[{"data":1,"prerenderedAt":4981},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-einer-summe":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-einer-summe":4969},[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":556,"category":441,"checks":4910,"conditions":4930,"conditionsHtml":4931,"deprecated":4932,"description":4904,"extension":4933,"figure":4932,"figureCaption":4932,"figureHtml":4932,"formulaId":4934,"latex":4935,"latexHtml":4936,"level":4937,"meta":4938,"navigation":4939,"path":4940,"redirectFrom":4941,"related":4942,"seo":4947,"stem":4948,"subject":583,"summary":4949,"tags":4950,"variables":4956,"__hash__":4968},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-einer-summe.md","Varianz einer Summe",[550,551,552,553,554,555],"Var(X+Y)","Varianz der Summe zweier Zufallsvariablen","Additionssatz Varianz","Varianz Summe unabhängiger Zufallsgrößen","Varianz Differenz","Satz von Bienaymé",{"type":557,"value":558,"toc":4903},"minimark",[559,564,656,659,1952,2448,2452,2566,2934,3109,3488,3491,3852,3855,3859],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572,573,620,621,651,652,655],"p",{},"Anders als beim Erwartungswert ist die Varianz einer Summe im Allgemeinen ",[569,570,571],"strong",{},"nicht"," die Summe der Varianzen. Es kommt ein Korrekturglied hinzu, das misst, wie ",[574,575,578,600],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,596],"semantics",{},[590,591,592],"mrow",{},[593,594,595],"mi",{},"X",[597,598,595],"annotation",{"encoding":599},"application\u002Fx-tex",[574,601,605],{"className":602,"ariaHidden":604},[603],"katex-html","true",[574,606,609,614],{"className":607},[608],"base",[574,610],{"className":611,"style":613},[612],"strut","height:0.6833em;",[574,615,595],{"className":616,"style":619},[617,618],"mord","mathnormal","margin-right:0.0785em;"," und ",[574,622,624,638],{"className":623},[577],[574,625,627],{"className":626},[581],[583,628,629],{"xmlns":585},[587,630,631,636],{},[590,632,633],{},[593,634,635],{},"Y",[597,637,635],{"encoding":599},[574,639,641],{"className":640,"ariaHidden":604},[603],[574,642,644,647],{"className":643},[608],[574,645],{"className":646,"style":613},[612],[574,648,635],{"className":649,"style":650},[617,618],"margin-right:0.2222em;"," gemeinsam schwanken: die ",[569,653,654],{},"Kovarianz",".",[565,657,658],{},"Wichtige Spezialfälle und Verallgemeinerungen:",[660,661,662,920,1132,1442],"ul",{},[663,664,665,668,669,776,777,655],"li",{},[569,666,667],{},"Unabhängig"," (oder nur unkorreliert): ",[574,670,672,713],{"className":671},[577],[574,673,675],{"className":674},[581],[583,676,677],{"xmlns":585},[587,678,679,710],{},[590,680,681,685,689,693,695,698,700,703,706],{},[593,682,684],{"mathvariant":683},"normal","Cov",[686,687,688],"mo",{},"⁡",[686,690,692],{"stretchy":691},"false","(",[593,694,595],{},[686,696,697],{"separator":604},",",[593,699,635],{},[686,701,702],{"stretchy":691},")",[686,704,705],{},"=",[707,708,709],"mn",{},"0",[597,711,712],{"encoding":599},"\\operatorname{Cov}(X, Y) = 0",[574,714,716,766],{"className":715,"ariaHidden":604},[603],[574,717,719,723,732,736,739,743,748,751,755,759,763],{"className":718},[608],[574,720],{"className":721,"style":722},[612],"height:1em;vertical-align:-0.25em;",[574,724,727],{"className":725},[726],"mop",[574,728,684],{"className":729,"style":731},[617,730],"mathrm","margin-right:0.0139em;",[574,733,692],{"className":734},[735],"mopen",[574,737,595],{"className":738,"style":619},[617,618],[574,740,697],{"className":741},[742],"mpunct",[574,744],{"className":745,"style":747},[746],"mspace","margin-right:0.1667em;",[574,749,635],{"className":750,"style":650},[617,618],[574,752,702],{"className":753},[754],"mclose",[574,756],{"className":757,"style":758},[746],"margin-right:0.2778em;",[574,760,705],{"className":761},[762],"mrel",[574,764],{"className":765,"style":758},[746],[574,767,769,773],{"className":768},[608],[574,770],{"className":771,"style":772},[612],"height:0.6444em;",[574,774,709],{"className":775},[617],", also ",[574,778,780,826],{"className":779},[577],[574,781,783],{"className":782},[581],[583,784,785],{"xmlns":585},[587,786,787,823],{},[590,788,789,792,794,796,799,801,803,805,807,809,811,813,815,817,819,821],{},[593,790,791],{},"V",[686,793,692],{"stretchy":691},[593,795,595],{},[686,797,798],{},"+",[593,800,635],{},[686,802,702],{"stretchy":691},[686,804,705],{},[593,806,791],{},[686,808,692],{"stretchy":691},[593,810,595],{},[686,812,702],{"stretchy":691},[686,814,798],{},[593,816,791],{},[686,818,692],{"stretchy":691},[593,820,635],{},[686,822,702],{"stretchy":691},[597,824,825],{"encoding":599},"V(X + Y) = V(X) + V(Y)",[574,827,829,854,875,902],{"className":828,"ariaHidden":604},[603],[574,830,832,835,838,841,844,847,851],{"className":831},[608],[574,833],{"className":834,"style":722},[612],[574,836,791],{"className":837,"style":650},[617,618],[574,839,692],{"className":840},[735],[574,842,595],{"className":843,"style":619},[617,618],[574,845],{"className":846,"style":650},[746],[574,848,798],{"className":849},[850],"mbin",[574,852],{"className":853,"style":650},[746],[574,855,857,860,863,866,869,872],{"className":856},[608],[574,858],{"className":859,"style":722},[612],[574,861,635],{"className":862,"style":650},[617,618],[574,864,702],{"className":865},[754],[574,867],{"className":868,"style":758},[746],[574,870,705],{"className":871},[762],[574,873],{"className":874,"style":758},[746],[574,876,878,881,884,887,890,893,896,899],{"className":877},[608],[574,879],{"className":880,"style":722},[612],[574,882,791],{"className":883,"style":650},[617,618],[574,885,692],{"className":886},[735],[574,888,595],{"className":889,"style":619},[617,618],[574,891,702],{"className":892},[754],[574,894],{"className":895,"style":650},[746],[574,897,798],{"className":898},[850],[574,900],{"className":901,"style":650},[746],[574,903,905,908,911,914,917],{"className":904},[608],[574,906],{"className":907,"style":722},[612],[574,909,791],{"className":910,"style":650},[617,618],[574,912,692],{"className":913},[735],[574,915,635],{"className":916,"style":650},[617,618],[574,918,702],{"className":919},[754],[663,921,922,925,926,1131],{},[569,923,924],{},"Differenz",": ",[574,927,929,993],{"className":928},[577],[574,930,932],{"className":931},[581],[583,933,934],{"xmlns":585},[587,935,936,990],{},[590,937,938,940,942,944,947,949,951,953,955,957,959,961,963,965,967,969,971,973,976,978,980,982,984,986,988],{},[593,939,791],{},[686,941,692],{"stretchy":691},[593,943,595],{},[686,945,946],{},"−",[593,948,635],{},[686,950,702],{"stretchy":691},[686,952,705],{},[593,954,791],{},[686,956,692],{"stretchy":691},[593,958,595],{},[686,960,702],{"stretchy":691},[686,962,798],{},[593,964,791],{},[686,966,692],{"stretchy":691},[593,968,635],{},[686,970,702],{"stretchy":691},[686,972,946],{},[707,974,975],{},"2",[593,977,684],{"mathvariant":683},[686,979,688],{},[686,981,692],{"stretchy":691},[593,983,595],{},[686,985,697],{"separator":604},[593,987,635],{},[686,989,702],{"stretchy":691},[597,991,992],{"encoding":599},"V(X - Y) = V(X) + V(Y) - 2\\operatorname{Cov}(X, Y)",[574,994,996,1020,1041,1068,1095],{"className":995,"ariaHidden":604},[603],[574,997,999,1002,1005,1008,1011,1014,1017],{"className":998},[608],[574,1000],{"className":1001,"style":722},[612],[574,1003,791],{"className":1004,"style":650},[617,618],[574,1006,692],{"className":1007},[735],[574,1009,595],{"className":1010,"style":619},[617,618],[574,1012],{"className":1013,"style":650},[746],[574,1015,946],{"className":1016},[850],[574,1018],{"className":1019,"style":650},[746],[574,1021,1023,1026,1029,1032,1035,1038],{"className":1022},[608],[574,1024],{"className":1025,"style":722},[612],[574,1027,635],{"className":1028,"style":650},[617,618],[574,1030,702],{"className":1031},[754],[574,1033],{"className":1034,"style":758},[746],[574,1036,705],{"className":1037},[762],[574,1039],{"className":1040,"style":758},[746],[574,1042,1044,1047,1050,1053,1056,1059,1062,1065],{"className":1043},[608],[574,1045],{"className":1046,"style":722},[612],[574,1048,791],{"className":1049,"style":650},[617,618],[574,1051,692],{"className":1052},[735],[574,1054,595],{"className":1055,"style":619},[617,618],[574,1057,702],{"className":1058},[754],[574,1060],{"className":1061,"style":650},[746],[574,1063,798],{"className":1064},[850],[574,1066],{"className":1067,"style":650},[746],[574,1069,1071,1074,1077,1080,1083,1086,1089,1092],{"className":1070},[608],[574,1072],{"className":1073,"style":722},[612],[574,1075,791],{"className":1076,"style":650},[617,618],[574,1078,692],{"className":1079},[735],[574,1081,635],{"className":1082,"style":650},[617,618],[574,1084,702],{"className":1085},[754],[574,1087],{"className":1088,"style":650},[746],[574,1090,946],{"className":1091},[850],[574,1093],{"className":1094,"style":650},[746],[574,1096,1098,1101,1104,1107,1113,1116,1119,1122,1125,1128],{"className":1097},[608],[574,1099],{"className":1100,"style":722},[612],[574,1102,975],{"className":1103},[617],[574,1105],{"className":1106,"style":747},[746],[574,1108,1110],{"className":1109},[726],[574,1111,684],{"className":1112,"style":731},[617,730],[574,1114,692],{"className":1115},[735],[574,1117,595],{"className":1118,"style":619},[617,618],[574,1120,697],{"className":1121},[742],[574,1123],{"className":1124,"style":747},[746],[574,1126,635],{"className":1127,"style":650},[617,618],[574,1129,702],{"className":1130},[754],". Bei Unabhängigkeit addieren sich die Varianzen auch hier.",[663,1133,1134,925,1137,655],{},[569,1135,1136],{},"Linearkombination",[574,1138,1140,1225],{"className":1139},[577],[574,1141,1143],{"className":1142},[581],[583,1144,1145],{"xmlns":585},[587,1146,1147,1222],{},[590,1148,1149,1151,1153,1156,1158,1160,1163,1165,1167,1169,1176,1178,1180,1182,1184,1186,1192,1194,1196,1198,1200,1202,1204,1206,1208,1210,1212,1214,1216,1218,1220],{},[593,1150,791],{},[686,1152,692],{"stretchy":691},[593,1154,1155],{},"a",[593,1157,595],{},[686,1159,798],{},[593,1161,1162],{},"b",[593,1164,635],{},[686,1166,702],{"stretchy":691},[686,1168,705],{},[1170,1171,1172,1174],"msup",{},[593,1173,1155],{},[707,1175,975],{},[593,1177,791],{},[686,1179,692],{"stretchy":691},[593,1181,595],{},[686,1183,702],{"stretchy":691},[686,1185,798],{},[1170,1187,1188,1190],{},[593,1189,1162],{},[707,1191,975],{},[593,1193,791],{},[686,1195,692],{"stretchy":691},[593,1197,635],{},[686,1199,702],{"stretchy":691},[686,1201,798],{},[707,1203,975],{},[593,1205,1155],{},[593,1207,1162],{},[593,1209,684],{"mathvariant":683},[686,1211,688],{},[686,1213,692],{"stretchy":691},[593,1215,595],{},[686,1217,697],{"separator":604},[593,1219,635],{},[686,1221,702],{"stretchy":691},[597,1223,1224],{"encoding":599},"V(aX + bY) = a^2 V(X) + b^2 V(Y) + 2ab\\operatorname{Cov}(X, Y)",[574,1226,1228,1255,1277,1346,1402],{"className":1227,"ariaHidden":604},[603],[574,1229,1231,1234,1237,1240,1243,1246,1249,1252],{"className":1230},[608],[574,1232],{"className":1233,"style":722},[612],[574,1235,791],{"className":1236,"style":650},[617,618],[574,1238,692],{"className":1239},[735],[574,1241,1155],{"className":1242},[617,618],[574,1244,595],{"className":1245,"style":619},[617,618],[574,1247],{"className":1248,"style":650},[746],[574,1250,798],{"className":1251},[850],[574,1253],{"className":1254,"style":650},[746],[574,1256,1258,1261,1265,1268,1271,1274],{"className":1257},[608],[574,1259],{"className":1260,"style":722},[612],[574,1262,1264],{"className":1263,"style":650},[617,618],"bY",[574,1266,702],{"className":1267},[754],[574,1269],{"className":1270,"style":758},[746],[574,1272,705],{"className":1273},[762],[574,1275],{"className":1276,"style":758},[746],[574,1278,1280,1284,1325,1328,1331,1334,1337,1340,1343],{"className":1279},[608],[574,1281],{"className":1282,"style":1283},[612],"height:1.0641em;vertical-align:-0.25em;",[574,1285,1287,1290],{"className":1286},[617],[574,1288,1155],{"className":1289},[617,618],[574,1291,1294],{"className":1292},[1293],"msupsub",[574,1295,1298],{"className":1296},[1297],"vlist-t",[574,1299,1302],{"className":1300},[1301],"vlist-r",[574,1303,1307],{"className":1304,"style":1306},[1305],"vlist","height:0.8141em;",[574,1308,1310,1315],{"style":1309},"top:-3.063em;margin-right:0.05em;",[574,1311],{"className":1312,"style":1314},[1313],"pstrut","height:2.7em;",[574,1316,1322],{"className":1317},[1318,1319,1320,1321],"sizing","reset-size6","size3","mtight",[574,1323,975],{"className":1324},[617,1321],[574,1326,791],{"className":1327,"style":650},[617,618],[574,1329,692],{"className":1330},[735],[574,1332,595],{"className":1333,"style":619},[617,618],[574,1335,702],{"className":1336},[754],[574,1338],{"className":1339,"style":650},[746],[574,1341,798],{"className":1342},[850],[574,1344],{"className":1345,"style":650},[746],[574,1347,1349,1352,1381,1384,1387,1390,1393,1396,1399],{"className":1348},[608],[574,1350],{"className":1351,"style":1283},[612],[574,1353,1355,1358],{"className":1354},[617],[574,1356,1162],{"className":1357},[617,618],[574,1359,1361],{"className":1360},[1293],[574,1362,1364],{"className":1363},[1297],[574,1365,1367],{"className":1366},[1301],[574,1368,1370],{"className":1369,"style":1306},[1305],[574,1371,1372,1375],{"style":1309},[574,1373],{"className":1374,"style":1314},[1313],[574,1376,1378],{"className":1377},[1318,1319,1320,1321],[574,1379,975],{"className":1380},[617,1321],[574,1382,791],{"className":1383,"style":650},[617,618],[574,1385,692],{"className":1386},[735],[574,1388,635],{"className":1389,"style":650},[617,618],[574,1391,702],{"className":1392},[754],[574,1394],{"className":1395,"style":650},[746],[574,1397,798],{"className":1398},[850],[574,1400],{"className":1401,"style":650},[746],[574,1403,1405,1408,1411,1415,1418,1424,1427,1430,1433,1436,1439],{"className":1404},[608],[574,1406],{"className":1407,"style":722},[612],[574,1409,975],{"className":1410},[617],[574,1412,1414],{"className":1413},[617,618],"ab",[574,1416],{"className":1417,"style":747},[746],[574,1419,1421],{"className":1420},[726],[574,1422,684],{"className":1423,"style":731},[617,730],[574,1425,692],{"className":1426},[735],[574,1428,595],{"className":1429,"style":619},[617,618],[574,1431,697],{"className":1432},[742],[574,1434],{"className":1435,"style":747},[746],[574,1437,635],{"className":1438,"style":650},[617,618],[574,1440,702],{"className":1441},[754],[663,1443,1444,925,1447,655],{},[569,1445,1446],{},"Viele Summanden",[574,1448,1450,1544],{"className":1449},[577],[574,1451,1453],{"className":1452},[581],[583,1454,1455],{"xmlns":585},[587,1456,1457,1541],{},[590,1458,1459,1461,1464,1473,1479,1481,1483,1489,1491,1493,1499,1501,1503,1505,1519,1521,1523,1525,1531,1533,1539],{},[593,1460,791],{},[686,1462,692],{"fence":691,"stretchy":604,"minsize":1463,"maxsize":1463},"1.2em",[1465,1466,1467,1470],"msub",{},[686,1468,1469],{},"∑",[593,1471,1472],{},"i",[1465,1474,1475,1477],{},[593,1476,595],{},[593,1478,1472],{},[686,1480,702],{"fence":691,"stretchy":604,"minsize":1463,"maxsize":1463},[686,1482,705],{},[1465,1484,1485,1487],{},[686,1486,1469],{},[593,1488,1472],{},[593,1490,791],{},[686,1492,692],{"stretchy":691},[1465,1494,1495,1497],{},[593,1496,595],{},[593,1498,1472],{},[686,1500,702],{"stretchy":691},[686,1502,798],{},[707,1504,975],{},[1465,1506,1507,1509],{},[686,1508,1469],{},[590,1510,1511,1513,1516],{},[593,1512,1472],{},[686,1514,1515],{},"\u003C",[593,1517,1518],{},"j",[593,1520,684],{"mathvariant":683},[686,1522,688],{},[686,1524,692],{"stretchy":691},[1465,1526,1527,1529],{},[593,1528,595],{},[593,1530,1472],{},[686,1532,697],{"separator":604},[1465,1534,1535,1537],{},[593,1536,595],{},[593,1538,1518],{},[686,1540,702],{"stretchy":691},[597,1542,1543],{"encoding":599},"V\\big(\\sum_i X_i\\big) = \\sum_i V(X_i) + 2\\sum_{i\u003Cj} \\operatorname{Cov}(X_i, X_j)",[574,1545,1547,1678,1786],{"className":1546,"ariaHidden":604},[603],[574,1548,1550,1554,1557,1565,1568,1617,1620,1663,1669,1672,1675],{"className":1549},[608],[574,1551],{"className":1552,"style":1553},[612],"height:1.2em;vertical-align:-0.35em;",[574,1555,791],{"className":1556,"style":650},[617,618],[574,1558,1560],{"className":1559},[617],[574,1561,692],{"className":1562},[1563,1564],"delimsizing","size1",[574,1566],{"className":1567,"style":747},[746],[574,1569,1571,1577],{"className":1570},[726],[574,1572,1469],{"className":1573,"style":1576},[726,1574,1575],"op-symbol","small-op","position:relative;top:0em;",[574,1578,1580],{"className":1579},[1293],[574,1581,1584,1608],{"className":1582},[1297,1583],"vlist-t2",[574,1585,1587,1603],{"className":1586},[1301],[574,1588,1591],{"className":1589,"style":1590},[1305],"height:0.162em;",[574,1592,1594,1597],{"style":1593},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[574,1595],{"className":1596,"style":1314},[1313],[574,1598,1600],{"className":1599},[1318,1319,1320,1321],[574,1601,1472],{"className":1602},[617,618,1321],[574,1604,1607],{"className":1605},[1606],"vlist-s","​",[574,1609,1611],{"className":1610},[1301],[574,1612,1615],{"className":1613,"style":1614},[1305],"height:0.2997em;",[574,1616],{},[574,1618],{"className":1619,"style":747},[746],[574,1621,1623,1626],{"className":1622},[617],[574,1624,595],{"className":1625,"style":619},[617,618],[574,1627,1629],{"className":1628},[1293],[574,1630,1632,1654],{"className":1631},[1297,1583],[574,1633,1635,1651],{"className":1634},[1301],[574,1636,1639],{"className":1637,"style":1638},[1305],"height:0.3117em;",[574,1640,1642,1645],{"style":1641},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[574,1643],{"className":1644,"style":1314},[1313],[574,1646,1648],{"className":1647},[1318,1319,1320,1321],[574,1649,1472],{"className":1650},[617,618,1321],[574,1652,1607],{"className":1653},[1606],[574,1655,1657],{"className":1656},[1301],[574,1658,1661],{"className":1659,"style":1660},[1305],"height:0.15em;",[574,1662],{},[574,1664,1666],{"className":1665},[617],[574,1667,702],{"className":1668},[1563,1564],[574,1670],{"className":1671,"style":758},[746],[574,1673,705],{"className":1674},[762],[574,1676],{"className":1677,"style":758},[746],[574,1679,1681,1685,1725,1728,1731,1734,1774,1777,1780,1783],{"className":1680},[608],[574,1682],{"className":1683,"style":1684},[612],"height:1.0497em;vertical-align:-0.2997em;",[574,1686,1688,1691],{"className":1687},[726],[574,1689,1469],{"className":1690,"style":1576},[726,1574,1575],[574,1692,1694],{"className":1693},[1293],[574,1695,1697,1717],{"className":1696},[1297,1583],[574,1698,1700,1714],{"className":1699},[1301],[574,1701,1703],{"className":1702,"style":1590},[1305],[574,1704,1705,1708],{"style":1593},[574,1706],{"className":1707,"style":1314},[1313],[574,1709,1711],{"className":1710},[1318,1319,1320,1321],[574,1712,1472],{"className":1713},[617,618,1321],[574,1715,1607],{"className":1716},[1606],[574,1718,1720],{"className":1719},[1301],[574,1721,1723],{"className":1722,"style":1614},[1305],[574,1724],{},[574,1726],{"className":1727,"style":747},[746],[574,1729,791],{"className":1730,"style":650},[617,618],[574,1732,692],{"className":1733},[735],[574,1735,1737,1740],{"className":1736},[617],[574,1738,595],{"className":1739,"style":619},[617,618],[574,1741,1743],{"className":1742},[1293],[574,1744,1746,1766],{"className":1745},[1297,1583],[574,1747,1749,1763],{"className":1748},[1301],[574,1750,1752],{"className":1751,"style":1638},[1305],[574,1753,1754,1757],{"style":1641},[574,1755],{"className":1756,"style":1314},[1313],[574,1758,1760],{"className":1759},[1318,1319,1320,1321],[574,1761,1472],{"className":1762},[617,618,1321],[574,1764,1607],{"className":1765},[1606],[574,1767,1769],{"className":1768},[1301],[574,1770,1772],{"className":1771,"style":1660},[1305],[574,1773],{},[574,1775,702],{"className":1776},[754],[574,1778],{"className":1779,"style":650},[746],[574,1781,798],{"className":1782},[850],[574,1784],{"className":1785,"style":650},[746],[574,1787,1789,1793,1796,1799,1850,1853,1859,1862,1902,1905,1908,1949],{"className":1788},[608],[574,1790],{"className":1791,"style":1792},[612],"height:1.1858em;vertical-align:-0.4358em;",[574,1794,975],{"className":1795},[617],[574,1797],{"className":1798,"style":747},[746],[574,1800,1802,1805],{"className":1801},[726],[574,1803,1469],{"className":1804,"style":1576},[726,1574,1575],[574,1806,1808],{"className":1807},[1293],[574,1809,1811,1841],{"className":1810},[1297,1583],[574,1812,1814,1838],{"className":1813},[1301],[574,1815,1817],{"className":1816,"style":1590},[1305],[574,1818,1819,1822],{"style":1593},[574,1820],{"className":1821,"style":1314},[1313],[574,1823,1825],{"className":1824},[1318,1319,1320,1321],[574,1826,1828,1831,1834],{"className":1827},[617,1321],[574,1829,1472],{"className":1830},[617,618,1321],[574,1832,1515],{"className":1833},[762,1321],[574,1835,1518],{"className":1836,"style":1837},[617,618,1321],"margin-right:0.0572em;",[574,1839,1607],{"className":1840},[1606],[574,1842,1844],{"className":1843},[1301],[574,1845,1848],{"className":1846,"style":1847},[1305],"height:0.4358em;",[574,1849],{},[574,1851],{"className":1852,"style":747},[746],[574,1854,1856],{"className":1855},[726],[574,1857,684],{"className":1858,"style":731},[617,730],[574,1860,692],{"className":1861},[735],[574,1863,1865,1868],{"className":1864},[617],[574,1866,595],{"className":1867,"style":619},[617,618],[574,1869,1871],{"className":1870},[1293],[574,1872,1874,1894],{"className":1873},[1297,1583],[574,1875,1877,1891],{"className":1876},[1301],[574,1878,1880],{"className":1879,"style":1638},[1305],[574,1881,1882,1885],{"style":1641},[574,1883],{"className":1884,"style":1314},[1313],[574,1886,1888],{"className":1887},[1318,1319,1320,1321],[574,1889,1472],{"className":1890},[617,618,1321],[574,1892,1607],{"className":1893},[1606],[574,1895,1897],{"className":1896},[1301],[574,1898,1900],{"className":1899,"style":1660},[1305],[574,1901],{},[574,1903,697],{"className":1904},[742],[574,1906],{"className":1907,"style":747},[746],[574,1909,1911,1914],{"className":1910},[617],[574,1912,595],{"className":1913,"style":619},[617,618],[574,1915,1917],{"className":1916},[1293],[574,1918,1920,1940],{"className":1919},[1297,1583],[574,1921,1923,1937],{"className":1922},[1301],[574,1924,1926],{"className":1925,"style":1638},[1305],[574,1927,1928,1931],{"style":1641},[574,1929],{"className":1930,"style":1314},[1313],[574,1932,1934],{"className":1933},[1318,1319,1320,1321],[574,1935,1518],{"className":1936,"style":1837},[617,618,1321],[574,1938,1607],{"className":1939},[1606],[574,1941,1943],{"className":1942},[1301],[574,1944,1947],{"className":1945,"style":1946},[1305],"height:0.2861em;",[574,1948],{},[574,1950,702],{"className":1951},[754],[565,1953,1954,1955,620,2087,2208,2209,2447],{},"Herleitung: Mit ",[574,1956,1958,1993],{"className":1957},[577],[574,1959,1961],{"className":1960},[581],[583,1962,1963],{"xmlns":585},[587,1964,1965,1990],{},[590,1966,1967,1975,1977,1979,1981,1984,1986,1988],{},[1968,1969,1970,1972],"mover",{"accent":604},[593,1971,595],{},[686,1973,1974],{},"~",[686,1976,705],{},[593,1978,595],{},[686,1980,946],{},[593,1982,1983],{},"E",[686,1985,692],{"stretchy":691},[593,1987,595],{},[686,1989,702],{"stretchy":691},[597,1991,1992],{"encoding":599},"\\tilde{X} = X - E(X)",[574,1994,1996,2049,2068],{"className":1995,"ariaHidden":604},[603],[574,1997,1999,2003,2040,2043,2046],{"className":1998},[608],[574,2000],{"className":2001,"style":2002},[612],"height:0.9202em;",[574,2004,2007],{"className":2005},[617,2006],"accent",[574,2008,2010],{"className":2009},[1297],[574,2011,2013],{"className":2012},[1301],[574,2014,2016,2026],{"className":2015,"style":2002},[1305],[574,2017,2019,2023],{"style":2018},"top:-3em;",[574,2020],{"className":2021,"style":2022},[1313],"height:3em;",[574,2024,595],{"className":2025,"style":619},[617,618],[574,2027,2029,2032],{"style":2028},"top:-3.6023em;",[574,2030],{"className":2031,"style":2022},[1313],[574,2033,2037],{"className":2034,"style":2036},[2035],"accent-body","left:-0.1667em;",[574,2038,1974],{"className":2039},[617],[574,2041],{"className":2042,"style":758},[746],[574,2044,705],{"className":2045},[762],[574,2047],{"className":2048,"style":758},[746],[574,2050,2052,2056,2059,2062,2065],{"className":2051},[608],[574,2053],{"className":2054,"style":2055},[612],"height:0.7667em;vertical-align:-0.0833em;",[574,2057,595],{"className":2058,"style":619},[617,618],[574,2060],{"className":2061,"style":650},[746],[574,2063,946],{"className":2064},[850],[574,2066],{"className":2067,"style":650},[746],[574,2069,2071,2074,2078,2081,2084],{"className":2070},[608],[574,2072],{"className":2073,"style":722},[612],[574,2075,1983],{"className":2076,"style":2077},[617,618],"margin-right:0.0576em;",[574,2079,692],{"className":2080},[735],[574,2082,595],{"className":2083,"style":619},[617,618],[574,2085,702],{"className":2086},[754],[574,2088,2090,2122],{"className":2089},[577],[574,2091,2093],{"className":2092},[581],[583,2094,2095],{"xmlns":585},[587,2096,2097,2119],{},[590,2098,2099,2105,2107,2109,2111,2113,2115,2117],{},[1968,2100,2101,2103],{"accent":604},[593,2102,635],{},[686,2104,1974],{},[686,2106,705],{},[593,2108,635],{},[686,2110,946],{},[593,2112,1983],{},[686,2114,692],{"stretchy":691},[593,2116,635],{},[686,2118,702],{"stretchy":691},[597,2120,2121],{"encoding":599},"\\tilde{Y} = Y - E(Y)",[574,2123,2125,2172,2190],{"className":2124,"ariaHidden":604},[603],[574,2126,2128,2131,2163,2166,2169],{"className":2127},[608],[574,2129],{"className":2130,"style":2002},[612],[574,2132,2134],{"className":2133},[617,2006],[574,2135,2137],{"className":2136},[1297],[574,2138,2140],{"className":2139},[1301],[574,2141,2143,2151],{"className":2142,"style":2002},[1305],[574,2144,2145,2148],{"style":2018},[574,2146],{"className":2147,"style":2022},[1313],[574,2149,635],{"className":2150,"style":650},[617,618],[574,2152,2153,2156],{"style":2028},[574,2154],{"className":2155,"style":2022},[1313],[574,2157,2160],{"className":2158,"style":2159},[2035],"left:-0.25em;",[574,2161,1974],{"className":2162},[617],[574,2164],{"className":2165,"style":758},[746],[574,2167,705],{"className":2168},[762],[574,2170],{"className":2171,"style":758},[746],[574,2173,2175,2178,2181,2184,2187],{"className":2174},[608],[574,2176],{"className":2177,"style":2055},[612],[574,2179,635],{"className":2180,"style":650},[617,618],[574,2182],{"className":2183,"style":650},[746],[574,2185,946],{"className":2186},[850],[574,2188],{"className":2189,"style":650},[746],[574,2191,2193,2196,2199,2202,2205],{"className":2192},[608],[574,2194],{"className":2195,"style":722},[612],[574,2197,1983],{"className":2198,"style":2077},[617,618],[574,2200,692],{"className":2201},[735],[574,2203,635],{"className":2204,"style":650},[617,618],[574,2206,702],{"className":2207},[754]," ist ",[574,2210,2212,2268],{"className":2211},[577],[574,2213,2215],{"className":2214},[581],[583,2216,2217],{"xmlns":585},[587,2218,2219,2265],{},[590,2220,2221,2223,2225,2227,2229,2231,2233,2235,2237,2240,2242,2248,2250,2256,2262],{},[593,2222,791],{},[686,2224,692],{"stretchy":691},[593,2226,595],{},[686,2228,798],{},[593,2230,635],{},[686,2232,702],{"stretchy":691},[686,2234,705],{},[593,2236,1983],{},[686,2238,2239],{"fence":691,"stretchy":604,"minsize":1463,"maxsize":1463},"[",[686,2241,692],{"stretchy":691},[1968,2243,2244,2246],{"accent":604},[593,2245,595],{},[686,2247,1974],{},[686,2249,798],{},[1968,2251,2252,2254],{"accent":604},[593,2253,635],{},[686,2255,1974],{},[1170,2257,2258,2260],{},[686,2259,702],{"stretchy":691},[707,2261,975],{},[686,2263,2264],{"fence":691,"stretchy":604,"minsize":1463,"maxsize":1463},"]",[597,2266,2267],{"encoding":599},"V(X + Y) = E\\big[(\\tilde{X} + \\tilde{Y})^2\\big]",[574,2269,2271,2295,2316,2375],{"className":2270,"ariaHidden":604},[603],[574,2272,2274,2277,2280,2283,2286,2289,2292],{"className":2273},[608],[574,2275],{"className":2276,"style":722},[612],[574,2278,791],{"className":2279,"style":650},[617,618],[574,2281,692],{"className":2282},[735],[574,2284,595],{"className":2285,"style":619},[617,618],[574,2287],{"className":2288,"style":650},[746],[574,2290,798],{"className":2291},[850],[574,2293],{"className":2294,"style":650},[746],[574,2296,2298,2301,2304,2307,2310,2313],{"className":2297},[608],[574,2299],{"className":2300,"style":722},[612],[574,2302,635],{"className":2303,"style":650},[617,618],[574,2305,702],{"className":2306},[754],[574,2308],{"className":2309,"style":758},[746],[574,2311,705],{"className":2312},[762],[574,2314],{"className":2315,"style":758},[746],[574,2317,2319,2323,2326,2332,2335,2366,2369,2372],{"className":2318},[608],[574,2320],{"className":2321,"style":2322},[612],"height:1.2702em;vertical-align:-0.35em;",[574,2324,1983],{"className":2325,"style":2077},[617,618],[574,2327,2329],{"className":2328},[617],[574,2330,2239],{"className":2331},[1563,1564],[574,2333,692],{"className":2334},[735],[574,2336,2338],{"className":2337},[617,2006],[574,2339,2341],{"className":2340},[1297],[574,2342,2344],{"className":2343},[1301],[574,2345,2347,2355],{"className":2346,"style":2002},[1305],[574,2348,2349,2352],{"style":2018},[574,2350],{"className":2351,"style":2022},[1313],[574,2353,595],{"className":2354,"style":619},[617,618],[574,2356,2357,2360],{"style":2028},[574,2358],{"className":2359,"style":2022},[1313],[574,2361,2363],{"className":2362,"style":2036},[2035],[574,2364,1974],{"className":2365},[617],[574,2367],{"className":2368,"style":650},[746],[574,2370,798],{"className":2371},[850],[574,2373],{"className":2374,"style":650},[746],[574,2376,2378,2381,2412,2441],{"className":2377},[608],[574,2379],{"className":2380,"style":2322},[612],[574,2382,2384],{"className":2383},[617,2006],[574,2385,2387],{"className":2386},[1297],[574,2388,2390],{"className":2389},[1301],[574,2391,2393,2401],{"className":2392,"style":2002},[1305],[574,2394,2395,2398],{"style":2018},[574,2396],{"className":2397,"style":2022},[1313],[574,2399,635],{"className":2400,"style":650},[617,618],[574,2402,2403,2406],{"style":2028},[574,2404],{"className":2405,"style":2022},[1313],[574,2407,2409],{"className":2408,"style":2159},[2035],[574,2410,1974],{"className":2411},[617],[574,2413,2415,2418],{"className":2414},[754],[574,2416,702],{"className":2417},[754],[574,2419,2421],{"className":2420},[1293],[574,2422,2424],{"className":2423},[1297],[574,2425,2427],{"className":2426},[1301],[574,2428,2430],{"className":2429,"style":1306},[1305],[574,2431,2432,2435],{"style":1309},[574,2433],{"className":2434,"style":1314},[1313],[574,2436,2438],{"className":2437},[1318,1319,1320,1321],[574,2439,975],{"className":2440},[617,1321],[574,2442,2444],{"className":2443},[617],[574,2445,2264],{"className":2446},[1563,1564],". Ausmultiplizieren nach der binomischen Formel liefert die drei Terme.",[560,2449,2451],{"id":2450},"beispiele","Beispiele",[565,2453,2454,2455,2565],{},"Zwei faire Würfel werden unabhängig geworfen. Jeder hat die Varianz ",[574,2456,2458,2479],{"className":2457},[577],[574,2459,2461],{"className":2460},[581],[583,2462,2463],{"xmlns":585},[587,2464,2465,2476],{},[590,2466,2467],{},[2468,2469,2470,2473],"mfrac",{},[707,2471,2472],{},"35",[707,2474,2475],{},"12",[597,2477,2478],{"encoding":599},"\\frac{35}{12}",[574,2480,2482],{"className":2481,"ariaHidden":604},[603],[574,2483,2485,2489],{"className":2484},[608],[574,2486],{"className":2487,"style":2488},[612],"height:1.1901em;vertical-align:-0.345em;",[574,2490,2492,2496,2562],{"className":2491},[617],[574,2493],{"className":2494},[735,2495],"nulldelimiter",[574,2497,2499],{"className":2498},[2468],[574,2500,2502,2553],{"className":2501},[1297,1583],[574,2503,2505,2550],{"className":2504},[1301],[574,2506,2509,2524,2535],{"className":2507,"style":2508},[1305],"height:0.8451em;",[574,2510,2512,2515],{"style":2511},"top:-2.655em;",[574,2513],{"className":2514,"style":2022},[1313],[574,2516,2518],{"className":2517},[1318,1319,1320,1321],[574,2519,2521],{"className":2520},[617,1321],[574,2522,2475],{"className":2523},[617,1321],[574,2525,2527,2530],{"style":2526},"top:-3.23em;",[574,2528],{"className":2529,"style":2022},[1313],[574,2531],{"className":2532,"style":2534},[2533],"frac-line","border-bottom-width:0.04em;",[574,2536,2538,2541],{"style":2537},"top:-3.394em;",[574,2539],{"className":2540,"style":2022},[1313],[574,2542,2544],{"className":2543},[1318,1319,1320,1321],[574,2545,2547],{"className":2546},[617,1321],[574,2548,2472],{"className":2549},[617,1321],[574,2551,1607],{"className":2552},[1606],[574,2554,2556],{"className":2555},[1301],[574,2557,2560],{"className":2558,"style":2559},[1305],"height:0.345em;",[574,2561],{},[574,2563],{"className":2564},[754,2495],", die Augensumme also",[574,2567,2570],{"className":2568},[2569],"katex-display",[574,2571,2573,2629],{"className":2572},[577],[574,2574,2576],{"className":2575},[581],[583,2577,2579],{"xmlns":585,"display":2578},"block",[587,2580,2581,2626],{},[590,2582,2583,2585,2587,2589,2591,2593,2595,2597,2603,2605,2611,2613,2620,2623],{},[593,2584,791],{},[686,2586,692],{"stretchy":691},[593,2588,595],{},[686,2590,798],{},[593,2592,635],{},[686,2594,702],{"stretchy":691},[686,2596,705],{},[2468,2598,2599,2601],{},[707,2600,2472],{},[707,2602,2475],{},[686,2604,798],{},[2468,2606,2607,2609],{},[707,2608,2472],{},[707,2610,2475],{},[686,2612,705],{},[2468,2614,2615,2617],{},[707,2616,2472],{},[707,2618,2619],{},"6",[686,2621,2622],{},"≈",[707,2624,2625],{},"5,83",[597,2627,2628],{"encoding":599},"V(X + Y) = \\frac{35}{12} + \\frac{35}{12} = \\frac{35}{6} \\approx 5{,}83",[574,2630,2632,2656,2677,2759,2836,2913],{"className":2631,"ariaHidden":604},[603],[574,2633,2635,2638,2641,2644,2647,2650,2653],{"className":2634},[608],[574,2636],{"className":2637,"style":722},[612],[574,2639,791],{"className":2640,"style":650},[617,618],[574,2642,692],{"className":2643},[735],[574,2645,595],{"className":2646,"style":619},[617,618],[574,2648],{"className":2649,"style":650},[746],[574,2651,798],{"className":2652},[850],[574,2654],{"className":2655,"style":650},[746],[574,2657,2659,2662,2665,2668,2671,2674],{"className":2658},[608],[574,2660],{"className":2661,"style":722},[612],[574,2663,635],{"className":2664,"style":650},[617,618],[574,2666,702],{"className":2667},[754],[574,2669],{"className":2670,"style":758},[746],[574,2672,705],{"className":2673},[762],[574,2675],{"className":2676,"style":758},[746],[574,2678,2680,2684,2750,2753,2756],{"className":2679},[608],[574,2681],{"className":2682,"style":2683},[612],"height:2.0074em;vertical-align:-0.686em;",[574,2685,2687,2690,2747],{"className":2686},[617],[574,2688],{"className":2689},[735,2495],[574,2691,2693],{"className":2692},[2468],[574,2694,2696,2738],{"className":2695},[1297,1583],[574,2697,2699,2735],{"className":2698},[1301],[574,2700,2703,2715,2723],{"className":2701,"style":2702},[1305],"height:1.3214em;",[574,2704,2706,2709],{"style":2705},"top:-2.314em;",[574,2707],{"className":2708,"style":2022},[1313],[574,2710,2712],{"className":2711},[617],[574,2713,2475],{"className":2714},[617],[574,2716,2717,2720],{"style":2526},[574,2718],{"className":2719,"style":2022},[1313],[574,2721],{"className":2722,"style":2534},[2533],[574,2724,2726,2729],{"style":2725},"top:-3.677em;",[574,2727],{"className":2728,"style":2022},[1313],[574,2730,2732],{"className":2731},[617],[574,2733,2472],{"className":2734},[617],[574,2736,1607],{"className":2737},[1606],[574,2739,2741],{"className":2740},[1301],[574,2742,2745],{"className":2743,"style":2744},[1305],"height:0.686em;",[574,2746],{},[574,2748],{"className":2749},[754,2495],[574,2751],{"className":2752,"style":650},[746],[574,2754,798],{"className":2755},[850],[574,2757],{"className":2758,"style":650},[746],[574,2760,2762,2765,2827,2830,2833],{"className":2761},[608],[574,2763],{"className":2764,"style":2683},[612],[574,2766,2768,2771,2824],{"className":2767},[617],[574,2769],{"className":2770},[735,2495],[574,2772,2774],{"className":2773},[2468],[574,2775,2777,2816],{"className":2776},[1297,1583],[574,2778,2780,2813],{"className":2779},[1301],[574,2781,2783,2794,2802],{"className":2782,"style":2702},[1305],[574,2784,2785,2788],{"style":2705},[574,2786],{"className":2787,"style":2022},[1313],[574,2789,2791],{"className":2790},[617],[574,2792,2475],{"className":2793},[617],[574,2795,2796,2799],{"style":2526},[574,2797],{"className":2798,"style":2022},[1313],[574,2800],{"className":2801,"style":2534},[2533],[574,2803,2804,2807],{"style":2725},[574,2805],{"className":2806,"style":2022},[1313],[574,2808,2810],{"className":2809},[617],[574,2811,2472],{"className":2812},[617],[574,2814,1607],{"className":2815},[1606],[574,2817,2819],{"className":2818},[1301],[574,2820,2822],{"className":2821,"style":2744},[1305],[574,2823],{},[574,2825],{"className":2826},[754,2495],[574,2828],{"className":2829,"style":758},[746],[574,2831,705],{"className":2832},[762],[574,2834],{"className":2835,"style":758},[746],[574,2837,2839,2842,2904,2907,2910],{"className":2838},[608],[574,2840],{"className":2841,"style":2683},[612],[574,2843,2845,2848,2901],{"className":2844},[617],[574,2846],{"className":2847},[735,2495],[574,2849,2851],{"className":2850},[2468],[574,2852,2854,2893],{"className":2853},[1297,1583],[574,2855,2857,2890],{"className":2856},[1301],[574,2858,2860,2871,2879],{"className":2859,"style":2702},[1305],[574,2861,2862,2865],{"style":2705},[574,2863],{"className":2864,"style":2022},[1313],[574,2866,2868],{"className":2867},[617],[574,2869,2619],{"className":2870},[617],[574,2872,2873,2876],{"style":2526},[574,2874],{"className":2875,"style":2022},[1313],[574,2877],{"className":2878,"style":2534},[2533],[574,2880,2881,2884],{"style":2725},[574,2882],{"className":2883,"style":2022},[1313],[574,2885,2887],{"className":2886},[617],[574,2888,2472],{"className":2889},[617],[574,2891,1607],{"className":2892},[1606],[574,2894,2896],{"className":2895},[1301],[574,2897,2899],{"className":2898,"style":2744},[1305],[574,2900],{},[574,2902],{"className":2903},[754,2495],[574,2905],{"className":2906,"style":758},[746],[574,2908,2622],{"className":2909},[762],[574,2911],{"className":2912,"style":758},[746],[574,2914,2916,2920,2924,2930],{"className":2915},[608],[574,2917],{"className":2918,"style":2919},[612],"height:0.8389em;vertical-align:-0.1944em;",[574,2921,2923],{"className":2922},[617],"5",[574,2925,2927],{"className":2926},[617],[574,2928,697],{"className":2929},[742],[574,2931,2933],{"className":2932},[617],"83",[565,2935,2936,2937,620,3004,3071,3072,3108],{},"Zwei Aktienrenditen haben die Varianzen ",[574,2938,2940,2965],{"className":2939},[577],[574,2941,2943],{"className":2942},[581],[583,2944,2945],{"xmlns":585},[587,2946,2947,2962],{},[590,2948,2949,2951,2953,2955,2957,2959],{},[593,2950,791],{},[686,2952,692],{"stretchy":691},[593,2954,595],{},[686,2956,702],{"stretchy":691},[686,2958,705],{},[707,2960,2961],{},"4",[597,2963,2964],{"encoding":599},"V(X) = 4",[574,2966,2968,2995],{"className":2967,"ariaHidden":604},[603],[574,2969,2971,2974,2977,2980,2983,2986,2989,2992],{"className":2970},[608],[574,2972],{"className":2973,"style":722},[612],[574,2975,791],{"className":2976,"style":650},[617,618],[574,2978,692],{"className":2979},[735],[574,2981,595],{"className":2982,"style":619},[617,618],[574,2984,702],{"className":2985},[754],[574,2987],{"className":2988,"style":758},[746],[574,2990,705],{"className":2991},[762],[574,2993],{"className":2994,"style":758},[746],[574,2996,2998,3001],{"className":2997},[608],[574,2999],{"className":3000,"style":772},[612],[574,3002,2961],{"className":3003},[617],[574,3005,3007,3032],{"className":3006},[577],[574,3008,3010],{"className":3009},[581],[583,3011,3012],{"xmlns":585},[587,3013,3014,3029],{},[590,3015,3016,3018,3020,3022,3024,3026],{},[593,3017,791],{},[686,3019,692],{"stretchy":691},[593,3021,635],{},[686,3023,702],{"stretchy":691},[686,3025,705],{},[707,3027,3028],{},"9",[597,3030,3031],{"encoding":599},"V(Y) = 9",[574,3033,3035,3062],{"className":3034,"ariaHidden":604},[603],[574,3036,3038,3041,3044,3047,3050,3053,3056,3059],{"className":3037},[608],[574,3039],{"className":3040,"style":722},[612],[574,3042,791],{"className":3043,"style":650},[617,618],[574,3045,692],{"className":3046},[735],[574,3048,635],{"className":3049,"style":650},[617,618],[574,3051,702],{"className":3052},[754],[574,3054],{"className":3055,"style":758},[746],[574,3057,705],{"className":3058},[762],[574,3060],{"className":3061,"style":758},[746],[574,3063,3065,3068],{"className":3064},[608],[574,3066],{"className":3067,"style":772},[612],[574,3069,3028],{"className":3070},[617]," und die Kovarianz ",[574,3073,3075,3092],{"className":3074},[577],[574,3076,3078],{"className":3077},[581],[583,3079,3080],{"xmlns":585},[587,3081,3082,3089],{},[590,3083,3084,3086],{},[686,3085,946],{},[707,3087,3088],{},"3",[597,3090,3091],{"encoding":599},"-3",[574,3093,3095],{"className":3094,"ariaHidden":604},[603],[574,3096,3098,3102,3105],{"className":3097},[608],[574,3099],{"className":3100,"style":3101},[612],"height:0.7278em;vertical-align:-0.0833em;",[574,3103,946],{"className":3104},[617],[574,3106,3088],{"className":3107},[617]," (sie bewegen sich eher gegenläufig):",[574,3110,3112],{"className":3111},[2569],[574,3113,3115,3211],{"className":3114},[577],[574,3116,3118],{"className":3117},[581],[583,3119,3120],{"xmlns":585,"display":2578},[587,3121,3122,3208],{},[590,3123,3124,3126,3128,3130,3132,3134,3136,3138,3140,3142,3144,3146,3148,3151,3153,3155,3157,3159,3161,3164,3166,3169,3171,3173,3175,3177,3179,3181,3183,3185,3187,3189,3191,3193,3195,3197,3199,3201,3203,3205],{},[593,3125,791],{},[686,3127,692],{"stretchy":691},[593,3129,595],{},[686,3131,798],{},[593,3133,635],{},[686,3135,702],{"stretchy":691},[686,3137,705],{},[707,3139,2961],{},[686,3141,798],{},[707,3143,3028],{},[686,3145,798],{},[707,3147,975],{},[686,3149,3150],{},"⋅",[686,3152,692],{"stretchy":691},[686,3154,946],{},[707,3156,3088],{},[686,3158,702],{"stretchy":691},[686,3160,705],{},[707,3162,3163],{},"7",[686,3165,697],{"separator":604},[746,3167],{"width":3168},"2em",[593,3170,791],{},[686,3172,692],{"stretchy":691},[593,3174,595],{},[686,3176,946],{},[593,3178,635],{},[686,3180,702],{"stretchy":691},[686,3182,705],{},[707,3184,2961],{},[686,3186,798],{},[707,3188,3028],{},[686,3190,946],{},[707,3192,975],{},[686,3194,3150],{},[686,3196,692],{"stretchy":691},[686,3198,946],{},[707,3200,3088],{},[686,3202,702],{"stretchy":691},[686,3204,705],{},[707,3206,3207],{},"19",[597,3209,3210],{"encoding":599},"V(X + Y) = 4 + 9 + 2 \\cdot (-3) = 7, \\qquad V(X - Y) = 4 + 9 - 2 \\cdot (-3) = 19",[574,3212,3214,3238,3259,3277,3295,3313,3340,3377,3398,3416,3434,3452,3479],{"className":3213,"ariaHidden":604},[603],[574,3215,3217,3220,3223,3226,3229,3232,3235],{"className":3216},[608],[574,3218],{"className":3219,"style":722},[612],[574,3221,791],{"className":3222,"style":650},[617,618],[574,3224,692],{"className":3225},[735],[574,3227,595],{"className":3228,"style":619},[617,618],[574,3230],{"className":3231,"style":650},[746],[574,3233,798],{"className":3234},[850],[574,3236],{"className":3237,"style":650},[746],[574,3239,3241,3244,3247,3250,3253,3256],{"className":3240},[608],[574,3242],{"className":3243,"style":722},[612],[574,3245,635],{"className":3246,"style":650},[617,618],[574,3248,702],{"className":3249},[754],[574,3251],{"className":3252,"style":758},[746],[574,3254,705],{"className":3255},[762],[574,3257],{"className":3258,"style":758},[746],[574,3260,3262,3265,3268,3271,3274],{"className":3261},[608],[574,3263],{"className":3264,"style":3101},[612],[574,3266,2961],{"className":3267},[617],[574,3269],{"className":3270,"style":650},[746],[574,3272,798],{"className":3273},[850],[574,3275],{"className":3276,"style":650},[746],[574,3278,3280,3283,3286,3289,3292],{"className":3279},[608],[574,3281],{"className":3282,"style":3101},[612],[574,3284,3028],{"className":3285},[617],[574,3287],{"className":3288,"style":650},[746],[574,3290,798],{"className":3291},[850],[574,3293],{"className":3294,"style":650},[746],[574,3296,3298,3301,3304,3307,3310],{"className":3297},[608],[574,3299],{"className":3300,"style":772},[612],[574,3302,975],{"className":3303},[617],[574,3305],{"className":3306,"style":650},[746],[574,3308,3150],{"className":3309},[850],[574,3311],{"className":3312,"style":650},[746],[574,3314,3316,3319,3322,3325,3328,3331,3334,3337],{"className":3315},[608],[574,3317],{"className":3318,"style":722},[612],[574,3320,692],{"className":3321},[735],[574,3323,946],{"className":3324},[617],[574,3326,3088],{"className":3327},[617],[574,3329,702],{"className":3330},[754],[574,3332],{"className":3333,"style":758},[746],[574,3335,705],{"className":3336},[762],[574,3338],{"className":3339,"style":758},[746],[574,3341,3343,3346,3349,3352,3356,3359,3362,3365,3368,3371,3374],{"className":3342},[608],[574,3344],{"className":3345,"style":722},[612],[574,3347,3163],{"className":3348},[617],[574,3350,697],{"className":3351},[742],[574,3353],{"className":3354,"style":3355},[746],"margin-right:2em;",[574,3357],{"className":3358,"style":747},[746],[574,3360,791],{"className":3361,"style":650},[617,618],[574,3363,692],{"className":3364},[735],[574,3366,595],{"className":3367,"style":619},[617,618],[574,3369],{"className":3370,"style":650},[746],[574,3372,946],{"className":3373},[850],[574,3375],{"className":3376,"style":650},[746],[574,3378,3380,3383,3386,3389,3392,3395],{"className":3379},[608],[574,3381],{"className":3382,"style":722},[612],[574,3384,635],{"className":3385,"style":650},[617,618],[574,3387,702],{"className":3388},[754],[574,3390],{"className":3391,"style":758},[746],[574,3393,705],{"className":3394},[762],[574,3396],{"className":3397,"style":758},[746],[574,3399,3401,3404,3407,3410,3413],{"className":3400},[608],[574,3402],{"className":3403,"style":3101},[612],[574,3405,2961],{"className":3406},[617],[574,3408],{"className":3409,"style":650},[746],[574,3411,798],{"className":3412},[850],[574,3414],{"className":3415,"style":650},[746],[574,3417,3419,3422,3425,3428,3431],{"className":3418},[608],[574,3420],{"className":3421,"style":3101},[612],[574,3423,3028],{"className":3424},[617],[574,3426],{"className":3427,"style":650},[746],[574,3429,946],{"className":3430},[850],[574,3432],{"className":3433,"style":650},[746],[574,3435,3437,3440,3443,3446,3449],{"className":3436},[608],[574,3438],{"className":3439,"style":772},[612],[574,3441,975],{"className":3442},[617],[574,3444],{"className":3445,"style":650},[746],[574,3447,3150],{"className":3448},[850],[574,3450],{"className":3451,"style":650},[746],[574,3453,3455,3458,3461,3464,3467,3470,3473,3476],{"className":3454},[608],[574,3456],{"className":3457,"style":722},[612],[574,3459,692],{"className":3460},[735],[574,3462,946],{"className":3463},[617],[574,3465,3088],{"className":3466},[617],[574,3468,702],{"className":3469},[754],[574,3471],{"className":3472,"style":758},[746],[574,3474,705],{"className":3475},[762],[574,3477],{"className":3478,"style":758},[746],[574,3480,3482,3485],{"className":3481},[608],[574,3483],{"className":3484,"style":772},[612],[574,3486,3207],{"className":3487},[617],[565,3489,3490],{},"Ein Portfolio aus je einer Hälfte hat die Varianz",[574,3492,3494],{"className":3493},[2569],[574,3495,3497,3570],{"className":3496},[577],[574,3498,3500],{"className":3499},[581],[583,3501,3502],{"xmlns":585,"display":2578},[587,3503,3504,3567],{},[590,3505,3506,3508,3510,3513,3515,3517,3519,3521,3523,3525,3528,3530,3532,3534,3536,3538,3540,3542,3544,3546,3548,3550,3552,3554,3556,3558,3560,3562,3564],{},[593,3507,791],{},[686,3509,692],{"stretchy":691},[707,3511,3512],{},"0,5",[593,3514,595],{},[686,3516,798],{},[707,3518,3512],{},[593,3520,635],{},[686,3522,702],{"stretchy":691},[686,3524,705],{},[707,3526,3527],{},"0,25",[686,3529,3150],{},[707,3531,2961],{},[686,3533,798],{},[707,3535,3527],{},[686,3537,3150],{},[707,3539,3028],{},[686,3541,798],{},[707,3543,975],{},[686,3545,3150],{},[707,3547,3512],{},[686,3549,3150],{},[707,3551,3512],{},[686,3553,3150],{},[686,3555,692],{"stretchy":691},[686,3557,946],{},[707,3559,3088],{},[686,3561,702],{"stretchy":691},[686,3563,705],{},[707,3565,3566],{},"1,75",[597,3568,3569],{"encoding":599},"V(0{,}5X + 0{,}5Y) = 0{,}25 \\cdot 4 + 0{,}25 \\cdot 9 + 2 \\cdot 0{,}5 \\cdot 0{,}5 \\cdot (-3) = 1{,}75",[574,3571,3573,3609,3642,3670,3688,3715,3733,3751,3778,3805,3832],{"className":3572,"ariaHidden":604},[603],[574,3574,3576,3579,3582,3585,3588,3594,3597,3600,3603,3606],{"className":3575},[608],[574,3577],{"className":3578,"style":722},[612],[574,3580,791],{"className":3581,"style":650},[617,618],[574,3583,692],{"className":3584},[735],[574,3586,709],{"className":3587},[617],[574,3589,3591],{"className":3590},[617],[574,3592,697],{"className":3593},[742],[574,3595,2923],{"className":3596},[617],[574,3598,595],{"className":3599,"style":619},[617,618],[574,3601],{"className":3602,"style":650},[746],[574,3604,798],{"className":3605},[850],[574,3607],{"className":3608,"style":650},[746],[574,3610,3612,3615,3618,3624,3627,3630,3633,3636,3639],{"className":3611},[608],[574,3613],{"className":3614,"style":722},[612],[574,3616,709],{"className":3617},[617],[574,3619,3621],{"className":3620},[617],[574,3622,697],{"className":3623},[742],[574,3625,2923],{"className":3626},[617],[574,3628,635],{"className":3629,"style":650},[617,618],[574,3631,702],{"className":3632},[754],[574,3634],{"className":3635,"style":758},[746],[574,3637,705],{"className":3638},[762],[574,3640],{"className":3641,"style":758},[746],[574,3643,3645,3648,3651,3657,3661,3664,3667],{"className":3644},[608],[574,3646],{"className":3647,"style":2919},[612],[574,3649,709],{"className":3650},[617],[574,3652,3654],{"className":3653},[617],[574,3655,697],{"className":3656},[742],[574,3658,3660],{"className":3659},[617],"25",[574,3662],{"className":3663,"style":650},[746],[574,3665,3150],{"className":3666},[850],[574,3668],{"className":3669,"style":650},[746],[574,3671,3673,3676,3679,3682,3685],{"className":3672},[608],[574,3674],{"className":3675,"style":3101},[612],[574,3677,2961],{"className":3678},[617],[574,3680],{"className":3681,"style":650},[746],[574,3683,798],{"className":3684},[850],[574,3686],{"className":3687,"style":650},[746],[574,3689,3691,3694,3697,3703,3706,3709,3712],{"className":3690},[608],[574,3692],{"className":3693,"style":2919},[612],[574,3695,709],{"className":3696},[617],[574,3698,3700],{"className":3699},[617],[574,3701,697],{"className":3702},[742],[574,3704,3660],{"className":3705},[617],[574,3707],{"className":3708,"style":650},[746],[574,3710,3150],{"className":3711},[850],[574,3713],{"className":3714,"style":650},[746],[574,3716,3718,3721,3724,3727,3730],{"className":3717},[608],[574,3719],{"className":3720,"style":3101},[612],[574,3722,3028],{"className":3723},[617],[574,3725],{"className":3726,"style":650},[746],[574,3728,798],{"className":3729},[850],[574,3731],{"className":3732,"style":650},[746],[574,3734,3736,3739,3742,3745,3748],{"className":3735},[608],[574,3737],{"className":3738,"style":772},[612],[574,3740,975],{"className":3741},[617],[574,3743],{"className":3744,"style":650},[746],[574,3746,3150],{"className":3747},[850],[574,3749],{"className":3750,"style":650},[746],[574,3752,3754,3757,3760,3766,3769,3772,3775],{"className":3753},[608],[574,3755],{"className":3756,"style":2919},[612],[574,3758,709],{"className":3759},[617],[574,3761,3763],{"className":3762},[617],[574,3764,697],{"className":3765},[742],[574,3767,2923],{"className":3768},[617],[574,3770],{"className":3771,"style":650},[746],[574,3773,3150],{"className":3774},[850],[574,3776],{"className":3777,"style":650},[746],[574,3779,3781,3784,3787,3793,3796,3799,3802],{"className":3780},[608],[574,3782],{"className":3783,"style":2919},[612],[574,3785,709],{"className":3786},[617],[574,3788,3790],{"className":3789},[617],[574,3791,697],{"className":3792},[742],[574,3794,2923],{"className":3795},[617],[574,3797],{"className":3798,"style":650},[746],[574,3800,3150],{"className":3801},[850],[574,3803],{"className":3804,"style":650},[746],[574,3806,3808,3811,3814,3817,3820,3823,3826,3829],{"className":3807},[608],[574,3809],{"className":3810,"style":722},[612],[574,3812,692],{"className":3813},[735],[574,3815,946],{"className":3816},[617],[574,3818,3088],{"className":3819},[617],[574,3821,702],{"className":3822},[754],[574,3824],{"className":3825,"style":758},[746],[574,3827,705],{"className":3828},[762],[574,3830],{"className":3831,"style":758},[746],[574,3833,3835,3838,3842,3848],{"className":3834},[608],[574,3836],{"className":3837,"style":2919},[612],[574,3839,3841],{"className":3840},[617],"1",[574,3843,3845],{"className":3844},[617],[574,3846,697],{"className":3847},[742],[574,3849,3851],{"className":3850},[617],"75",[565,3853,3854],{},"und schwankt damit weniger als jede Aktie allein (Diversifikation).",[560,3856,3858],{"id":3857},"typische-fehler","Typische Fehler",[660,3860,3861,4003,4272,4586],{},[663,3862,3863,4002],{},[574,3864,3866,3909],{"className":3865},[577],[574,3867,3869],{"className":3868},[581],[583,3870,3871],{"xmlns":585},[587,3872,3873,3907],{},[590,3874,3875,3877,3879,3881,3883,3885,3887,3889,3891,3893,3895,3897,3899,3901,3903,3905],{},[593,3876,791],{},[686,3878,692],{"stretchy":691},[593,3880,595],{},[686,3882,798],{},[593,3884,635],{},[686,3886,702],{"stretchy":691},[686,3888,705],{},[593,3890,791],{},[686,3892,692],{"stretchy":691},[593,3894,595],{},[686,3896,702],{"stretchy":691},[686,3898,798],{},[593,3900,791],{},[686,3902,692],{"stretchy":691},[593,3904,635],{},[686,3906,702],{"stretchy":691},[597,3908,825],{"encoding":599},[574,3910,3912,3936,3957,3984],{"className":3911,"ariaHidden":604},[603],[574,3913,3915,3918,3921,3924,3927,3930,3933],{"className":3914},[608],[574,3916],{"className":3917,"style":722},[612],[574,3919,791],{"className":3920,"style":650},[617,618],[574,3922,692],{"className":3923},[735],[574,3925,595],{"className":3926,"style":619},[617,618],[574,3928],{"className":3929,"style":650},[746],[574,3931,798],{"className":3932},[850],[574,3934],{"className":3935,"style":650},[746],[574,3937,3939,3942,3945,3948,3951,3954],{"className":3938},[608],[574,3940],{"className":3941,"style":722},[612],[574,3943,635],{"className":3944,"style":650},[617,618],[574,3946,702],{"className":3947},[754],[574,3949],{"className":3950,"style":758},[746],[574,3952,705],{"className":3953},[762],[574,3955],{"className":3956,"style":758},[746],[574,3958,3960,3963,3966,3969,3972,3975,3978,3981],{"className":3959},[608],[574,3961],{"className":3962,"style":722},[612],[574,3964,791],{"className":3965,"style":650},[617,618],[574,3967,692],{"className":3968},[735],[574,3970,595],{"className":3971,"style":619},[617,618],[574,3973,702],{"className":3974},[754],[574,3976],{"className":3977,"style":650},[746],[574,3979,798],{"className":3980},[850],[574,3982],{"className":3983,"style":650},[746],[574,3985,3987,3990,3993,3996,3999],{"className":3986},[608],[574,3988],{"className":3989,"style":722},[612],[574,3991,791],{"className":3992,"style":650},[617,618],[574,3994,692],{"className":3995},[735],[574,3997,635],{"className":3998,"style":650},[617,618],[574,4000,702],{"className":4001},[754]," ohne Unabhängigkeit verwenden.",[663,4004,4005,4006,4049,4050,4190,4191,655],{},"Bei der Differenz die Varianzen subtrahieren. Für unabhängige ",[574,4007,4009,4027],{"className":4008},[577],[574,4010,4012],{"className":4011},[581],[583,4013,4014],{"xmlns":585},[587,4015,4016,4024],{},[590,4017,4018,4020,4022],{},[593,4019,595],{},[686,4021,697],{"separator":604},[593,4023,635],{},[597,4025,4026],{"encoding":599},"X, Y",[574,4028,4030],{"className":4029,"ariaHidden":604},[603],[574,4031,4033,4037,4040,4043,4046],{"className":4032},[608],[574,4034],{"className":4035,"style":4036},[612],"height:0.8778em;vertical-align:-0.1944em;",[574,4038,595],{"className":4039,"style":619},[617,618],[574,4041,697],{"className":4042},[742],[574,4044],{"className":4045,"style":747},[746],[574,4047,635],{"className":4048,"style":650},[617,618]," gilt ",[574,4051,4053,4097],{"className":4052},[577],[574,4054,4056],{"className":4055},[581],[583,4057,4058],{"xmlns":585},[587,4059,4060,4094],{},[590,4061,4062,4064,4066,4068,4070,4072,4074,4076,4078,4080,4082,4084,4086,4088,4090,4092],{},[593,4063,791],{},[686,4065,692],{"stretchy":691},[593,4067,595],{},[686,4069,946],{},[593,4071,635],{},[686,4073,702],{"stretchy":691},[686,4075,705],{},[593,4077,791],{},[686,4079,692],{"stretchy":691},[593,4081,595],{},[686,4083,702],{"stretchy":691},[686,4085,798],{},[593,4087,791],{},[686,4089,692],{"stretchy":691},[593,4091,635],{},[686,4093,702],{"stretchy":691},[597,4095,4096],{"encoding":599},"V(X - Y) = V(X) + V(Y)",[574,4098,4100,4124,4145,4172],{"className":4099,"ariaHidden":604},[603],[574,4101,4103,4106,4109,4112,4115,4118,4121],{"className":4102},[608],[574,4104],{"className":4105,"style":722},[612],[574,4107,791],{"className":4108,"style":650},[617,618],[574,4110,692],{"className":4111},[735],[574,4113,595],{"className":4114,"style":619},[617,618],[574,4116],{"className":4117,"style":650},[746],[574,4119,946],{"className":4120},[850],[574,4122],{"className":4123,"style":650},[746],[574,4125,4127,4130,4133,4136,4139,4142],{"className":4126},[608],[574,4128],{"className":4129,"style":722},[612],[574,4131,635],{"className":4132,"style":650},[617,618],[574,4134,702],{"className":4135},[754],[574,4137],{"className":4138,"style":758},[746],[574,4140,705],{"className":4141},[762],[574,4143],{"className":4144,"style":758},[746],[574,4146,4148,4151,4154,4157,4160,4163,4166,4169],{"className":4147},[608],[574,4149],{"className":4150,"style":722},[612],[574,4152,791],{"className":4153,"style":650},[617,618],[574,4155,692],{"className":4156},[735],[574,4158,595],{"className":4159,"style":619},[617,618],[574,4161,702],{"className":4162},[754],[574,4164],{"className":4165,"style":650},[746],[574,4167,798],{"className":4168},[850],[574,4170],{"className":4171,"style":650},[746],[574,4173,4175,4178,4181,4184,4187],{"className":4174},[608],[574,4176],{"className":4177,"style":722},[612],[574,4179,791],{"className":4180,"style":650},[617,618],[574,4182,692],{"className":4183},[735],[574,4185,635],{"className":4186,"style":650},[617,618],[574,4188,702],{"className":4189},[754],", nicht ",[574,4192,4194,4224],{"className":4193},[577],[574,4195,4197],{"className":4196},[581],[583,4198,4199],{"xmlns":585},[587,4200,4201,4221],{},[590,4202,4203,4205,4207,4209,4211,4213,4215,4217,4219],{},[593,4204,791],{},[686,4206,692],{"stretchy":691},[593,4208,595],{},[686,4210,702],{"stretchy":691},[686,4212,946],{},[593,4214,791],{},[686,4216,692],{"stretchy":691},[593,4218,635],{},[686,4220,702],{"stretchy":691},[597,4222,4223],{"encoding":599},"V(X) - V(Y)",[574,4225,4227,4254],{"className":4226,"ariaHidden":604},[603],[574,4228,4230,4233,4236,4239,4242,4245,4248,4251],{"className":4229},[608],[574,4231],{"className":4232,"style":722},[612],[574,4234,791],{"className":4235,"style":650},[617,618],[574,4237,692],{"className":4238},[735],[574,4240,595],{"className":4241,"style":619},[617,618],[574,4243,702],{"className":4244},[754],[574,4246],{"className":4247,"style":650},[746],[574,4249,946],{"className":4250},[850],[574,4252],{"className":4253,"style":650},[746],[574,4255,4257,4260,4263,4266,4269],{"className":4256},[608],[574,4258],{"className":4259,"style":722},[612],[574,4261,791],{"className":4262,"style":650},[617,618],[574,4264,692],{"className":4265},[735],[574,4267,635],{"className":4268,"style":650},[617,618],[574,4270,702],{"className":4271},[754],[663,4273,4274,4275,4585],{},"Standardabweichungen addieren. Addiert werden die Varianzen; ",[574,4276,4278,4329],{"className":4277},[577],[574,4279,4281],{"className":4280},[581],[583,4282,4283],{"xmlns":585},[587,4284,4285,4326],{},[590,4286,4287,4300,4302],{},[1465,4288,4289,4292],{},[593,4290,4291],{},"σ",[590,4293,4294,4296,4298],{},[593,4295,595],{},[686,4297,798],{},[593,4299,635],{},[686,4301,705],{},[4303,4304,4305],"msqrt",{},[590,4306,4307,4316,4318],{},[4308,4309,4310,4312,4314],"msubsup",{},[593,4311,4291],{},[593,4313,595],{},[707,4315,975],{},[686,4317,798],{},[4308,4319,4320,4322,4324],{},[593,4321,4291],{},[593,4323,635],{},[707,4325,975],{},[597,4327,4328],{"encoding":599},"\\sigma_{X+Y} = \\sqrt{\\sigma_X^2 + \\sigma_Y^2}",[574,4330,4332,4401],{"className":4331,"ariaHidden":604},[603],[574,4333,4335,4339,4392,4395,4398],{"className":4334},[608],[574,4336],{"className":4337,"style":4338},[612],"height:0.6389em;vertical-align:-0.2083em;",[574,4340,4342,4346],{"className":4341},[617],[574,4343,4291],{"className":4344,"style":4345},[617,618],"margin-right:0.0359em;",[574,4347,4349],{"className":4348},[1293],[574,4350,4352,4383],{"className":4351},[1297,1583],[574,4353,4355,4380],{"className":4354},[1301],[574,4356,4359],{"className":4357,"style":4358},[1305],"height:0.3283em;",[574,4360,4362,4365],{"style":4361},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[574,4363],{"className":4364,"style":1314},[1313],[574,4366,4368],{"className":4367},[1318,1319,1320,1321],[574,4369,4371,4374,4377],{"className":4370},[617,1321],[574,4372,595],{"className":4373,"style":619},[617,618,1321],[574,4375,798],{"className":4376},[850,1321],[574,4378,635],{"className":4379,"style":650},[617,618,1321],[574,4381,1607],{"className":4382},[1606],[574,4384,4386],{"className":4385},[1301],[574,4387,4390],{"className":4388,"style":4389},[1305],"height:0.2083em;",[574,4391],{},[574,4393],{"className":4394,"style":758},[746],[574,4396,705],{"className":4397},[762],[574,4399],{"className":4400,"style":758},[746],[574,4402,4404,4408],{"className":4403},[608],[574,4405],{"className":4406,"style":4407},[612],"height:1.24em;vertical-align:-0.3038em;",[574,4409,4412],{"className":4410},[617,4411],"sqrt",[574,4413,4415,4576],{"className":4414},[1297,1583],[574,4416,4418,4573],{"className":4417},[1301],[574,4419,4422,4550],{"className":4420,"style":4421},[1305],"height:0.9362em;",[574,4423,4427,4431],{"className":4424,"style":4426},[4425],"svg-align","top:-3.2em;",[574,4428],{"className":4429,"style":4430},[1313],"height:3.2em;",[574,4432,4435,4490,4493,4496,4499],{"className":4433,"style":4434},[617],"padding-left:1em;",[574,4436,4438,4441],{"className":4437},[617],[574,4439,4291],{"className":4440,"style":4345},[617,618],[574,4442,4444],{"className":4443},[1293],[574,4445,4447,4481],{"className":4446},[1297,1583],[574,4448,4450,4478],{"className":4449},[1301],[574,4451,4454,4466],{"className":4452,"style":4453},[1305],"height:0.7959em;",[574,4455,4457,4460],{"style":4456},"top:-2.4065em;margin-left:-0.0359em;margin-right:0.05em;",[574,4458],{"className":4459,"style":1314},[1313],[574,4461,4463],{"className":4462},[1318,1319,1320,1321],[574,4464,595],{"className":4465,"style":619},[617,618,1321],[574,4467,4469,4472],{"style":4468},"top:-3.0448em;margin-right:0.05em;",[574,4470],{"className":4471,"style":1314},[1313],[574,4473,4475],{"className":4474},[1318,1319,1320,1321],[574,4476,975],{"className":4477},[617,1321],[574,4479,1607],{"className":4480},[1606],[574,4482,4484],{"className":4483},[1301],[574,4485,4488],{"className":4486,"style":4487},[1305],"height:0.2935em;",[574,4489],{},[574,4491],{"className":4492,"style":650},[746],[574,4494,798],{"className":4495},[850],[574,4497],{"className":4498,"style":650},[746],[574,4500,4502,4505],{"className":4501},[617],[574,4503,4291],{"className":4504,"style":4345},[617,618],[574,4506,4508],{"className":4507},[1293],[574,4509,4511,4542],{"className":4510},[1297,1583],[574,4512,4514,4539],{"className":4513},[1301],[574,4515,4517,4528],{"className":4516,"style":4453},[1305],[574,4518,4519,4522],{"style":4456},[574,4520],{"className":4521,"style":1314},[1313],[574,4523,4525],{"className":4524},[1318,1319,1320,1321],[574,4526,635],{"className":4527,"style":650},[617,618,1321],[574,4529,4530,4533],{"style":4468},[574,4531],{"className":4532,"style":1314},[1313],[574,4534,4536],{"className":4535},[1318,1319,1320,1321],[574,4537,975],{"className":4538},[617,1321],[574,4540,1607],{"className":4541},[1606],[574,4543,4545],{"className":4544},[1301],[574,4546,4548],{"className":4547,"style":4487},[1305],[574,4549],{},[574,4551,4553,4556],{"style":4552},"top:-2.8962em;",[574,4554],{"className":4555,"style":4430},[1313],[574,4557,4561],{"className":4558,"style":4560},[4559],"hide-tail","min-width:1.02em;height:1.28em;",[4562,4563,4569],"svg",{"xmlns":4564,"width":4565,"height":4566,"viewBox":4567,"preserveAspectRatio":4568},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[4570,4571],"path",{"d":4572},"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",[574,4574,1607],{"className":4575},[1606],[574,4577,4579],{"className":4578},[1301],[574,4580,4583],{"className":4581,"style":4582},[1305],"height:0.3038em;",[574,4584],{}," bei Unabhängigkeit.",[663,4587,4588,4589,4638,4639,4705,4706,620,4734,4762,4763,4190,4854,655],{},"Bei ",[574,4590,4592,4614],{"className":4591},[577],[574,4593,4595],{"className":4594},[581],[583,4596,4597],{"xmlns":585},[587,4598,4599,4611],{},[590,4600,4601,4603,4605,4607,4609],{},[593,4602,791],{},[686,4604,692],{"stretchy":691},[707,4606,975],{},[593,4608,595],{},[686,4610,702],{"stretchy":691},[597,4612,4613],{"encoding":599},"V(2X)",[574,4615,4617],{"className":4616,"ariaHidden":604},[603],[574,4618,4620,4623,4626,4629,4632,4635],{"className":4619},[608],[574,4621],{"className":4622,"style":722},[612],[574,4624,791],{"className":4625,"style":650},[617,618],[574,4627,692],{"className":4628},[735],[574,4630,975],{"className":4631},[617],[574,4633,595],{"className":4634,"style":619},[617,618],[574,4636,702],{"className":4637},[754]," wie bei ",[574,4640,4642,4666],{"className":4641},[577],[574,4643,4645],{"className":4644},[581],[583,4646,4647],{"xmlns":585},[587,4648,4649,4663],{},[590,4650,4651,4653,4655,4657,4659,4661],{},[593,4652,791],{},[686,4654,692],{"stretchy":691},[593,4656,595],{},[686,4658,798],{},[593,4660,635],{},[686,4662,702],{"stretchy":691},[597,4664,4665],{"encoding":599},"V(X + Y)",[574,4667,4669,4693],{"className":4668,"ariaHidden":604},[603],[574,4670,4672,4675,4678,4681,4684,4687,4690],{"className":4671},[608],[574,4673],{"className":4674,"style":722},[612],[574,4676,791],{"className":4677,"style":650},[617,618],[574,4679,692],{"className":4680},[735],[574,4682,595],{"className":4683,"style":619},[617,618],[574,4685],{"className":4686,"style":650},[746],[574,4688,798],{"className":4689},[850],[574,4691],{"className":4692,"style":650},[746],[574,4694,4696,4699,4702],{"className":4695},[608],[574,4697],{"className":4698,"style":722},[612],[574,4700,635],{"className":4701,"style":650},[617,618],[574,4703,702],{"className":4704},[754]," für unabhängige Summanden rechnen. ",[574,4707,4709,4722],{"className":4708},[577],[574,4710,4712],{"className":4711},[581],[583,4713,4714],{"xmlns":585},[587,4715,4716,4720],{},[590,4717,4718],{},[593,4719,595],{},[597,4721,595],{"encoding":599},[574,4723,4725],{"className":4724,"ariaHidden":604},[603],[574,4726,4728,4731],{"className":4727},[608],[574,4729],{"className":4730,"style":613},[612],[574,4732,595],{"className":4733,"style":619},[617,618],[574,4735,4737,4750],{"className":4736},[577],[574,4738,4740],{"className":4739},[581],[583,4741,4742],{"xmlns":585},[587,4743,4744,4748],{},[590,4745,4746],{},[593,4747,595],{},[597,4749,595],{"encoding":599},[574,4751,4753],{"className":4752,"ariaHidden":604},[603],[574,4754,4756,4759],{"className":4755},[608],[574,4757],{"className":4758,"style":613},[612],[574,4760,595],{"className":4761,"style":619},[617,618]," sind vollständig abhängig: ",[574,4764,4766,4800],{"className":4765},[577],[574,4767,4769],{"className":4768},[581],[583,4770,4771],{"xmlns":585},[587,4772,4773,4797],{},[590,4774,4775,4777,4779,4781,4783,4785,4787,4789,4791,4793,4795],{},[593,4776,791],{},[686,4778,692],{"stretchy":691},[707,4780,975],{},[593,4782,595],{},[686,4784,702],{"stretchy":691},[686,4786,705],{},[707,4788,2961],{},[593,4790,791],{},[686,4792,692],{"stretchy":691},[593,4794,595],{},[686,4796,702],{"stretchy":691},[597,4798,4799],{"encoding":599},"V(2X) = 4V(X)",[574,4801,4803,4833],{"className":4802,"ariaHidden":604},[603],[574,4804,4806,4809,4812,4815,4818,4821,4824,4827,4830],{"className":4805},[608],[574,4807],{"className":4808,"style":722},[612],[574,4810,791],{"className":4811,"style":650},[617,618],[574,4813,692],{"className":4814},[735],[574,4816,975],{"className":4817},[617],[574,4819,595],{"className":4820,"style":619},[617,618],[574,4822,702],{"className":4823},[754],[574,4825],{"className":4826,"style":758},[746],[574,4828,705],{"className":4829},[762],[574,4831],{"className":4832,"style":758},[746],[574,4834,4836,4839,4842,4845,4848,4851],{"className":4835},[608],[574,4837],{"className":4838,"style":722},[612],[574,4840,2961],{"className":4841},[617],[574,4843,791],{"className":4844,"style":650},[617,618],[574,4846,692],{"className":4847},[735],[574,4849,595],{"className":4850,"style":619},[617,618],[574,4852,702],{"className":4853},[754],[574,4855,4857,4879],{"className":4856},[577],[574,4858,4860],{"className":4859},[581],[583,4861,4862],{"xmlns":585},[587,4863,4864,4876],{},[590,4865,4866,4868,4870,4872,4874],{},[707,4867,975],{},[593,4869,791],{},[686,4871,692],{"stretchy":691},[593,4873,595],{},[686,4875,702],{"stretchy":691},[597,4877,4878],{"encoding":599},"2V(X)",[574,4880,4882],{"className":4881,"ariaHidden":604},[603],[574,4883,4885,4888,4891,4894,4897,4900],{"className":4884},[608],[574,4886],{"className":4887,"style":722},[612],[574,4889,975],{"className":4890},[617],[574,4892,791],{"className":4893,"style":650},[617,618],[574,4895,692],{"className":4896},[735],[574,4898,595],{"className":4899,"style":619},[617,618],[574,4901,702],{"className":4902},[754],{"title":4904,"searchDepth":4905,"depth":4905,"links":4906},"",2,[4907,4908,4909],{"id":562,"depth":4905,"text":563},{"id":2450,"depth":4905,"text":2451},{"id":3857,"depth":4905,"text":3858},[4911,4914,4917,4920,4923,4925,4927],{"lhs":4912,"rhs":4913},"((x1 + y1) - (x2 + y2))^2 \u002F 4","(x1 - x2)^2\u002F4 + (y1 - y2)^2\u002F4 + 2*(x1 - x2)*(y1 - y2)\u002F4",{"lhs":4915,"rhs":4916},"((a*x1 + b*y1) - (a*x2 + b*y2))^2 \u002F 4","a^2*(x1 - x2)^2\u002F4 + b^2*(y1 - y2)^2\u002F4 + 2*a*b*(x1 - x2)*(y1 - y2)\u002F4",{"lhs":4918,"rhs":4919},"35\u002F12 + 35\u002F12","35\u002F6",{"lhs":4921,"rhs":4922},"round(35\u002F6, 2)","5.83",{"lhs":4924,"rhs":3163},"4 + 9 + 2*(-3)",{"lhs":4926,"rhs":3207},"4 + 9 - 2*(-3)",{"lhs":4928,"rhs":4929},"0.5^2 * 4 + 0.5^2 * 9 + 2 * 0.5 * 0.5 * (-3)","1.75","E(X^2) \u003C \\infty,\\ E(Y^2) \u003C \\infty","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>X\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(X^2) < \\infty,\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:1.0641em;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\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;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=\"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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\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>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>Y\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(Y^2) < \\infty\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:1.0641em;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\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;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=\"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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","variance-of-sum","V(X + Y) = V(X) + V(Y) + 2\\operatorname{Cov}(X, Y)","\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>+\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi mathvariant=\"normal\">Cov\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V(X + Y) = V(X) + V(Y) + 2\\operatorname{Cov}(X, Y)\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=\"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:0.2222em;\">Y\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: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:0.2222em;\">\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:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\" style=\"margin-right:0.0139em;\">Cov\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-einer-summe",[],[4943,4944,4945,4946],"covariance","variance-random-variable","variance-linear-transformation","expectation-linearity",{"title":548,"description":4904},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-einer-summe","Die Varianz einer Summe ist die Summe der Varianzen plus zweimal die Kovarianz; bei Unabhängigkeit fällt die Kovarianz weg.",[4951,4952,4953,4954,4955],"varianz","kovarianz","summe von zufallsgrößen","unabhängigkeit","rechenregeln",[4957,4961,4964],{"symbol":4958,"meaning":4959,"symbolHtml":4960},"V(X)","Varianz der Zufallsgröße X, auch Var(X) 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":4026,"meaning":4962,"symbolHtml":4963},"Zufallsgrößen auf demselben Wahrscheinlichkeitsraum","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X, Y\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4965,"meaning":4966,"symbolHtml":4967},"\\operatorname{Cov}(X, Y)","Kovarianz von X und Y","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Cov\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Cov}(X, Y)\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=\"mop\">\u003Cspan class=\"mord mathrm\" style=\"margin-right:0.0139em;\">Cov\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","uAPNhKgfR9qb06vVRvQMIfLzkMJnody1tEFTDrBnT_o",[4970,4972,4975,4978],{"stem":4971,"title":654,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fkovarianz",{"stem":4973,"title":4974,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Flinearitaet-des-erwartungswerts","Linearität des Erwartungswerts",{"stem":4976,"title":4977,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation","Varianz bei linearer Transformation",{"stem":4979,"title":4980,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Varianz einer Zufallsgröße",1793824288233]