,1843],{"className":1844,"style":649},[624],[568,1846,686],{"className":1847,"style":708},[629,630],[568,1849,600],{"className":1850},[657],[568,1852,603],{"className":1853,"style":661},[629,630],[568,1855,606],{"className":1856},[665],[568,1858],{"className":1859,"style":635},[634],[568,1861,593],{"className":1862},[639],[568,1864],{"className":1865,"style":635},[634],[568,1867,1869,1873,2142,2145,2148],{"className":1868},[620],[568,1870],{"className":1871,"style":1872},[624],"height:2.1771em;vertical-align:-0.686em;",[568,1874,1876,1880,2139],{"className":1875},[629],[568,1877],{"className":1878},[657,1879],"nulldelimiter",[568,1881,1883],{"className":1882},[1758],[568,1884,1886,2130],{"className":1885},[796,797],[568,1887,1889,2127],{"className":1888},[801],[568,1890,1893,1906,1917],{"className":1891,"style":1892},[805],"height:1.4911em;",[568,1894,1896,1900],{"style":1895},"top:-2.314em;",[568,1897],{"className":1898,"style":1899},[813],"height:3em;",[568,1901,1903],{"className":1902},[629],[568,1904,1804],{"className":1905},[629],[568,1907,1909,1912],{"style":1908},"top:-3.23em;",[568,1910],{"className":1911,"style":1899},[813],[568,1913],{"className":1914,"style":1916},[1915],"frac-line","border-bottom-width:0.04em;",[568,1918,1920,1923],{"style":1919},"top:-3.677em;",[568,1921],{"className":1922,"style":1899},[813],[568,1924,1926,1929,1932,1935,1938,1941,1944,1950,1953,1984,1987,1990,1993,1996,1999,2002,2005,2008,2011,2017,2020,2049,2052,2055,2058,2062,2065,2068,2071,2074,2077,2080,2083,2086,2089,2095,2098],{"className":1925},[629],[568,1927,600],{"className":1928},[657],[568,1930,1187],{"className":1931},[629],[568,1933],{"className":1934,"style":708},[634],[568,1936,860],{"className":1937},[922],[568,1939],{"className":1940,"style":708},[634],[568,1942,1719],{"className":1943},[629],[568,1945,1947],{"className":1946},[629],[568,1948,1727],{"className":1949},[1726],[568,1951,1731],{"className":1952},[629],[568,1954,1956,1959],{"className":1955},[665],[568,1957,606],{"className":1958},[665],[568,1960,1962],{"className":1961},[792],[568,1963,1965],{"className":1964},[796],[568,1966,1968],{"className":1967},[801],[568,1969,1972],{"className":1970,"style":1971},[805],"height:0.8141em;",[568,1973,1975,1978],{"style":1974},"top:-3.063em;margin-right:0.05em;",[568,1976],{"className":1977,"style":814},[813],[568,1979,1981],{"className":1980},[818,819,820,821],[568,1982,1160],{"className":1983},[629,821],[568,1985],{"className":1986,"style":708},[634],[568,1988,1778],{"className":1989},[922],[568,1991],{"className":1992,"style":708},[634],[568,1994,600],{"className":1995},[657],[568,1997,1160],{"className":1998},[629],[568,2000],{"className":2001,"style":708},[634],[568,2003,860],{"className":2004},[922],[568,2006],{"className":2007,"style":708},[634],[568,2009,1719],{"className":2010},[629],[568,2012,2014],{"className":2013},[629],[568,2015,1727],{"className":2016},[1726],[568,2018,1731],{"className":2019},[629],[568,2021,2023,2026],{"className":2022},[665],[568,2024,606],{"className":2025},[665],[568,2027,2029],{"className":2028},[792],[568,2030,2032],{"className":2031},[796],[568,2033,2035],{"className":2034},[801],[568,2036,2038],{"className":2037,"style":1971},[805],[568,2039,2040,2043],{"style":1974},[568,2041],{"className":2042,"style":814},[813],[568,2044,2046],{"className":2045},[818,819,820,821],[568,2047,1160],{"className":2048},[629,821],[568,2050],{"className":2051,"style":708},[634],[568,2053,1778],{"className":2054},[922],[568,2056],{"className":2057,"style":708},[634],[568,2059,1797],{"className":2060},[2061],"minner",[568,2063],{"className":2064,"style":708},[634],[568,2066,1778],{"className":2067},[922],[568,2069],{"className":2070,"style":708},[634],[568,2072,600],{"className":2073},[657],[568,2075,1804],{"className":2076},[629],[568,2078],{"className":2079,"style":708},[634],[568,2081,860],{"className":2082},[922],[568,2084],{"className":2085,"style":708},[634],[568,2087,1719],{"className":2088},[629],[568,2090,2092],{"className":2091},[629],[568,2093,1727],{"className":2094},[1726],[568,2096,1731],{"className":2097},[629],[568,2099,2101,2104],{"className":2100},[665],[568,2102,606],{"className":2103},[665],[568,2105,2107],{"className":2106},[792],[568,2108,2110],{"className":2109},[796],[568,2111,2113],{"className":2112},[801],[568,2114,2116],{"className":2115,"style":1971},[805],[568,2117,2118,2121],{"style":1974},[568,2119],{"className":2120,"style":814},[813],[568,2122,2124],{"className":2123},[818,819,820,821],[568,2125,1160],{"className":2126},[629,821],[568,2128,829],{"className":2129},[828],[568,2131,2133],{"className":2132},[801],[568,2134,2137],{"className":2135,"style":2136},[805],"height:0.686em;",[568,2138],{},[568,2140],{"className":2141},[665,1879],[568,2143],{"className":2144,"style":635},[634],[568,2146,593],{"className":2147},[639],[568,2149],{"className":2150,"style":635},[634],[568,2152,2154,2158,2221,2224,2227],{"className":2153},[620],[568,2155],{"className":2156,"style":2157},[624],"height:2.0074em;vertical-align:-0.686em;",[568,2159,2161,2164,2218],{"className":2160},[629],[568,2162],{"className":2163},[657,1879],[568,2165,2167],{"className":2166},[1758],[568,2168,2170,2210],{"className":2169},[796,797],[568,2171,2173,2207],{"className":2172},[801],[568,2174,2177,2188,2196],{"className":2175,"style":2176},[805],"height:1.3214em;",[568,2178,2179,2182],{"style":1895},[568,2180],{"className":2181,"style":1899},[813],[568,2183,2185],{"className":2184},[629],[568,2186,1826],{"className":2187},[629],[568,2189,2190,2193],{"style":1908},[568,2191],{"className":2192,"style":1899},[813],[568,2194],{"className":2195,"style":1916},[1915],[568,2197,2198,2201],{"style":1919},[568,2199],{"className":2200,"style":1899},[813],[568,2202,2204],{"className":2203},[629],[568,2205,1823],{"className":2206},[629],[568,2208,829],{"className":2209},[828],[568,2211,2213],{"className":2212},[801],[568,2214,2216],{"className":2215,"style":2136},[805],[568,2217],{},[568,2219],{"className":2220},[665,1879],[568,2222],{"className":2223,"style":635},[634],[568,2225,1829],{"className":2226},[639],[568,2228],{"className":2229,"style":635},[634],[568,2231,2233,2236,2239,2245],{"className":2232},[620],[568,2234],{"className":2235,"style":1715},[624],[568,2237,1160],{"className":2238},[629],[568,2240,2242],{"className":2241},[629],[568,2243,1727],{"className":2244},[1726],[568,2246,2248],{"className":2247},[629],"92",[564,2250,2251,2252,2572,2573,2861],{},"Mit dem Verschiebungssatz: ",[568,2253,2255,2323],{"className":2254},[571],[568,2256,2258],{"className":2257},[575],[577,2259,2260],{"xmlns":579},[581,2261,2262,2320],{},[584,2263,2264,2266,2268,2274,2276,2278,2311,2313],{},[587,2265,596],{},[591,2267,600],{"stretchy":599},[1153,2269,2270,2272],{},[587,2271,603],{},[1158,2273,1160],{},[591,2275,606],{"stretchy":599},[591,2277,593],{},[1758,2279,2280,2309],{},[584,2281,2282,2284,2286,2289,2291,2294,2296,2299,2301,2304,2306],{},[1158,2283,1187],{},[591,2285,1778],{},[1158,2287,2288],{},"4",[591,2290,1778],{},[1158,2292,2293],{},"9",[591,2295,1778],{},[1158,2297,2298],{},"16",[591,2300,1778],{},[1158,2302,2303],{},"25",[591,2305,1778],{},[1158,2307,2308],{},"36",[1158,2310,1804],{},[591,2312,593],{},[1758,2314,2315,2318],{},[1158,2316,2317],{},"91",[1158,2319,1804],{},[608,2321,2322],{"encoding":610},"E(X^2) = \\frac{1 + 4 + 9 + 16 + 25 + 36}{6} = \\frac{91}{6}",[568,2324,2326,2380,2498],{"className":2325,"ariaHidden":616},[615],[568,2327,2329,2333,2336,2339,2368,2371,2374,2377],{"className":2328},[620],[568,2330],{"className":2331,"style":2332},[624],"height:1.0641em;vertical-align:-0.25em;",[568,2334,596],{"className":2335,"style":653},[629,630],[568,2337,600],{"className":2338},[657],[568,2340,2342,2345],{"className":2341},[629],[568,2343,603],{"className":2344,"style":661},[629,630],[568,2346,2348],{"className":2347},[792],[568,2349,2351],{"className":2350},[796],[568,2352,2354],{"className":2353},[801],[568,2355,2357],{"className":2356,"style":1971},[805],[568,2358,2359,2362],{"style":1974},[568,2360],{"className":2361,"style":814},[813],[568,2363,2365],{"className":2364},[818,819,820,821],[568,2366,1160],{"className":2367},[629,821],[568,2369,606],{"className":2370},[665],[568,2372],{"className":2373,"style":635},[634],[568,2375,593],{"className":2376},[639],[568,2378],{"className":2379,"style":635},[634],[568,2381,2383,2387,2489,2492,2495],{"className":2382},[620],[568,2384],{"className":2385,"style":2386},[624],"height:1.1901em;vertical-align:-0.345em;",[568,2388,2390,2393,2486],{"className":2389},[629],[568,2391],{"className":2392},[657,1879],[568,2394,2396],{"className":2395},[1758],[568,2397,2399,2477],{"className":2398},[796,797],[568,2400,2402,2474],{"className":2401},[801],[568,2403,2406,2421,2429],{"className":2404,"style":2405},[805],"height:0.8451em;",[568,2407,2409,2412],{"style":2408},"top:-2.655em;",[568,2410],{"className":2411,"style":1899},[813],[568,2413,2415],{"className":2414},[818,819,820,821],[568,2416,2418],{"className":2417},[629,821],[568,2419,1804],{"className":2420},[629,821],[568,2422,2423,2426],{"style":1908},[568,2424],{"className":2425,"style":1899},[813],[568,2427],{"className":2428,"style":1916},[1915],[568,2430,2432,2435],{"style":2431},"top:-3.394em;",[568,2433],{"className":2434,"style":1899},[813],[568,2436,2438],{"className":2437},[818,819,820,821],[568,2439,2441,2444,2447,2450,2453,2456,2459,2462,2465,2468,2471],{"className":2440},[629,821],[568,2442,1187],{"className":2443},[629,821],[568,2445,1778],{"className":2446},[922,821],[568,2448,2288],{"className":2449},[629,821],[568,2451,1778],{"className":2452},[922,821],[568,2454,2293],{"className":2455},[629,821],[568,2457,1778],{"className":2458},[922,821],[568,2460,2298],{"className":2461},[629,821],[568,2463,1778],{"className":2464},[922,821],[568,2466,2303],{"className":2467},[629,821],[568,2469,1778],{"className":2470},[922,821],[568,2472,2308],{"className":2473},[629,821],[568,2475,829],{"className":2476},[828],[568,2478,2480],{"className":2479},[801],[568,2481,2484],{"className":2482,"style":2483},[805],"height:0.345em;",[568,2485],{},[568,2487],{"className":2488},[665,1879],[568,2490],{"className":2491,"style":635},[634],[568,2493,593],{"className":2494},[639],[568,2496],{"className":2497,"style":635},[634],[568,2499,2501,2504],{"className":2500},[620],[568,2502],{"className":2503,"style":2386},[624],[568,2505,2507,2510,2569],{"className":2506},[629],[568,2508],{"className":2509},[657,1879],[568,2511,2513],{"className":2512},[1758],[568,2514,2516,2561],{"className":2515},[796,797],[568,2517,2519,2558],{"className":2518},[801],[568,2520,2522,2536,2544],{"className":2521,"style":2405},[805],[568,2523,2524,2527],{"style":2408},[568,2525],{"className":2526,"style":1899},[813],[568,2528,2530],{"className":2529},[818,819,820,821],[568,2531,2533],{"className":2532},[629,821],[568,2534,1804],{"className":2535},[629,821],[568,2537,2538,2541],{"style":1908},[568,2539],{"className":2540,"style":1899},[813],[568,2542],{"className":2543,"style":1916},[1915],[568,2545,2546,2549],{"style":2431},[568,2547],{"className":2548,"style":1899},[813],[568,2550,2552],{"className":2551},[818,819,820,821],[568,2553,2555],{"className":2554},[629,821],[568,2556,2317],{"className":2557},[629,821],[568,2559,829],{"className":2560},[828],[568,2562,2564],{"className":2563},[801],[568,2565,2567],{"className":2566,"style":2483},[805],[568,2568],{},[568,2570],{"className":2571},[665,1879],", also ",[568,2574,2576,2620],{"className":2575},[571],[568,2577,2579],{"className":2578},[575],[577,2580,2581],{"xmlns":579},[581,2582,2583,2617],{},[584,2584,2585,2587,2589,2591,2593,2595,2601,2603,2609,2611],{},[587,2586,686],{},[591,2588,600],{"stretchy":599},[587,2590,603],{},[591,2592,606],{"stretchy":599},[591,2594,593],{},[1758,2596,2597,2599],{},[1158,2598,2317],{},[1158,2600,1804],{},[591,2602,860],{},[1153,2604,2605,2607],{},[1158,2606,1684],{},[1158,2608,1160],{},[591,2610,593],{},[1758,2612,2613,2615],{},[1158,2614,1823],{},[1158,2616,1826],{},[608,2618,2619],{"encoding":610},"V(X) = \\frac{91}{6} - 3{,}5^2 = \\frac{35}{12}",[568,2621,2623,2650,2733,2787],{"className":2622,"ariaHidden":616},[615],[568,2624,2626,2629,2632,2635,2638,2641,2644,2647],{"className":2625},[620],[568,2627],{"className":2628,"style":649},[624],[568,2630,686],{"className":2631,"style":708},[629,630],[568,2633,600],{"className":2634},[657],[568,2636,603],{"className":2637,"style":661},[629,630],[568,2639,606],{"className":2640},[665],[568,2642],{"className":2643,"style":635},[634],[568,2645,593],{"className":2646},[639],[568,2648],{"className":2649,"style":635},[634],[568,2651,2653,2656,2724,2727,2730],{"className":2652},[620],[568,2654],{"className":2655,"style":2386},[624],[568,2657,2659,2662,2721],{"className":2658},[629],[568,2660],{"className":2661},[657,1879],[568,2663,2665],{"className":2664},[1758],[568,2666,2668,2713],{"className":2667},[796,797],[568,2669,2671,2710],{"className":2670},[801],[568,2672,2674,2688,2696],{"className":2673,"style":2405},[805],[568,2675,2676,2679],{"style":2408},[568,2677],{"className":2678,"style":1899},[813],[568,2680,2682],{"className":2681},[818,819,820,821],[568,2683,2685],{"className":2684},[629,821],[568,2686,1804],{"className":2687},[629,821],[568,2689,2690,2693],{"style":1908},[568,2691],{"className":2692,"style":1899},[813],[568,2694],{"className":2695,"style":1916},[1915],[568,2697,2698,2701],{"style":2431},[568,2699],{"className":2700,"style":1899},[813],[568,2702,2704],{"className":2703},[818,819,820,821],[568,2705,2707],{"className":2706},[629,821],[568,2708,2317],{"className":2709},[629,821],[568,2711,829],{"className":2712},[828],[568,2714,2716],{"className":2715},[801],[568,2717,2719],{"className":2718,"style":2483},[805],[568,2720],{},[568,2722],{"className":2723},[665,1879],[568,2725],{"className":2726,"style":708},[634],[568,2728,860],{"className":2729},[922],[568,2731],{"className":2732,"style":708},[634],[568,2734,2736,2740,2743,2749,2778,2781,2784],{"className":2735},[620],[568,2737],{"className":2738,"style":2739},[624],"height:1.0085em;vertical-align:-0.1944em;",[568,2741,1719],{"className":2742},[629],[568,2744,2746],{"className":2745},[629],[568,2747,1727],{"className":2748},[1726],[568,2750,2752,2755],{"className":2751},[629],[568,2753,1731],{"className":2754},[629],[568,2756,2758],{"className":2757},[792],[568,2759,2761],{"className":2760},[796],[568,2762,2764],{"className":2763},[801],[568,2765,2767],{"className":2766,"style":1971},[805],[568,2768,2769,2772],{"style":1974},[568,2770],{"className":2771,"style":814},[813],[568,2773,2775],{"className":2774},[818,819,820,821],[568,2776,1160],{"className":2777},[629,821],[568,2779],{"className":2780,"style":635},[634],[568,2782,593],{"className":2783},[639],[568,2785],{"className":2786,"style":635},[634],[568,2788,2790,2793],{"className":2789},[620],[568,2791],{"className":2792,"style":2386},[624],[568,2794,2796,2799,2858],{"className":2795},[629],[568,2797],{"className":2798},[657,1879],[568,2800,2802],{"className":2801},[1758],[568,2803,2805,2850],{"className":2804},[796,797],[568,2806,2808,2847],{"className":2807},[801],[568,2809,2811,2825,2833],{"className":2810,"style":2405},[805],[568,2812,2813,2816],{"style":2408},[568,2814],{"className":2815,"style":1899},[813],[568,2817,2819],{"className":2818},[818,819,820,821],[568,2820,2822],{"className":2821},[629,821],[568,2823,1826],{"className":2824},[629,821],[568,2826,2827,2830],{"style":1908},[568,2828],{"className":2829,"style":1899},[813],[568,2831],{"className":2832,"style":1916},[1915],[568,2834,2835,2838],{"style":2431},[568,2836],{"className":2837,"style":1899},[813],[568,2839,2841],{"className":2840},[818,819,820,821],[568,2842,2844],{"className":2843},[629,821],[568,2845,1823],{"className":2846},[629,821],[568,2848,829],{"className":2849},[828],[568,2851,2853],{"className":2852},[801],[568,2854,2856],{"className":2855,"style":2483},[805],[568,2857],{},[568,2859],{"className":2860},[665,1879],".",[564,2863,2864,2865,2895,2896,2935,2936,2964,2965,3004,3005,2964,3033,3072,3073,3293],{},"Ein Spiel zahlt ",[568,2866,2868,2882],{"className":2867},[571],[568,2869,2871],{"className":2870},[575],[577,2872,2873],{"xmlns":579},[581,2874,2875,2880],{},[584,2876,2877],{},[1158,2878,2879],{},"0",[608,2881,2879],{"encoding":610},[568,2883,2885],{"className":2884,"ariaHidden":616},[615],[568,2886,2888,2892],{"className":2887},[620],[568,2889],{"className":2890,"style":2891},[624],"height:0.6444em;",[568,2893,2879],{"className":2894},[629]," € mit Wahrscheinlichkeit ",[568,2897,2899,2914],{"className":2898},[571],[568,2900,2902],{"className":2901},[575],[577,2903,2904],{"xmlns":579},[581,2905,2906,2911],{},[584,2907,2908],{},[1158,2909,2910],{},"0,5",[608,2912,2913],{"encoding":610},"0{,}5",[568,2915,2917],{"className":2916,"ariaHidden":616},[615],[568,2918,2920,2923,2926,2932],{"className":2919},[620],[568,2921],{"className":2922,"style":1715},[624],[568,2924,2879],{"className":2925},[629],[568,2927,2929],{"className":2928},[629],[568,2930,1727],{"className":2931},[1726],[568,2933,1731],{"className":2934},[629],", ",[568,2937,2939,2952],{"className":2938},[571],[568,2940,2942],{"className":2941},[575],[577,2943,2944],{"xmlns":579},[581,2945,2946,2950],{},[584,2947,2948],{},[1158,2949,1160],{},[608,2951,1160],{"encoding":610},[568,2953,2955],{"className":2954,"ariaHidden":616},[615],[568,2956,2958,2961],{"className":2957},[620],[568,2959],{"className":2960,"style":2891},[624],[568,2962,1160],{"className":2963},[629]," € mit ",[568,2966,2968,2983],{"className":2967},[571],[568,2969,2971],{"className":2970},[575],[577,2972,2973],{"xmlns":579},[581,2974,2975,2980],{},[584,2976,2977],{},[1158,2978,2979],{},"0,3",[608,2981,2982],{"encoding":610},"0{,}3",[568,2984,2986],{"className":2985,"ariaHidden":616},[615],[568,2987,2989,2992,2995,3001],{"className":2988},[620],[568,2990],{"className":2991,"style":1715},[624],[568,2993,2879],{"className":2994},[629],[568,2996,2998],{"className":2997},[629],[568,2999,1727],{"className":3000},[1726],[568,3002,1719],{"className":3003},[629]," und ",[568,3006,3008,3021],{"className":3007},[571],[568,3009,3011],{"className":3010},[575],[577,3012,3013],{"xmlns":579},[581,3014,3015,3019],{},[584,3016,3017],{},[1158,3018,1731],{},[608,3020,1731],{"encoding":610},[568,3022,3024],{"className":3023,"ariaHidden":616},[615],[568,3025,3027,3030],{"className":3026},[620],[568,3028],{"className":3029,"style":2891},[624],[568,3031,1731],{"className":3032},[629],[568,3034,3036,3051],{"className":3035},[571],[568,3037,3039],{"className":3038},[575],[577,3040,3041],{"xmlns":579},[581,3042,3043,3048],{},[584,3044,3045],{},[1158,3046,3047],{},"0,2",[608,3049,3050],{"encoding":610},"0{,}2",[568,3052,3054],{"className":3053,"ariaHidden":616},[615],[568,3055,3057,3060,3063,3069],{"className":3056},[620],[568,3058],{"className":3059,"style":1715},[624],[568,3061,2879],{"className":3062},[629],[568,3064,3066],{"className":3065},[629],[568,3067,1727],{"className":3068},[1726],[568,3070,1160],{"className":3071},[629],". Erwartungswert: ",[568,3074,3076,3119],{"className":3075},[571],[568,3077,3079],{"className":3078},[575],[577,3080,3081],{"xmlns":579},[581,3082,3083,3116],{},[584,3084,3085,3087,3089,3091,3093,3095,3097,3099,3101,3103,3105,3107,3109,3111,3113],{},[587,3086,589],{},[591,3088,593],{},[1158,3090,2879],{},[591,3092,1202],{},[1158,3094,2910],{},[591,3096,1778],{},[1158,3098,1160],{},[591,3100,1202],{},[1158,3102,2979],{},[591,3104,1778],{},[1158,3106,1731],{},[591,3108,1202],{},[1158,3110,3047],{},[591,3112,593],{},[1158,3114,3115],{},"1,6",[608,3117,3118],{"encoding":610},"\\mu = 0 \\cdot 0{,}5 + 2 \\cdot 0{,}3 + 5 \\cdot 0{,}2 = 1{,}6",[568,3120,3122,3140,3158,3185,3203,3230,3248,3275],{"className":3121,"ariaHidden":616},[615],[568,3123,3125,3128,3131,3134,3137],{"className":3124},[620],[568,3126],{"className":3127,"style":625},[624],[568,3129,589],{"className":3130},[629,630],[568,3132],{"className":3133,"style":635},[634],[568,3135,593],{"className":3136},[639],[568,3138],{"className":3139,"style":635},[634],[568,3141,3143,3146,3149,3152,3155],{"className":3142},[620],[568,3144],{"className":3145,"style":2891},[624],[568,3147,2879],{"className":3148},[629],[568,3150],{"className":3151,"style":708},[634],[568,3153,1202],{"className":3154},[922],[568,3156],{"className":3157,"style":708},[634],[568,3159,3161,3164,3167,3173,3176,3179,3182],{"className":3160},[620],[568,3162],{"className":3163,"style":1715},[624],[568,3165,2879],{"className":3166},[629],[568,3168,3170],{"className":3169},[629],[568,3171,1727],{"className":3172},[1726],[568,3174,1731],{"className":3175},[629],[568,3177],{"className":3178,"style":708},[634],[568,3180,1778],{"className":3181},[922],[568,3183],{"className":3184,"style":708},[634],[568,3186,3188,3191,3194,3197,3200],{"className":3187},[620],[568,3189],{"className":3190,"style":2891},[624],[568,3192,1160],{"className":3193},[629],[568,3195],{"className":3196,"style":708},[634],[568,3198,1202],{"className":3199},[922],[568,3201],{"className":3202,"style":708},[634],[568,3204,3206,3209,3212,3218,3221,3224,3227],{"className":3205},[620],[568,3207],{"className":3208,"style":1715},[624],[568,3210,2879],{"className":3211},[629],[568,3213,3215],{"className":3214},[629],[568,3216,1727],{"className":3217},[1726],[568,3219,1719],{"className":3220},[629],[568,3222],{"className":3223,"style":708},[634],[568,3225,1778],{"className":3226},[922],[568,3228],{"className":3229,"style":708},[634],[568,3231,3233,3236,3239,3242,3245],{"className":3232},[620],[568,3234],{"className":3235,"style":2891},[624],[568,3237,1731],{"className":3238},[629],[568,3240],{"className":3241,"style":708},[634],[568,3243,1202],{"className":3244},[922],[568,3246],{"className":3247,"style":708},[634],[568,3249,3251,3254,3257,3263,3266,3269,3272],{"className":3250},[620],[568,3252],{"className":3253,"style":1715},[624],[568,3255,2879],{"className":3256},[629],[568,3258,3260],{"className":3259},[629],[568,3261,1727],{"className":3262},[1726],[568,3264,1160],{"className":3265},[629],[568,3267],{"className":3268,"style":635},[634],[568,3270,593],{"className":3271},[639],[568,3273],{"className":3274,"style":635},[634],[568,3276,3278,3281,3284,3290],{"className":3277},[620],[568,3279],{"className":3280,"style":1715},[624],[568,3282,1187],{"className":3283},[629],[568,3285,3287],{"className":3286},[629],[568,3288,1727],{"className":3289},[1726],[568,3291,1804],{"className":3292},[629],". Varianz:",[568,3295,3297],{"className":3296},[1124],[568,3298,3300,3385],{"className":3299},[571],[568,3301,3303],{"className":3302},[575],[577,3304,3305],{"xmlns":579,"display":1133},[581,3306,3307,3382],{},[584,3308,3309,3311,3313,3315,3317,3319,3321,3323,3325,3327,3333,3335,3337,3339,3341,3343,3345,3347,3353,3355,3357,3359,3361,3363,3365,3367,3373,3375,3377,3379],{},[587,3310,686],{},[591,3312,600],{"stretchy":599},[587,3314,603],{},[591,3316,606],{"stretchy":599},[591,3318,593],{},[591,3320,600],{"stretchy":599},[1158,3322,2879],{},[591,3324,860],{},[1158,3326,3115],{},[1153,3328,3329,3331],{},[591,3330,606],{"stretchy":599},[1158,3332,1160],{},[591,3334,1202],{},[1158,3336,2910],{},[591,3338,1778],{},[591,3340,600],{"stretchy":599},[1158,3342,1160],{},[591,3344,860],{},[1158,3346,3115],{},[1153,3348,3349,3351],{},[591,3350,606],{"stretchy":599},[1158,3352,1160],{},[591,3354,1202],{},[1158,3356,2979],{},[591,3358,1778],{},[591,3360,600],{"stretchy":599},[1158,3362,1731],{},[591,3364,860],{},[1158,3366,3115],{},[1153,3368,3369,3371],{},[591,3370,606],{"stretchy":599},[1158,3372,1160],{},[591,3374,1202],{},[1158,3376,3047],{},[591,3378,593],{},[1158,3380,3381],{},"3,64",[608,3383,3384],{"encoding":610},"V(X) = (0 - 1{,}6)^2 \\cdot 0{,}5 + (2 - 1{,}6)^2 \\cdot 0{,}3 + (5 - 1{,}6)^2 \\cdot 0{,}2 = 3{,}64",[568,3386,3388,3415,3436,3492,3519,3540,3596,3623,3644,3700,3727],{"className":3387,"ariaHidden":616},[615],[568,3389,3391,3394,3397,3400,3403,3406,3409,3412],{"className":3390},[620],[568,3392],{"className":3393,"style":649},[624],[568,3395,686],{"className":3396,"style":708},[629,630],[568,3398,600],{"className":3399},[657],[568,3401,603],{"className":3402,"style":661},[629,630],[568,3404,606],{"className":3405},[665],[568,3407],{"className":3408,"style":635},[634],[568,3410,593],{"className":3411},[639],[568,3413],{"className":3414,"style":635},[634],[568,3416,3418,3421,3424,3427,3430,3433],{"className":3417},[620],[568,3419],{"className":3420,"style":649},[624],[568,3422,600],{"className":3423},[657],[568,3425,2879],{"className":3426},[629],[568,3428],{"className":3429,"style":708},[634],[568,3431,860],{"className":3432},[922],[568,3434],{"className":3435,"style":708},[634],[568,3437,3439,3442,3445,3451,3454,3483,3486,3489],{"className":3438},[620],[568,3440],{"className":3441,"style":1267},[624],[568,3443,1187],{"className":3444},[629],[568,3446,3448],{"className":3447},[629],[568,3449,1727],{"className":3450},[1726],[568,3452,1804],{"className":3453},[629],[568,3455,3457,3460],{"className":3456},[665],[568,3458,606],{"className":3459},[665],[568,3461,3463],{"className":3462},[792],[568,3464,3466],{"className":3465},[796],[568,3467,3469],{"className":3468},[801],[568,3470,3472],{"className":3471,"style":1292},[805],[568,3473,3474,3477],{"style":1295},[568,3475],{"className":3476,"style":814},[813],[568,3478,3480],{"className":3479},[818,819,820,821],[568,3481,1160],{"className":3482},[629,821],[568,3484],{"className":3485,"style":708},[634],[568,3487,1202],{"className":3488},[922],[568,3490],{"className":3491,"style":708},[634],[568,3493,3495,3498,3501,3507,3510,3513,3516],{"className":3494},[620],[568,3496],{"className":3497,"style":1715},[624],[568,3499,2879],{"className":3500},[629],[568,3502,3504],{"className":3503},[629],[568,3505,1727],{"className":3506},[1726],[568,3508,1731],{"className":3509},[629],[568,3511],{"className":3512,"style":708},[634],[568,3514,1778],{"className":3515},[922],[568,3517],{"className":3518,"style":708},[634],[568,3520,3522,3525,3528,3531,3534,3537],{"className":3521},[620],[568,3523],{"className":3524,"style":649},[624],[568,3526,600],{"className":3527},[657],[568,3529,1160],{"className":3530},[629],[568,3532],{"className":3533,"style":708},[634],[568,3535,860],{"className":3536},[922],[568,3538],{"className":3539,"style":708},[634],[568,3541,3543,3546,3549,3555,3558,3587,3590,3593],{"className":3542},[620],[568,3544],{"className":3545,"style":1267},[624],[568,3547,1187],{"className":3548},[629],[568,3550,3552],{"className":3551},[629],[568,3553,1727],{"className":3554},[1726],[568,3556,1804],{"className":3557},[629],[568,3559,3561,3564],{"className":3560},[665],[568,3562,606],{"className":3563},[665],[568,3565,3567],{"className":3566},[792],[568,3568,3570],{"className":3569},[796],[568,3571,3573],{"className":3572},[801],[568,3574,3576],{"className":3575,"style":1292},[805],[568,3577,3578,3581],{"style":1295},[568,3579],{"className":3580,"style":814},[813],[568,3582,3584],{"className":3583},[818,819,820,821],[568,3585,1160],{"className":3586},[629,821],[568,3588],{"className":3589,"style":708},[634],[568,3591,1202],{"className":3592},[922],[568,3594],{"className":3595,"style":708},[634],[568,3597,3599,3602,3605,3611,3614,3617,3620],{"className":3598},[620],[568,3600],{"className":3601,"style":1715},[624],[568,3603,2879],{"className":3604},[629],[568,3606,3608],{"className":3607},[629],[568,3609,1727],{"className":3610},[1726],[568,3612,1719],{"className":3613},[629],[568,3615],{"className":3616,"style":708},[634],[568,3618,1778],{"className":3619},[922],[568,3621],{"className":3622,"style":708},[634],[568,3624,3626,3629,3632,3635,3638,3641],{"className":3625},[620],[568,3627],{"className":3628,"style":649},[624],[568,3630,600],{"className":3631},[657],[568,3633,1731],{"className":3634},[629],[568,3636],{"className":3637,"style":708},[634],[568,3639,860],{"className":3640},[922],[568,3642],{"className":3643,"style":708},[634],[568,3645,3647,3650,3653,3659,3662,3691,3694,3697],{"className":3646},[620],[568,3648],{"className":3649,"style":1267},[624],[568,3651,1187],{"className":3652},[629],[568,3654,3656],{"className":3655},[629],[568,3657,1727],{"className":3658},[1726],[568,3660,1804],{"className":3661},[629],[568,3663,3665,3668],{"className":3664},[665],[568,3666,606],{"className":3667},[665],[568,3669,3671],{"className":3670},[792],[568,3672,3674],{"className":3673},[796],[568,3675,3677],{"className":3676},[801],[568,3678,3680],{"className":3679,"style":1292},[805],[568,3681,3682,3685],{"style":1295},[568,3683],{"className":3684,"style":814},[813],[568,3686,3688],{"className":3687},[818,819,820,821],[568,3689,1160],{"className":3690},[629,821],[568,3692],{"className":3693,"style":708},[634],[568,3695,1202],{"className":3696},[922],[568,3698],{"className":3699,"style":708},[634],[568,3701,3703,3706,3709,3715,3718,3721,3724],{"className":3702},[620],[568,3704],{"className":3705,"style":1715},[624],[568,3707,2879],{"className":3708},[629],[568,3710,3712],{"className":3711},[629],[568,3713,1727],{"className":3714},[1726],[568,3716,1160],{"className":3717},[629],[568,3719],{"className":3720,"style":635},[634],[568,3722,593],{"className":3723},[639],[568,3725],{"className":3726,"style":635},[634],[568,3728,3730,3733,3736,3742],{"className":3729},[620],[568,3731],{"className":3732,"style":1715},[624],[568,3734,1719],{"className":3735},[629],[568,3737,3739],{"className":3738},[629],[568,3740,1727],{"className":3741},[1726],[568,3743,3745],{"className":3744},[629],"64",[564,3747,3748,3749,3004,4014,4144,4145,4293],{},"Probe mit dem Verschiebungssatz: ",[568,3750,3752,3805],{"className":3751},[571],[568,3753,3755],{"className":3754},[575],[577,3756,3757],{"xmlns":579},[581,3758,3759,3802],{},[584,3760,3761,3763,3765,3771,3773,3775,3777,3779,3781,3783,3785,3787,3789,3791,3793,3795,3797,3799],{},[587,3762,596],{},[591,3764,600],{"stretchy":599},[1153,3766,3767,3769],{},[587,3768,603],{},[1158,3770,1160],{},[591,3772,606],{"stretchy":599},[591,3774,593],{},[1158,3776,2879],{},[591,3778,1202],{},[1158,3780,2910],{},[591,3782,1778],{},[1158,3784,2288],{},[591,3786,1202],{},[1158,3788,2979],{},[591,3790,1778],{},[1158,3792,2303],{},[591,3794,1202],{},[1158,3796,3047],{},[591,3798,593],{},[1158,3800,3801],{},"6,2",[608,3803,3804],{"encoding":610},"E(X^2) = 0 \\cdot 0{,}5 + 4 \\cdot 0{,}3 + 25 \\cdot 0{,}2 = 6{,}2",[568,3806,3808,3861,3879,3906,3924,3951,3969,3996],{"className":3807,"ariaHidden":616},[615],[568,3809,3811,3814,3817,3820,3849,3852,3855,3858],{"className":3810},[620],[568,3812],{"className":3813,"style":2332},[624],[568,3815,596],{"className":3816,"style":653},[629,630],[568,3818,600],{"className":3819},[657],[568,3821,3823,3826],{"className":3822},[629],[568,3824,603],{"className":3825,"style":661},[629,630],[568,3827,3829],{"className":3828},[792],[568,3830,3832],{"className":3831},[796],[568,3833,3835],{"className":3834},[801],[568,3836,3838],{"className":3837,"style":1971},[805],[568,3839,3840,3843],{"style":1974},[568,3841],{"className":3842,"style":814},[813],[568,3844,3846],{"className":3845},[818,819,820,821],[568,3847,1160],{"className":3848},[629,821],[568,3850,606],{"className":3851},[665],[568,3853],{"className":3854,"style":635},[634],[568,3856,593],{"className":3857},[639],[568,3859],{"className":3860,"style":635},[634],[568,3862,3864,3867,3870,3873,3876],{"className":3863},[620],[568,3865],{"className":3866,"style":2891},[624],[568,3868,2879],{"className":3869},[629],[568,3871],{"className":3872,"style":708},[634],[568,3874,1202],{"className":3875},[922],[568,3877],{"className":3878,"style":708},[634],[568,3880,3882,3885,3888,3894,3897,3900,3903],{"className":3881},[620],[568,3883],{"className":3884,"style":1715},[624],[568,3886,2879],{"className":3887},[629],[568,3889,3891],{"className":3890},[629],[568,3892,1727],{"className":3893},[1726],[568,3895,1731],{"className":3896},[629],[568,3898],{"className":3899,"style":708},[634],[568,3901,1778],{"className":3902},[922],[568,3904],{"className":3905,"style":708},[634],[568,3907,3909,3912,3915,3918,3921],{"className":3908},[620],[568,3910],{"className":3911,"style":2891},[624],[568,3913,2288],{"className":3914},[629],[568,3916],{"className":3917,"style":708},[634],[568,3919,1202],{"className":3920},[922],[568,3922],{"className":3923,"style":708},[634],[568,3925,3927,3930,3933,3939,3942,3945,3948],{"className":3926},[620],[568,3928],{"className":3929,"style":1715},[624],[568,3931,2879],{"className":3932},[629],[568,3934,3936],{"className":3935},[629],[568,3937,1727],{"className":3938},[1726],[568,3940,1719],{"className":3941},[629],[568,3943],{"className":3944,"style":708},[634],[568,3946,1778],{"className":3947},[922],[568,3949],{"className":3950,"style":708},[634],[568,3952,3954,3957,3960,3963,3966],{"className":3953},[620],[568,3955],{"className":3956,"style":2891},[624],[568,3958,2303],{"className":3959},[629],[568,3961],{"className":3962,"style":708},[634],[568,3964,1202],{"className":3965},[922],[568,3967],{"className":3968,"style":708},[634],[568,3970,3972,3975,3978,3984,3987,3990,3993],{"className":3971},[620],[568,3973],{"className":3974,"style":1715},[624],[568,3976,2879],{"className":3977},[629],[568,3979,3981],{"className":3980},[629],[568,3982,1727],{"className":3983},[1726],[568,3985,1160],{"className":3986},[629],[568,3988],{"className":3989,"style":635},[634],[568,3991,593],{"className":3992},[639],[568,3994],{"className":3995,"style":635},[634],[568,3997,3999,4002,4005,4011],{"className":3998},[620],[568,4000],{"className":4001,"style":1715},[624],[568,4003,1804],{"className":4004},[629],[568,4006,4008],{"className":4007},[629],[568,4009,1727],{"className":4010},[1726],[568,4012,1160],{"className":4013},[629],[568,4015,4017,4043],{"className":4016},[571],[568,4018,4020],{"className":4019},[575],[577,4021,4022],{"xmlns":579},[581,4023,4024,4040],{},[584,4025,4026,4028,4030,4036,4038],{},[1158,4027,3801],{},[591,4029,860],{},[1153,4031,4032,4034],{},[1158,4033,3115],{},[1158,4035,1160],{},[591,4037,593],{},[1158,4039,3381],{},[608,4041,4042],{"encoding":610},"6{,}2 - 1{,}6^2 = 3{,}64",[568,4044,4046,4073,4126],{"className":4045,"ariaHidden":616},[615],[568,4047,4049,4052,4055,4061,4064,4067,4070],{"className":4048},[620],[568,4050],{"className":4051,"style":1715},[624],[568,4053,1804],{"className":4054},[629],[568,4056,4058],{"className":4057},[629],[568,4059,1727],{"className":4060},[1726],[568,4062,1160],{"className":4063},[629],[568,4065],{"className":4066,"style":708},[634],[568,4068,860],{"className":4069},[922],[568,4071],{"className":4072,"style":708},[634],[568,4074,4076,4079,4082,4088,4117,4120,4123],{"className":4075},[620],[568,4077],{"className":4078,"style":2739},[624],[568,4080,1187],{"className":4081},[629],[568,4083,4085],{"className":4084},[629],[568,4086,1727],{"className":4087},[1726],[568,4089,4091,4094],{"className":4090},[629],[568,4092,1804],{"className":4093},[629],[568,4095,4097],{"className":4096},[792],[568,4098,4100],{"className":4099},[796],[568,4101,4103],{"className":4102},[801],[568,4104,4106],{"className":4105,"style":1971},[805],[568,4107,4108,4111],{"style":1974},[568,4109],{"className":4110,"style":814},[813],[568,4112,4114],{"className":4113},[818,819,820,821],[568,4115,1160],{"className":4116},[629,821],[568,4118],{"className":4119,"style":635},[634],[568,4121,593],{"className":4122},[639],[568,4124],{"className":4125,"style":635},[634],[568,4127,4129,4132,4135,4141],{"className":4128},[620],[568,4130],{"className":4131,"style":1715},[624],[568,4133,1719],{"className":4134},[629],[568,4136,4138],{"className":4137},[629],[568,4139,1727],{"className":4140},[1726],[568,4142,3745],{"className":4143},[629],". Die Standardabweichung ist ",[568,4146,4148,4173],{"className":4147},[571],[568,4149,4151],{"className":4150},[575],[577,4152,4153],{"xmlns":579},[581,4154,4155,4170],{},[584,4156,4157,4159,4161,4165,4167],{},[587,4158,960],{},[591,4160,593],{},[964,4162,4163],{},[1158,4164,3381],{},[591,4166,1829],{},[1158,4168,4169],{},"1,91",[608,4171,4172],{"encoding":610},"\\sigma = \\sqrt{3{,}64} \\approx 1{,}91",[568,4174,4176,4194,4275],{"className":4175,"ariaHidden":616},[615],[568,4177,4179,4182,4185,4188,4191],{"className":4178},[620],[568,4180],{"className":4181,"style":988},[624],[568,4183,960],{"className":4184,"style":992},[629,630],[568,4186],{"className":4187,"style":635},[634],[568,4189,593],{"className":4190},[639],[568,4192],{"className":4193,"style":635},[634],[568,4195,4197,4201,4266,4269,4272],{"className":4196},[620],[568,4198],{"className":4199,"style":4200},[624],"height:1.04em;vertical-align:-0.23em;",[568,4202,4204],{"className":4203},[629,1012],[568,4205,4207,4257],{"className":4206},[796,797],[568,4208,4210,4254],{"className":4209},[801],[568,4211,4214,4237],{"className":4212,"style":4213},[805],"height:0.81em;",[568,4215,4218,4221],{"className":4216,"style":4217},[1026],"top:-3em;",[568,4219],{"className":4220,"style":1899},[813],[568,4222,4225,4228,4234],{"className":4223,"style":4224},[629],"padding-left:0.833em;",[568,4226,1719],{"className":4227},[629],[568,4229,4231],{"className":4230},[629],[568,4232,1727],{"className":4233},[1726],[568,4235,3745],{"className":4236},[629],[568,4238,4240,4243],{"style":4239},"top:-2.77em;",[568,4241],{"className":4242,"style":1899},[813],[568,4244,4247],{"className":4245,"style":4246},[1057],"min-width:0.853em;height:1.08em;",[1060,4248,4251],{"xmlns":1062,"width":1063,"height":4249,"viewBox":4250,"preserveAspectRatio":1066},"1.08em","0 0 400000 1080",[1068,4252],{"d":4253},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[568,4255,829],{"className":4256},[828],[568,4258,4260],{"className":4259},[801],[568,4261,4264],{"className":4262,"style":4263},[805],"height:0.23em;",[568,4265],{},[568,4267],{"className":4268,"style":635},[634],[568,4270,1829],{"className":4271},[639],[568,4273],{"className":4274,"style":635},[634],[568,4276,4278,4281,4284,4290],{"className":4277},[620],[568,4279],{"className":4280,"style":1715},[624],[568,4282,1187],{"className":4283},[629],[568,4285,4287],{"className":4286},[629],[568,4288,1727],{"className":4289},[1726],[568,4291,2317],{"className":4292},[629]," €.",[559,4295,4297],{"id":4296},"typische-fehler","Typische Fehler",[4299,4300,4301,4305,4499,4737],"ul",{},[4302,4303,4304],"li",{},"Die Abweichungen nicht mit den Wahrscheinlichkeiten gewichten, sondern einfach mitteln. Das geht nur, wenn alle Werte gleich wahrscheinlich sind, wie beim Würfel.",[4302,4306,4307,4308,4336,4337,4396,4397,4498],{},"Beim Verschiebungssatz ",[568,4309,4311,4324],{"className":4310},[571],[568,4312,4314],{"className":4313},[575],[577,4315,4316],{"xmlns":579},[581,4317,4318,4322],{},[584,4319,4320],{},[587,4321,589],{},[608,4323,735],{"encoding":610},[568,4325,4327],{"className":4326,"ariaHidden":616},[615],[568,4328,4330,4333],{"className":4329},[620],[568,4331],{"className":4332,"style":625},[624],[568,4334,589],{"className":4335},[629,630]," statt ",[568,4338,4340,4358],{"className":4339},[571],[568,4341,4343],{"className":4342},[575],[577,4344,4345],{"xmlns":579},[581,4346,4347,4355],{},[584,4348,4349],{},[1153,4350,4351,4353],{},[587,4352,589],{},[1158,4354,1160],{},[608,4356,4357],{"encoding":610},"\\mu^2",[568,4359,4361],{"className":4360,"ariaHidden":616},[615],[568,4362,4364,4367],{"className":4363},[620],[568,4365],{"className":4366,"style":2739},[624],[568,4368,4370,4373],{"className":4369},[629],[568,4371,589],{"className":4372},[629,630],[568,4374,4376],{"className":4375},[792],[568,4377,4379],{"className":4378},[796],[568,4380,4382],{"className":4381},[801],[568,4383,4385],{"className":4384,"style":1971},[805],[568,4386,4387,4390],{"style":1974},[568,4388],{"className":4389,"style":814},[813],[568,4391,4393],{"className":4392},[818,819,820,821],[568,4394,1160],{"className":4395},[629,821]," abziehen. ",[568,4398,4400,4423],{"className":4399},[571],[568,4401,4403],{"className":4402},[575],[577,4404,4405],{"xmlns":579},[581,4406,4407,4420],{},[584,4408,4409,4411,4413,4415,4417],{},[1158,4410,3801],{},[591,4412,860],{},[1158,4414,3115],{},[591,4416,593],{},[1158,4418,4419],{},"4,6",[608,4421,4422],{"encoding":610},"6{,}2 - 1{,}6 = 4{,}6",[568,4424,4426,4453,4480],{"className":4425,"ariaHidden":616},[615],[568,4427,4429,4432,4435,4441,4444,4447,4450],{"className":4428},[620],[568,4430],{"className":4431,"style":1715},[624],[568,4433,1804],{"className":4434},[629],[568,4436,4438],{"className":4437},[629],[568,4439,1727],{"className":4440},[1726],[568,4442,1160],{"className":4443},[629],[568,4445],{"className":4446,"style":708},[634],[568,4448,860],{"className":4449},[922],[568,4451],{"className":4452,"style":708},[634],[568,4454,4456,4459,4462,4468,4471,4474,4477],{"className":4455},[620],[568,4457],{"className":4458,"style":1715},[624],[568,4460,1187],{"className":4461},[629],[568,4463,4465],{"className":4464},[629],[568,4466,1727],{"className":4467},[1726],[568,4469,1804],{"className":4470},[629],[568,4472],{"className":4473,"style":635},[634],[568,4475,593],{"className":4476},[639],[568,4478],{"className":4479,"style":635},[634],[568,4481,4483,4486,4489,4495],{"className":4482},[620],[568,4484],{"className":4485,"style":1715},[624],[568,4487,2288],{"className":4488},[629],[568,4490,4492],{"className":4491},[629],[568,4493,1727],{"className":4494},[1726],[568,4496,1804],{"className":4497},[629]," ist falsch.",[4302,4500,4501,3004,4575,4659,4660,4733,4734,2861],{},[568,4502,4504,4528],{"className":4503},[571],[568,4505,4507],{"className":4506},[575],[577,4508,4509],{"xmlns":579},[581,4510,4511,4525],{},[584,4512,4513,4515,4517,4523],{},[587,4514,596],{},[591,4516,600],{"stretchy":599},[1153,4518,4519,4521],{},[587,4520,603],{},[1158,4522,1160],{},[591,4524,606],{"stretchy":599},[608,4526,4527],{"encoding":610},"E(X^2)",[568,4529,4531],{"className":4530,"ariaHidden":616},[615],[568,4532,4534,4537,4540,4543,4572],{"className":4533},[620],[568,4535],{"className":4536,"style":2332},[624],[568,4538,596],{"className":4539,"style":653},[629,630],[568,4541,600],{"className":4542},[657],[568,4544,4546,4549],{"className":4545},[629],[568,4547,603],{"className":4548,"style":661},[629,630],[568,4550,4552],{"className":4551},[792],[568,4553,4555],{"className":4554},[796],[568,4556,4558],{"className":4557},[801],[568,4559,4561],{"className":4560,"style":1971},[805],[568,4562,4563,4566],{"style":1974},[568,4564],{"className":4565,"style":814},[813],[568,4567,4569],{"className":4568},[818,819,820,821],[568,4570,1160],{"className":4571},[629,821],[568,4573,606],{"className":4574},[665],[568,4576,4578,4606],{"className":4577},[571],[568,4579,4581],{"className":4580},[575],[577,4582,4583],{"xmlns":579},[581,4584,4585,4603],{},[584,4586,4587,4589,4591,4593,4595,4597],{},[591,4588,600],{"stretchy":599},[587,4590,596],{},[591,4592,600],{"stretchy":599},[587,4594,603],{},[591,4596,606],{"stretchy":599},[1153,4598,4599,4601],{},[591,4600,606],{"stretchy":599},[1158,4602,1160],{},[608,4604,4605],{"encoding":610},"(E(X))^2",[568,4607,4609],{"className":4608,"ariaHidden":616},[615],[568,4610,4612,4615,4618,4621,4624,4627,4630],{"className":4611},[620],[568,4613],{"className":4614,"style":2332},[624],[568,4616,600],{"className":4617},[657],[568,4619,596],{"className":4620,"style":653},[629,630],[568,4622,600],{"className":4623},[657],[568,4625,603],{"className":4626,"style":661},[629,630],[568,4628,606],{"className":4629},[665],[568,4631,4633,4636],{"className":4632},[665],[568,4634,606],{"className":4635},[665],[568,4637,4639],{"className":4638},[792],[568,4640,4642],{"className":4641},[796],[568,4643,4645],{"className":4644},[801],[568,4646,4648],{"className":4647,"style":1971},[805],[568,4649,4650,4653],{"style":1974},[568,4651],{"className":4652,"style":814},[813],[568,4654,4656],{"className":4655},[818,819,820,821],[568,4657,1160],{"className":4658},[629,821]," verwechseln. ",[568,4661,4663,4686],{"className":4662},[571],[568,4664,4666],{"className":4665},[575],[577,4667,4668],{"xmlns":579},[581,4669,4670,4684],{},[584,4671,4672,4674,4676,4682],{},[587,4673,596],{},[591,4675,600],{"stretchy":599},[1153,4677,4678,4680],{},[587,4679,603],{},[1158,4681,1160],{},[591,4683,606],{"stretchy":599},[608,4685,4527],{"encoding":610},[568,4687,4689],{"className":4688,"ariaHidden":616},[615],[568,4690,4692,4695,4698,4701,4730],{"className":4691},[620],[568,4693],{"className":4694,"style":2332},[624],[568,4696,596],{"className":4697,"style":653},[629,630],[568,4699,600],{"className":4700},[657],[568,4702,4704,4707],{"className":4703},[629],[568,4705,603],{"className":4706,"style":661},[629,630],[568,4708,4710],{"className":4709},[792],[568,4711,4713],{"className":4712},[796],[568,4714,4716],{"className":4715},[801],[568,4717,4719],{"className":4718,"style":1971},[805],[568,4720,4721,4724],{"style":1974},[568,4722],{"className":4723,"style":814},[813],[568,4725,4727],{"className":4726},[818,819,820,821],[568,4728,1160],{"className":4729},[629,821],[568,4731,606],{"className":4732},[665]," ist der Erwartungswert der ",[668,4735,4736],{},"quadrierten Werte",[4302,4738,4739],{},"Varianz und Standardabweichung verwechseln. Die Varianz hat die quadrierte Einheit, hier €², und ist deshalb nicht direkt mit den Werten vergleichbar.",{"title":4741,"searchDepth":4742,"depth":4742,"links":4743},"",2,[4744,4745,4746],{"id":561,"depth":4742,"text":562},{"id":1632,"depth":4742,"text":1633},{"id":4296,"depth":4742,"text":4297},[4748,4751,4754,4757,4760,4762,4765,4768,4771,4773,4776],{"lhs":4749,"rhs":4750},"(a - (a*p + b*(1-p)))^2 * p + (b - (a*p + b*(1-p)))^2 * (1-p)","a^2*p + b^2*(1-p) - (a*p + b*(1-p))^2",{"lhs":4752,"rhs":4753},"((1-3.5)^2 + (2-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (5-3.5)^2 + (6-3.5)^2) \u002F 6","35\u002F12",{"lhs":4755,"rhs":4756},"round(35\u002F12, 2)","2.92",{"lhs":4758,"rhs":4759},"(1 + 4 + 9 + 16 + 25 + 36) \u002F 6","91\u002F6",{"lhs":4761,"rhs":4753},"91\u002F6 - 3.5^2",{"lhs":4763,"rhs":4764},"0 * 0.5 + 2 * 0.3 + 5 * 0.2","1.6",{"lhs":4766,"rhs":4767},"(0 - 1.6)^2 * 0.5 + (2 - 1.6)^2 * 0.3 + (5 - 1.6)^2 * 0.2","3.64",{"lhs":4769,"rhs":4770},"0^2 * 0.5 + 2^2 * 0.3 + 5^2 * 0.2","6.2",{"lhs":4772,"rhs":4767},"6.2 - 1.6^2",{"lhs":4774,"rhs":4775},"round(sqrt(3.64), 2)","1.91",{"lhs":4777,"rhs":4778},"6.2 - 1.6","4.6","X \\text{ nimmt genau die verschiedenen Werte } x_1, \\ldots, x_n \\text{ an},\\ \\mu = E(X)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">nimmt genau die verschiedenen Werte\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_1, \\ldots,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">an\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu = E(X)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","variance-random-variable","V(X) = \\sum_{i=1}^{n} (x_i - \\mu)^2 \\cdot P(X = x_i)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>μ\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V(X) = \\sum_{i=1}^{n} (x_i - \\mu)^2 \\cdot P(X = x_i)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2777em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1141em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse",[],[4792,4793,4794,4795],"expected-value","standard-deviation","empirical-variance","variance-linear-transformation",{"title":548,"description":4741},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Die Varianz ist die mit den Wahrscheinlichkeiten gewichtete Summe der quadrierten Abweichungen vom Erwartungswert.",[4800,4801,4802,4803,4804],"varianz","zufallsgröße","streuung","standardabweichung","wahrscheinlichkeitsverteilung",[4806,4809,4812,4815,4819,4822,4825],{"symbol":695,"meaning":4807,"symbolHtml":4808},"Varianz der Zufallsgröße X, auch Var(X) oder σ² geschrieben","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V(X)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":603,"meaning":4810,"symbolHtml":4811},"Zufallsgröße","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":772,"meaning":4813,"symbolHtml":4814},"die möglichen Werte von X","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4816,"meaning":4817,"symbolHtml":4818},"P(X = x_i)","Wahrscheinlichkeit, dass X den Wert x_i annimmt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X = x_i)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":735,"meaning":4820,"symbolHtml":4821},"Erwartungswert E(X)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1190,"meaning":4823,"symbolHtml":4824},"Anzahl der möglichen Werte","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":769,"meaning":4826,"symbolHtml":4827},"Laufindex von 1 bis n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">i\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6595em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">i\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","AeB5E6JH3KEqfWz6jguDDt6aznvx4Br8F18-3QnzLJk",[4830,4833,4836,4838],{"stem":4831,"title":4832,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fempirische-varianz","Empirische Varianz",{"stem":4834,"title":4835,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert","Erwartungswert",{"stem":4837,"title":944,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstandardabweichung",{"stem":4839,"title":4840,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation","Varianz bei linearer Transformation",1793824288359]