[{"data":1,"prerenderedAt":4271},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdiskrete-gleichverteilung":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdiskrete-gleichverteilung":4259},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":441,"checks":4182,"conditions":4215,"conditionsHtml":4216,"deprecated":4217,"description":4175,"extension":4218,"figure":4217,"figureCaption":4217,"figureHtml":4217,"formulaId":4219,"latex":4220,"latexHtml":4221,"level":4222,"meta":4223,"navigation":4224,"path":4225,"redirectFrom":4226,"related":4227,"seo":4232,"stem":4233,"subject":585,"summary":4234,"tags":4235,"variables":4241,"__hash__":4258},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdiskrete-gleichverteilung.md","Diskrete Gleichverteilung",[550,551,552,553,554],"Gleichverteilung diskret","Erwartungswert Gleichverteilung","Varianz Gleichverteilung","Laplace-Verteilung","gleich wahrscheinliche Werte",{"type":556,"value":557,"toc":4174},"minimark",[558,563,572,1060,1201,1205,1426,1789,2196,2672,2676,2730,3247,3308,3694,3698],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571],"p",{},"Eine Zufallsgröße heißt ",[568,569,570],"strong",{},"gleichverteilt",", wenn alle ihre Werte dieselbe Wahrscheinlichkeit haben. Das ist die Zufallsgröße eines Laplace-Experiments, z.B. die Augenzahl eines fairen Würfels.",[564,573,574,575,674,675,775,776,958,959,1059],{},"Die Formeln für Erwartungswert und Varianz gelten für die Werte ",[576,577,580,622],"span",{"className":578},[579],"katex",[576,581,584],{"className":582},[583],"katex-mathml",[585,586,588],"math",{"xmlns":587},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[589,590,591,617],"semantics",{},[592,593,594,598,603,606,608,611,613],"mrow",{},[595,596,597],"mn",{},"1",[599,600,602],"mo",{"separator":601},"true",",",[595,604,605],{},"2",[599,607,602],{"separator":601},[599,609,610],{},"…",[599,612,602],{"separator":601},[614,615,616],"mi",{},"n",[618,619,621],"annotation",{"encoding":620},"application\u002Fx-tex","1, 2, \\ldots, n",[576,623,626],{"className":624,"ariaHidden":601},[625],"katex-html",[576,627,630,635,639,643,648,651,654,657,661,664,667,670],{"className":628},[629],"base",[576,631],{"className":632,"style":634},[633],"strut","height:0.8389em;vertical-align:-0.1944em;",[576,636,597],{"className":637},[638],"mord",[576,640,602],{"className":641},[642],"mpunct",[576,644],{"className":645,"style":647},[646],"mspace","margin-right:0.1667em;",[576,649,605],{"className":650},[638],[576,652,602],{"className":653},[642],[576,655],{"className":656,"style":647},[646],[576,658,610],{"className":659},[660],"minner",[576,662],{"className":663,"style":647},[646],[576,665,602],{"className":666},[642],[576,668],{"className":669,"style":647},[646],[576,671,616],{"className":672},[638,673],"mathnormal",". Liegen die Werte anders, z.B. ",[576,676,678,711],{"className":677},[579],[576,679,681],{"className":680},[583],[585,682,683],{"xmlns":587},[589,684,685,708],{},[592,686,687,690,692,694,697,699,701,703,705],{},[614,688,689],{},"a",[599,691,602],{"separator":601},[614,693,689],{},[599,695,696],{},"+",[595,698,597],{},[599,700,602],{"separator":601},[599,702,610],{},[599,704,602],{"separator":601},[614,706,707],{},"b",[618,709,710],{"encoding":620},"a, a+1, \\ldots, b",[576,712,714,744],{"className":713,"ariaHidden":601},[625],[576,715,717,721,724,727,730,733,737,741],{"className":716},[629],[576,718],{"className":719,"style":720},[633],"height:0.7778em;vertical-align:-0.1944em;",[576,722,689],{"className":723},[638,673],[576,725,602],{"className":726},[642],[576,728],{"className":729,"style":647},[646],[576,731,689],{"className":732},[638,673],[576,734],{"className":735,"style":736},[646],"margin-right:0.2222em;",[576,738,696],{"className":739},[740],"mbin",[576,742],{"className":743,"style":736},[646],[576,745,747,751,754,757,760,763,766,769,772],{"className":746},[629],[576,748],{"className":749,"style":750},[633],"height:0.8889em;vertical-align:-0.1944em;",[576,752,597],{"className":753},[638],[576,755,602],{"className":756},[642],[576,758],{"className":759,"style":647},[646],[576,761,610],{"className":762},[660],[576,764],{"className":765,"style":647},[646],[576,767,602],{"className":768},[642],[576,770],{"className":771,"style":647},[646],[576,773,707],{"className":774},[638,673],", verschiebt man: ",[576,777,779,820],{"className":778},[579],[576,780,782],{"className":781},[583],[585,783,784],{"xmlns":587},[589,785,786,817],{},[592,787,788,791,795,798,801,804],{},[614,789,790],{},"E",[599,792,794],{"stretchy":793},"false","(",[614,796,797],{},"X",[599,799,800],{"stretchy":793},")",[599,802,803],{},"=",[805,806,807,815],"mfrac",{},[592,808,809,811,813],{},[614,810,689],{},[599,812,696],{},[614,814,707],{},[595,816,605],{},[618,818,819],{"encoding":620},"E(X) = \\frac{a+b}{2}",[576,821,823,857],{"className":822,"ariaHidden":601},[625],[576,824,826,830,834,838,842,846,850,854],{"className":825},[629],[576,827],{"className":828,"style":829},[633],"height:1em;vertical-align:-0.25em;",[576,831,790],{"className":832,"style":833},[638,673],"margin-right:0.0576em;",[576,835,794],{"className":836},[837],"mopen",[576,839,797],{"className":840,"style":841},[638,673],"margin-right:0.0785em;",[576,843,800],{"className":844},[845],"mclose",[576,847],{"className":848,"style":849},[646],"margin-right:0.2778em;",[576,851,803],{"className":852},[853],"mrel",[576,855],{"className":856,"style":849},[646],[576,858,860,864],{"className":859},[629],[576,861],{"className":862,"style":863},[633],"height:1.2251em;vertical-align:-0.345em;",[576,865,867,871,955],{"className":866},[638],[576,868],{"className":869},[837,870],"nulldelimiter",[576,872,874],{"className":873},[805],[576,875,879,946],{"className":876},[877,878],"vlist-t","vlist-t2",[576,880,883,941],{"className":881},[882],"vlist-r",[576,884,888,909,920],{"className":885,"style":887},[886],"vlist","height:0.8801em;",[576,889,891,896],{"style":890},"top:-2.655em;",[576,892],{"className":893,"style":895},[894],"pstrut","height:3em;",[576,897,903],{"className":898},[899,900,901,902],"sizing","reset-size6","size3","mtight",[576,904,906],{"className":905},[638,902],[576,907,605],{"className":908},[638,902],[576,910,912,915],{"style":911},"top:-3.23em;",[576,913],{"className":914,"style":895},[894],[576,916],{"className":917,"style":919},[918],"frac-line","border-bottom-width:0.04em;",[576,921,923,926],{"style":922},"top:-3.394em;",[576,924],{"className":925,"style":895},[894],[576,927,929],{"className":928},[899,900,901,902],[576,930,932,935,938],{"className":931},[638,902],[576,933,689],{"className":934},[638,673,902],[576,936,696],{"className":937},[740,902],[576,939,707],{"className":940},[638,673,902],[576,942,945],{"className":943},[944],"vlist-s","​",[576,947,949],{"className":948},[882],[576,950,953],{"className":951,"style":952},[886],"height:0.345em;",[576,954],{},[576,956],{"className":957},[845,870],", und die Varianz bleibt die von ",[576,960,962,989],{"className":961},[579],[576,963,965],{"className":964},[583],[585,966,967],{"xmlns":587},[589,968,969,986],{},[592,970,971,973,975,977,980,982,984],{},[614,972,616],{},[599,974,803],{},[614,976,707],{},[599,978,979],{},"−",[614,981,689],{},[599,983,696],{},[595,985,597],{},[618,987,988],{"encoding":620},"n = b - a + 1",[576,990,992,1011,1030,1049],{"className":991,"ariaHidden":601},[625],[576,993,995,999,1002,1005,1008],{"className":994},[629],[576,996],{"className":997,"style":998},[633],"height:0.4306em;",[576,1000,616],{"className":1001},[638,673],[576,1003],{"className":1004,"style":849},[646],[576,1006,803],{"className":1007},[853],[576,1009],{"className":1010,"style":849},[646],[576,1012,1014,1018,1021,1024,1027],{"className":1013},[629],[576,1015],{"className":1016,"style":1017},[633],"height:0.7778em;vertical-align:-0.0833em;",[576,1019,707],{"className":1020},[638,673],[576,1022],{"className":1023,"style":736},[646],[576,1025,979],{"className":1026},[740],[576,1028],{"className":1029,"style":736},[646],[576,1031,1033,1037,1040,1043,1046],{"className":1032},[629],[576,1034],{"className":1035,"style":1036},[633],"height:0.6667em;vertical-align:-0.0833em;",[576,1038,689],{"className":1039},[638,673],[576,1041],{"className":1042,"style":736},[646],[576,1044,696],{"className":1045},[740],[576,1047],{"className":1048,"style":736},[646],[576,1050,1052,1056],{"className":1051},[629],[576,1053],{"className":1054,"style":1055},[633],"height:0.6444em;",[576,1057,597],{"className":1058},[638]," Werten.",[564,1061,1062,1063,1200],{},"Der Erwartungswert liegt genau in der Mitte zwischen kleinstem und größtem Wert. Die Standardabweichung ist ",[576,1064,1066,1097],{"className":1065},[579],[576,1067,1069],{"className":1068},[583],[585,1070,1071],{"xmlns":587},[589,1072,1073,1094],{},[592,1074,1075,1078,1080],{},[614,1076,1077],{},"σ",[599,1079,803],{},[1081,1082,1083],"msqrt",{},[592,1084,1085,1088,1090,1092],{},[614,1086,1087],{},"V",[599,1089,794],{"stretchy":793},[614,1091,797],{},[599,1093,800],{"stretchy":793},[618,1095,1096],{"encoding":620},"\\sigma = \\sqrt{V(X)}",[576,1098,1100,1119],{"className":1099,"ariaHidden":601},[625],[576,1101,1103,1106,1110,1113,1116],{"className":1102},[629],[576,1104],{"className":1105,"style":998},[633],[576,1107,1077],{"className":1108,"style":1109},[638,673],"margin-right:0.0359em;",[576,1111],{"className":1112,"style":849},[646],[576,1114,803],{"className":1115},[853],[576,1117],{"className":1118,"style":849},[646],[576,1120,1122,1126],{"className":1121},[629],[576,1123],{"className":1124,"style":1125},[633],"height:1.24em;vertical-align:-0.305em;",[576,1127,1130],{"className":1128},[638,1129],"sqrt",[576,1131,1133,1191],{"className":1132},[877,878],[576,1134,1136,1188],{"className":1135},[882],[576,1137,1140,1165],{"className":1138,"style":1139},[886],"height:0.935em;",[576,1141,1145,1149],{"className":1142,"style":1144},[1143],"svg-align","top:-3.2em;",[576,1146],{"className":1147,"style":1148},[894],"height:3.2em;",[576,1150,1153,1156,1159,1162],{"className":1151,"style":1152},[638],"padding-left:1em;",[576,1154,1087],{"className":1155,"style":736},[638,673],[576,1157,794],{"className":1158},[837],[576,1160,797],{"className":1161,"style":841},[638,673],[576,1163,800],{"className":1164},[845],[576,1166,1168,1171],{"style":1167},"top:-2.895em;",[576,1169],{"className":1170,"style":1148},[894],[576,1172,1176],{"className":1173,"style":1175},[1174],"hide-tail","min-width:1.02em;height:1.28em;",[1177,1178,1184],"svg",{"xmlns":1179,"width":1180,"height":1181,"viewBox":1182,"preserveAspectRatio":1183},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[1185,1186],"path",{"d":1187},"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",[576,1189,945],{"className":1190},[944],[576,1192,1194],{"className":1193},[882],[576,1195,1198],{"className":1196,"style":1197},[886],"height:0.305em;",[576,1199],{},".",[559,1202,1204],{"id":1203},"herleitung","Herleitung",[564,1206,1207,1208,1425],{},"Mit der Gaußschen Summenformel ",[576,1209,1211,1257],{"className":1210},[579],[576,1212,1214],{"className":1213},[583],[585,1215,1216],{"xmlns":587},[589,1217,1218,1254],{},[592,1219,1220,1222,1224,1226,1228,1230,1232,1234,1236],{},[595,1221,597],{},[599,1223,696],{},[595,1225,605],{},[599,1227,696],{},[599,1229,610],{},[599,1231,696],{},[614,1233,616],{},[599,1235,803],{},[805,1237,1238,1252],{},[592,1239,1240,1242,1244,1246,1248,1250],{},[614,1241,616],{},[599,1243,794],{"stretchy":793},[614,1245,616],{},[599,1247,696],{},[595,1249,597],{},[599,1251,800],{"stretchy":793},[595,1253,605],{},[618,1255,1256],{"encoding":620},"1 + 2 + \\ldots + n = \\frac{n(n+1)}{2}",[576,1258,1260,1279,1297,1315,1333],{"className":1259,"ariaHidden":601},[625],[576,1261,1263,1267,1270,1273,1276],{"className":1262},[629],[576,1264],{"className":1265,"style":1266},[633],"height:0.7278em;vertical-align:-0.0833em;",[576,1268,597],{"className":1269},[638],[576,1271],{"className":1272,"style":736},[646],[576,1274,696],{"className":1275},[740],[576,1277],{"className":1278,"style":736},[646],[576,1280,1282,1285,1288,1291,1294],{"className":1281},[629],[576,1283],{"className":1284,"style":1266},[633],[576,1286,605],{"className":1287},[638],[576,1289],{"className":1290,"style":736},[646],[576,1292,696],{"className":1293},[740],[576,1295],{"className":1296,"style":736},[646],[576,1298,1300,1303,1306,1309,1312],{"className":1299},[629],[576,1301],{"className":1302,"style":1036},[633],[576,1304,610],{"className":1305},[660],[576,1307],{"className":1308,"style":736},[646],[576,1310,696],{"className":1311},[740],[576,1313],{"className":1314,"style":736},[646],[576,1316,1318,1321,1324,1327,1330],{"className":1317},[629],[576,1319],{"className":1320,"style":998},[633],[576,1322,616],{"className":1323},[638,673],[576,1325],{"className":1326,"style":849},[646],[576,1328,803],{"className":1329},[853],[576,1331],{"className":1332,"style":849},[646],[576,1334,1336,1340],{"className":1335},[629],[576,1337],{"className":1338,"style":1339},[633],"height:1.355em;vertical-align:-0.345em;",[576,1341,1343,1346,1422],{"className":1342},[638],[576,1344],{"className":1345},[837,870],[576,1347,1349],{"className":1348},[805],[576,1350,1352,1414],{"className":1351},[877,878],[576,1353,1355,1411],{"className":1354},[882],[576,1356,1359,1373,1381],{"className":1357,"style":1358},[886],"height:1.01em;",[576,1360,1361,1364],{"style":890},[576,1362],{"className":1363,"style":895},[894],[576,1365,1367],{"className":1366},[899,900,901,902],[576,1368,1370],{"className":1369},[638,902],[576,1371,605],{"className":1372},[638,902],[576,1374,1375,1378],{"style":911},[576,1376],{"className":1377,"style":895},[894],[576,1379],{"className":1380,"style":919},[918],[576,1382,1384,1387],{"style":1383},"top:-3.485em;",[576,1385],{"className":1386,"style":895},[894],[576,1388,1390],{"className":1389},[899,900,901,902],[576,1391,1393,1396,1399,1402,1405,1408],{"className":1392},[638,902],[576,1394,616],{"className":1395},[638,673,902],[576,1397,794],{"className":1398},[837,902],[576,1400,616],{"className":1401},[638,673,902],[576,1403,696],{"className":1404},[740,902],[576,1406,597],{"className":1407},[638,902],[576,1409,800],{"className":1410},[845,902],[576,1412,945],{"className":1413},[944],[576,1415,1417],{"className":1416},[882],[576,1418,1420],{"className":1419,"style":952},[886],[576,1421],{},[576,1423],{"className":1424},[845,870],":",[576,1427,1430],{"className":1428},[1429],"katex-display",[576,1431,1433,1497],{"className":1432},[579],[576,1434,1436],{"className":1435},[583],[585,1437,1439],{"xmlns":587,"display":1438},"block",[589,1440,1441,1494],{},[592,1442,1443,1445,1447,1449,1451,1453,1459,1462,1480,1482],{},[614,1444,790],{},[599,1446,794],{"stretchy":793},[614,1448,797],{},[599,1450,800],{"stretchy":793},[599,1452,803],{},[805,1454,1455,1457],{},[595,1456,597],{},[614,1458,616],{},[599,1460,1461],{},"⋅",[805,1463,1464,1478],{},[592,1465,1466,1468,1470,1472,1474,1476],{},[614,1467,616],{},[599,1469,794],{"stretchy":793},[614,1471,616],{},[599,1473,696],{},[595,1475,597],{},[599,1477,800],{"stretchy":793},[595,1479,605],{},[599,1481,803],{},[805,1483,1484,1492],{},[592,1485,1486,1488,1490],{},[614,1487,616],{},[599,1489,696],{},[595,1491,597],{},[595,1493,605],{},[618,1495,1496],{"encoding":620},"E(X) = \\frac{1}{n} \\cdot \\frac{n(n+1)}{2} = \\frac{n+1}{2}",[576,1498,1500,1527,1609,1709],{"className":1499,"ariaHidden":601},[625],[576,1501,1503,1506,1509,1512,1515,1518,1521,1524],{"className":1502},[629],[576,1504],{"className":1505,"style":829},[633],[576,1507,790],{"className":1508,"style":833},[638,673],[576,1510,794],{"className":1511},[837],[576,1513,797],{"className":1514,"style":841},[638,673],[576,1516,800],{"className":1517},[845],[576,1519],{"className":1520,"style":849},[646],[576,1522,803],{"className":1523},[853],[576,1525],{"className":1526,"style":849},[646],[576,1528,1530,1534,1600,1603,1606],{"className":1529},[629],[576,1531],{"className":1532,"style":1533},[633],"height:2.0074em;vertical-align:-0.686em;",[576,1535,1537,1540,1597],{"className":1536},[638],[576,1538],{"className":1539},[837,870],[576,1541,1543],{"className":1542},[805],[576,1544,1546,1588],{"className":1545},[877,878],[576,1547,1549,1585],{"className":1548},[882],[576,1550,1553,1565,1573],{"className":1551,"style":1552},[886],"height:1.3214em;",[576,1554,1556,1559],{"style":1555},"top:-2.314em;",[576,1557],{"className":1558,"style":895},[894],[576,1560,1562],{"className":1561},[638],[576,1563,616],{"className":1564},[638,673],[576,1566,1567,1570],{"style":911},[576,1568],{"className":1569,"style":895},[894],[576,1571],{"className":1572,"style":919},[918],[576,1574,1576,1579],{"style":1575},"top:-3.677em;",[576,1577],{"className":1578,"style":895},[894],[576,1580,1582],{"className":1581},[638],[576,1583,597],{"className":1584},[638],[576,1586,945],{"className":1587},[944],[576,1589,1591],{"className":1590},[882],[576,1592,1595],{"className":1593,"style":1594},[886],"height:0.686em;",[576,1596],{},[576,1598],{"className":1599},[845,870],[576,1601],{"className":1602,"style":736},[646],[576,1604,1461],{"className":1605},[740],[576,1607],{"className":1608,"style":736},[646],[576,1610,1612,1616,1700,1703,1706],{"className":1611},[629],[576,1613],{"className":1614,"style":1615},[633],"height:2.113em;vertical-align:-0.686em;",[576,1617,1619,1622,1697],{"className":1618},[638],[576,1620],{"className":1621},[837,870],[576,1623,1625],{"className":1624},[805],[576,1626,1628,1689],{"className":1627},[877,878],[576,1629,1631,1686],{"className":1630},[882],[576,1632,1635,1646,1654],{"className":1633,"style":1634},[886],"height:1.427em;",[576,1636,1637,1640],{"style":1555},[576,1638],{"className":1639,"style":895},[894],[576,1641,1643],{"className":1642},[638],[576,1644,605],{"className":1645},[638],[576,1647,1648,1651],{"style":911},[576,1649],{"className":1650,"style":895},[894],[576,1652],{"className":1653,"style":919},[918],[576,1655,1656,1659],{"style":1575},[576,1657],{"className":1658,"style":895},[894],[576,1660,1662,1665,1668,1671,1674,1677,1680,1683],{"className":1661},[638],[576,1663,616],{"className":1664},[638,673],[576,1666,794],{"className":1667},[837],[576,1669,616],{"className":1670},[638,673],[576,1672],{"className":1673,"style":736},[646],[576,1675,696],{"className":1676},[740],[576,1678],{"className":1679,"style":736},[646],[576,1681,597],{"className":1682},[638],[576,1684,800],{"className":1685},[845],[576,1687,945],{"className":1688},[944],[576,1690,1692],{"className":1691},[882],[576,1693,1695],{"className":1694,"style":1594},[886],[576,1696],{},[576,1698],{"className":1699},[845,870],[576,1701],{"className":1702,"style":849},[646],[576,1704,803],{"className":1705},[853],[576,1707],{"className":1708,"style":849},[646],[576,1710,1712,1715],{"className":1711},[629],[576,1713],{"className":1714,"style":1533},[633],[576,1716,1718,1721,1786],{"className":1717},[638],[576,1719],{"className":1720},[837,870],[576,1722,1724],{"className":1723},[805],[576,1725,1727,1778],{"className":1726},[877,878],[576,1728,1730,1775],{"className":1729},[882],[576,1731,1733,1744,1752],{"className":1732,"style":1552},[886],[576,1734,1735,1738],{"style":1555},[576,1736],{"className":1737,"style":895},[894],[576,1739,1741],{"className":1740},[638],[576,1742,605],{"className":1743},[638],[576,1745,1746,1749],{"style":911},[576,1747],{"className":1748,"style":895},[894],[576,1750],{"className":1751,"style":919},[918],[576,1753,1754,1757],{"style":1575},[576,1755],{"className":1756,"style":895},[894],[576,1758,1760,1763,1766,1769,1772],{"className":1759},[638],[576,1761,616],{"className":1762},[638,673],[576,1764],{"className":1765,"style":736},[646],[576,1767,696],{"className":1768},[740],[576,1770],{"className":1771,"style":736},[646],[576,1773,597],{"className":1774},[638],[576,1776,945],{"className":1777},[944],[576,1779,1781],{"className":1780},[882],[576,1782,1784],{"className":1783,"style":1594},[886],[576,1785],{},[576,1787],{"className":1788},[845,870],[564,1790,1791,1792,2016,2017,2195],{},"Mit der Summe der Quadratzahlen ist ",[576,1793,1795,1851],{"className":1794},[579],[576,1796,1798],{"className":1797},[583],[585,1799,1800],{"xmlns":587},[589,1801,1802,1848],{},[592,1803,1804,1806,1808,1815,1817,1819],{},[614,1805,790],{},[599,1807,794],{"stretchy":793},[1809,1810,1811,1813],"msup",{},[614,1812,797],{},[595,1814,605],{},[599,1816,800],{"stretchy":793},[599,1818,803],{},[805,1820,1821,1845],{},[592,1822,1823,1825,1827,1829,1831,1833,1835,1837,1839,1841,1843],{},[599,1824,794],{"stretchy":793},[614,1826,616],{},[599,1828,696],{},[595,1830,597],{},[599,1832,800],{"stretchy":793},[599,1834,794],{"stretchy":793},[595,1836,605],{},[614,1838,616],{},[599,1840,696],{},[595,1842,597],{},[599,1844,800],{"stretchy":793},[595,1846,1847],{},"6",[618,1849,1850],{"encoding":620},"E(X^2) = \\frac{(n+1)(2n+1)}{6}",[576,1852,1854,1912],{"className":1853,"ariaHidden":601},[625],[576,1855,1857,1861,1864,1867,1900,1903,1906,1909],{"className":1856},[629],[576,1858],{"className":1859,"style":1860},[633],"height:1.0641em;vertical-align:-0.25em;",[576,1862,790],{"className":1863,"style":833},[638,673],[576,1865,794],{"className":1866},[837],[576,1868,1870,1873],{"className":1869},[638],[576,1871,797],{"className":1872,"style":841},[638,673],[576,1874,1877],{"className":1875},[1876],"msupsub",[576,1878,1880],{"className":1879},[877],[576,1881,1883],{"className":1882},[882],[576,1884,1887],{"className":1885,"style":1886},[886],"height:0.8141em;",[576,1888,1890,1894],{"style":1889},"top:-3.063em;margin-right:0.05em;",[576,1891],{"className":1892,"style":1893},[894],"height:2.7em;",[576,1895,1897],{"className":1896},[899,900,901,902],[576,1898,605],{"className":1899},[638,902],[576,1901,800],{"className":1902},[845],[576,1904],{"className":1905,"style":849},[646],[576,1907,803],{"className":1908},[853],[576,1910],{"className":1911,"style":849},[646],[576,1913,1915,1918],{"className":1914},[629],[576,1916],{"className":1917,"style":1339},[633],[576,1919,1921,1924,2013],{"className":1920},[638],[576,1922],{"className":1923},[837,870],[576,1925,1927],{"className":1926},[805],[576,1928,1930,2005],{"className":1929},[877,878],[576,1931,1933,2002],{"className":1932},[882],[576,1934,1936,1950,1958],{"className":1935,"style":1358},[886],[576,1937,1938,1941],{"style":890},[576,1939],{"className":1940,"style":895},[894],[576,1942,1944],{"className":1943},[899,900,901,902],[576,1945,1947],{"className":1946},[638,902],[576,1948,1847],{"className":1949},[638,902],[576,1951,1952,1955],{"style":911},[576,1953],{"className":1954,"style":895},[894],[576,1956],{"className":1957,"style":919},[918],[576,1959,1960,1963],{"style":1383},[576,1961],{"className":1962,"style":895},[894],[576,1964,1966],{"className":1965},[899,900,901,902],[576,1967,1969,1972,1975,1978,1981,1984,1987,1990,1993,1996,1999],{"className":1968},[638,902],[576,1970,794],{"className":1971},[837,902],[576,1973,616],{"className":1974},[638,673,902],[576,1976,696],{"className":1977},[740,902],[576,1979,597],{"className":1980},[638,902],[576,1982,800],{"className":1983},[845,902],[576,1985,794],{"className":1986},[837,902],[576,1988,605],{"className":1989},[638,902],[576,1991,616],{"className":1992},[638,673,902],[576,1994,696],{"className":1995},[740,902],[576,1997,597],{"className":1998},[638,902],[576,2000,800],{"className":2001},[845,902],[576,2003,945],{"className":2004},[944],[576,2006,2008],{"className":2007},[882],[576,2009,2011],{"className":2010,"style":952},[886],[576,2012],{},[576,2014],{"className":2015},[845,870],". Nach dem Verschiebungssatz ",[576,2018,2020,2068],{"className":2019},[579],[576,2021,2023],{"className":2022},[583],[585,2024,2025],{"xmlns":587},[589,2026,2027,2065],{},[592,2028,2029,2031,2033,2035,2037,2039,2041,2043,2049,2051,2053,2055,2057,2059],{},[614,2030,1087],{},[599,2032,794],{"stretchy":793},[614,2034,797],{},[599,2036,800],{"stretchy":793},[599,2038,803],{},[614,2040,790],{},[599,2042,794],{"stretchy":793},[1809,2044,2045,2047],{},[614,2046,797],{},[595,2048,605],{},[599,2050,800],{"stretchy":793},[599,2052,979],{},[614,2054,790],{},[599,2056,794],{"stretchy":793},[614,2058,797],{},[1809,2060,2061,2063],{},[599,2062,800],{"stretchy":793},[595,2064,605],{},[618,2066,2067],{"encoding":620},"V(X) = E(X^2) - E(X)^2",[576,2069,2071,2098,2151],{"className":2070,"ariaHidden":601},[625],[576,2072,2074,2077,2080,2083,2086,2089,2092,2095],{"className":2073},[629],[576,2075],{"className":2076,"style":829},[633],[576,2078,1087],{"className":2079,"style":736},[638,673],[576,2081,794],{"className":2082},[837],[576,2084,797],{"className":2085,"style":841},[638,673],[576,2087,800],{"className":2088},[845],[576,2090],{"className":2091,"style":849},[646],[576,2093,803],{"className":2094},[853],[576,2096],{"className":2097,"style":849},[646],[576,2099,2101,2104,2107,2110,2139,2142,2145,2148],{"className":2100},[629],[576,2102],{"className":2103,"style":1860},[633],[576,2105,790],{"className":2106,"style":833},[638,673],[576,2108,794],{"className":2109},[837],[576,2111,2113,2116],{"className":2112},[638],[576,2114,797],{"className":2115,"style":841},[638,673],[576,2117,2119],{"className":2118},[1876],[576,2120,2122],{"className":2121},[877],[576,2123,2125],{"className":2124},[882],[576,2126,2128],{"className":2127,"style":1886},[886],[576,2129,2130,2133],{"style":1889},[576,2131],{"className":2132,"style":1893},[894],[576,2134,2136],{"className":2135},[899,900,901,902],[576,2137,605],{"className":2138},[638,902],[576,2140,800],{"className":2141},[845],[576,2143],{"className":2144,"style":736},[646],[576,2146,979],{"className":2147},[740],[576,2149],{"className":2150,"style":736},[646],[576,2152,2154,2157,2160,2163,2166],{"className":2153},[629],[576,2155],{"className":2156,"style":1860},[633],[576,2158,790],{"className":2159,"style":833},[638,673],[576,2161,794],{"className":2162},[837],[576,2164,797],{"className":2165,"style":841},[638,673],[576,2167,2169,2172],{"className":2168},[845],[576,2170,800],{"className":2171},[845],[576,2173,2175],{"className":2174},[1876],[576,2176,2178],{"className":2177},[877],[576,2179,2181],{"className":2180},[882],[576,2182,2184],{"className":2183,"style":1886},[886],[576,2185,2186,2189],{"style":1889},[576,2187],{"className":2188,"style":1893},[894],[576,2190,2192],{"className":2191},[899,900,901,902],[576,2193,605],{"className":2194},[638,902]," folgt",[576,2197,2199],{"className":2198},[1429],[576,2200,2202,2294],{"className":2201},[579],[576,2203,2205],{"className":2204},[583],[585,2206,2207],{"xmlns":587,"display":1438},[589,2208,2209,2291],{},[592,2210,2211,2213,2215,2217,2219,2221,2249,2251,2272,2274],{},[614,2212,1087],{},[599,2214,794],{"stretchy":793},[614,2216,797],{},[599,2218,800],{"stretchy":793},[599,2220,803],{},[805,2222,2223,2247],{},[592,2224,2225,2227,2229,2231,2233,2235,2237,2239,2241,2243,2245],{},[599,2226,794],{"stretchy":793},[614,2228,616],{},[599,2230,696],{},[595,2232,597],{},[599,2234,800],{"stretchy":793},[599,2236,794],{"stretchy":793},[595,2238,605],{},[614,2240,616],{},[599,2242,696],{},[595,2244,597],{},[599,2246,800],{"stretchy":793},[595,2248,1847],{},[599,2250,979],{},[805,2252,2253,2269],{},[592,2254,2255,2257,2259,2261,2263],{},[599,2256,794],{"stretchy":793},[614,2258,616],{},[599,2260,696],{},[595,2262,597],{},[1809,2264,2265,2267],{},[599,2266,800],{"stretchy":793},[595,2268,605],{},[595,2270,2271],{},"4",[599,2273,803],{},[805,2275,2276,2288],{},[592,2277,2278,2284,2286],{},[1809,2279,2280,2282],{},[614,2281,616],{},[595,2283,605],{},[599,2285,979],{},[595,2287,597],{},[595,2289,2290],{},"12",[618,2292,2293],{"encoding":620},"V(X) = \\frac{(n+1)(2n+1)}{6} - \\frac{(n+1)^2}{4} = \\frac{n^2-1}{12}",[576,2295,2297,2324,2443,2566],{"className":2296,"ariaHidden":601},[625],[576,2298,2300,2303,2306,2309,2312,2315,2318,2321],{"className":2299},[629],[576,2301],{"className":2302,"style":829},[633],[576,2304,1087],{"className":2305,"style":736},[638,673],[576,2307,794],{"className":2308},[837],[576,2310,797],{"className":2311,"style":841},[638,673],[576,2313,800],{"className":2314},[845],[576,2316],{"className":2317,"style":849},[646],[576,2319,803],{"className":2320},[853],[576,2322],{"className":2323,"style":849},[646],[576,2325,2327,2330,2434,2437,2440],{"className":2326},[629],[576,2328],{"className":2329,"style":1615},[633],[576,2331,2333,2336,2431],{"className":2332},[638],[576,2334],{"className":2335},[837,870],[576,2337,2339],{"className":2338},[805],[576,2340,2342,2423],{"className":2341},[877,878],[576,2343,2345,2420],{"className":2344},[882],[576,2346,2348,2359,2367],{"className":2347,"style":1634},[886],[576,2349,2350,2353],{"style":1555},[576,2351],{"className":2352,"style":895},[894],[576,2354,2356],{"className":2355},[638],[576,2357,1847],{"className":2358},[638],[576,2360,2361,2364],{"style":911},[576,2362],{"className":2363,"style":895},[894],[576,2365],{"className":2366,"style":919},[918],[576,2368,2369,2372],{"style":1575},[576,2370],{"className":2371,"style":895},[894],[576,2373,2375,2378,2381,2384,2387,2390,2393,2396,2399,2402,2405,2408,2411,2414,2417],{"className":2374},[638],[576,2376,794],{"className":2377},[837],[576,2379,616],{"className":2380},[638,673],[576,2382],{"className":2383,"style":736},[646],[576,2385,696],{"className":2386},[740],[576,2388],{"className":2389,"style":736},[646],[576,2391,597],{"className":2392},[638],[576,2394,800],{"className":2395},[845],[576,2397,794],{"className":2398},[837],[576,2400,605],{"className":2401},[638],[576,2403,616],{"className":2404},[638,673],[576,2406],{"className":2407,"style":736},[646],[576,2409,696],{"className":2410},[740],[576,2412],{"className":2413,"style":736},[646],[576,2415,597],{"className":2416},[638],[576,2418,800],{"className":2419},[845],[576,2421,945],{"className":2422},[944],[576,2424,2426],{"className":2425},[882],[576,2427,2429],{"className":2428,"style":1594},[886],[576,2430],{},[576,2432],{"className":2433},[845,870],[576,2435],{"className":2436,"style":736},[646],[576,2438,979],{"className":2439},[740],[576,2441],{"className":2442,"style":736},[646],[576,2444,2446,2450,2557,2560,2563],{"className":2445},[629],[576,2447],{"className":2448,"style":2449},[633],"height:2.1771em;vertical-align:-0.686em;",[576,2451,2453,2456,2554],{"className":2452},[638],[576,2454],{"className":2455},[837,870],[576,2457,2459],{"className":2458},[805],[576,2460,2462,2546],{"className":2461},[877,878],[576,2463,2465,2543],{"className":2464},[882],[576,2466,2469,2480,2488],{"className":2467,"style":2468},[886],"height:1.4911em;",[576,2470,2471,2474],{"style":1555},[576,2472],{"className":2473,"style":895},[894],[576,2475,2477],{"className":2476},[638],[576,2478,2271],{"className":2479},[638],[576,2481,2482,2485],{"style":911},[576,2483],{"className":2484,"style":895},[894],[576,2486],{"className":2487,"style":919},[918],[576,2489,2490,2493],{"style":1575},[576,2491],{"className":2492,"style":895},[894],[576,2494,2496,2499,2502,2505,2508,2511,2514],{"className":2495},[638],[576,2497,794],{"className":2498},[837],[576,2500,616],{"className":2501},[638,673],[576,2503],{"className":2504,"style":736},[646],[576,2506,696],{"className":2507},[740],[576,2509],{"className":2510,"style":736},[646],[576,2512,597],{"className":2513},[638],[576,2515,2517,2520],{"className":2516},[845],[576,2518,800],{"className":2519},[845],[576,2521,2523],{"className":2522},[1876],[576,2524,2526],{"className":2525},[877],[576,2527,2529],{"className":2528},[882],[576,2530,2532],{"className":2531,"style":1886},[886],[576,2533,2534,2537],{"style":1889},[576,2535],{"className":2536,"style":1893},[894],[576,2538,2540],{"className":2539},[899,900,901,902],[576,2541,605],{"className":2542},[638,902],[576,2544,945],{"className":2545},[944],[576,2547,2549],{"className":2548},[882],[576,2550,2552],{"className":2551,"style":1594},[886],[576,2553],{},[576,2555],{"className":2556},[845,870],[576,2558],{"className":2559,"style":849},[646],[576,2561,803],{"className":2562},[853],[576,2564],{"className":2565,"style":849},[646],[576,2567,2569,2572],{"className":2568},[629],[576,2570],{"className":2571,"style":2449},[633],[576,2573,2575,2578,2669],{"className":2574},[638],[576,2576],{"className":2577},[837,870],[576,2579,2581],{"className":2580},[805],[576,2582,2584,2661],{"className":2583},[877,878],[576,2585,2587,2658],{"className":2586},[882],[576,2588,2590,2601,2609],{"className":2589,"style":2468},[886],[576,2591,2592,2595],{"style":1555},[576,2593],{"className":2594,"style":895},[894],[576,2596,2598],{"className":2597},[638],[576,2599,2290],{"className":2600},[638],[576,2602,2603,2606],{"style":911},[576,2604],{"className":2605,"style":895},[894],[576,2607],{"className":2608,"style":919},[918],[576,2610,2611,2614],{"style":1575},[576,2612],{"className":2613,"style":895},[894],[576,2615,2617,2646,2649,2652,2655],{"className":2616},[638],[576,2618,2620,2623],{"className":2619},[638],[576,2621,616],{"className":2622},[638,673],[576,2624,2626],{"className":2625},[1876],[576,2627,2629],{"className":2628},[877],[576,2630,2632],{"className":2631},[882],[576,2633,2635],{"className":2634,"style":1886},[886],[576,2636,2637,2640],{"style":1889},[576,2638],{"className":2639,"style":1893},[894],[576,2641,2643],{"className":2642},[899,900,901,902],[576,2644,605],{"className":2645},[638,902],[576,2647],{"className":2648,"style":736},[646],[576,2650,979],{"className":2651},[740],[576,2653],{"className":2654,"style":736},[646],[576,2656,597],{"className":2657},[638],[576,2659,945],{"className":2660},[944],[576,2662,2664],{"className":2663},[882],[576,2665,2667],{"className":2666,"style":1594},[886],[576,2668],{},[576,2670],{"className":2671},[845,870],[559,2673,2675],{"id":2674},"beispiele","Beispiele",[564,2677,2678,2679,1425],{},"Augenzahl eines fairen Würfels, ",[576,2680,2682,2700],{"className":2681},[579],[576,2683,2685],{"className":2684},[583],[585,2686,2687],{"xmlns":587},[589,2688,2689,2697],{},[592,2690,2691,2693,2695],{},[614,2692,616],{},[599,2694,803],{},[595,2696,1847],{},[618,2698,2699],{"encoding":620},"n = 6",[576,2701,2703,2721],{"className":2702,"ariaHidden":601},[625],[576,2704,2706,2709,2712,2715,2718],{"className":2705},[629],[576,2707],{"className":2708,"style":998},[633],[576,2710,616],{"className":2711},[638,673],[576,2713],{"className":2714,"style":849},[646],[576,2716,803],{"className":2717},[853],[576,2719],{"className":2720,"style":849},[646],[576,2722,2724,2727],{"className":2723},[629],[576,2725],{"className":2726,"style":1055},[633],[576,2728,1847],{"className":2729},[638],[576,2731,2733],{"className":2732},[1429],[576,2734,2736,2835],{"className":2735},[579],[576,2737,2739],{"className":2738},[583],[585,2740,2741],{"xmlns":587,"display":1438},[589,2742,2743,2832],{},[592,2744,2745,2748,2750,2752,2754,2757,2759,2761,2767,2769,2772,2774,2776,2778,2780,2782,2789,2791,2794,2796,2798,2800,2802,2804,2806,2808,2815,2818,2821,2823,2825,2827,2829],{},[614,2746,2747],{},"P",[599,2749,794],{"stretchy":793},[614,2751,797],{},[599,2753,803],{},[614,2755,2756],{},"k",[599,2758,800],{"stretchy":793},[599,2760,803],{},[805,2762,2763,2765],{},[595,2764,597],{},[595,2766,1847],{},[599,2768,602],{"separator":601},[646,2770],{"width":2771},"2em",[614,2773,790],{},[599,2775,794],{"stretchy":793},[614,2777,797],{},[599,2779,800],{"stretchy":793},[599,2781,803],{},[805,2783,2784,2787],{},[595,2785,2786],{},"7",[595,2788,605],{},[599,2790,803],{},[595,2792,2793],{},"3,5",[599,2795,602],{"separator":601},[646,2797],{"width":2771},[614,2799,1087],{},[599,2801,794],{"stretchy":793},[614,2803,797],{},[599,2805,800],{"stretchy":793},[599,2807,803],{},[805,2809,2810,2813],{},[595,2811,2812],{},"35",[595,2814,2290],{},[599,2816,2817],{},"≈",[595,2819,2820],{},"2,92",[599,2822,602],{"separator":601},[646,2824],{"width":2771},[614,2826,1077],{},[599,2828,2817],{},[595,2830,2831],{},"1,71",[618,2833,2834],{"encoding":620},"P(X = k) = \\frac{1}{6}, \\qquad E(X) = \\frac{7}{2} = 3{,}5, \\qquad V(X) = \\frac{35}{12} \\approx 2{,}92, \\qquad \\sigma \\approx 1{,}71",[576,2836,2838,2863,2885,2984,3061,3111,3188,3228],{"className":2837,"ariaHidden":601},[625],[576,2839,2841,2844,2848,2851,2854,2857,2860],{"className":2840},[629],[576,2842],{"className":2843,"style":829},[633],[576,2845,2747],{"className":2846,"style":2847},[638,673],"margin-right:0.1389em;",[576,2849,794],{"className":2850},[837],[576,2852,797],{"className":2853,"style":841},[638,673],[576,2855],{"className":2856,"style":849},[646],[576,2858,803],{"className":2859},[853],[576,2861],{"className":2862,"style":849},[646],[576,2864,2866,2869,2873,2876,2879,2882],{"className":2865},[629],[576,2867],{"className":2868,"style":829},[633],[576,2870,2756],{"className":2871,"style":2872},[638,673],"margin-right:0.0315em;",[576,2874,800],{"className":2875},[845],[576,2877],{"className":2878,"style":849},[646],[576,2880,803],{"className":2881},[853],[576,2883],{"className":2884,"style":849},[646],[576,2886,2888,2891,2953,2956,2960,2963,2966,2969,2972,2975,2978,2981],{"className":2887},[629],[576,2889],{"className":2890,"style":1533},[633],[576,2892,2894,2897,2950],{"className":2893},[638],[576,2895],{"className":2896},[837,870],[576,2898,2900],{"className":2899},[805],[576,2901,2903,2942],{"className":2902},[877,878],[576,2904,2906,2939],{"className":2905},[882],[576,2907,2909,2920,2928],{"className":2908,"style":1552},[886],[576,2910,2911,2914],{"style":1555},[576,2912],{"className":2913,"style":895},[894],[576,2915,2917],{"className":2916},[638],[576,2918,1847],{"className":2919},[638],[576,2921,2922,2925],{"style":911},[576,2923],{"className":2924,"style":895},[894],[576,2926],{"className":2927,"style":919},[918],[576,2929,2930,2933],{"style":1575},[576,2931],{"className":2932,"style":895},[894],[576,2934,2936],{"className":2935},[638],[576,2937,597],{"className":2938},[638],[576,2940,945],{"className":2941},[944],[576,2943,2945],{"className":2944},[882],[576,2946,2948],{"className":2947,"style":1594},[886],[576,2949],{},[576,2951],{"className":2952},[845,870],[576,2954,602],{"className":2955},[642],[576,2957],{"className":2958,"style":2959},[646],"margin-right:2em;",[576,2961],{"className":2962,"style":647},[646],[576,2964,790],{"className":2965,"style":833},[638,673],[576,2967,794],{"className":2968},[837],[576,2970,797],{"className":2971,"style":841},[638,673],[576,2973,800],{"className":2974},[845],[576,2976],{"className":2977,"style":849},[646],[576,2979,803],{"className":2980},[853],[576,2982],{"className":2983,"style":849},[646],[576,2985,2987,2990,3052,3055,3058],{"className":2986},[629],[576,2988],{"className":2989,"style":1533},[633],[576,2991,2993,2996,3049],{"className":2992},[638],[576,2994],{"className":2995},[837,870],[576,2997,2999],{"className":2998},[805],[576,3000,3002,3041],{"className":3001},[877,878],[576,3003,3005,3038],{"className":3004},[882],[576,3006,3008,3019,3027],{"className":3007,"style":1552},[886],[576,3009,3010,3013],{"style":1555},[576,3011],{"className":3012,"style":895},[894],[576,3014,3016],{"className":3015},[638],[576,3017,605],{"className":3018},[638],[576,3020,3021,3024],{"style":911},[576,3022],{"className":3023,"style":895},[894],[576,3025],{"className":3026,"style":919},[918],[576,3028,3029,3032],{"style":1575},[576,3030],{"className":3031,"style":895},[894],[576,3033,3035],{"className":3034},[638],[576,3036,2786],{"className":3037},[638],[576,3039,945],{"className":3040},[944],[576,3042,3044],{"className":3043},[882],[576,3045,3047],{"className":3046,"style":1594},[886],[576,3048],{},[576,3050],{"className":3051},[845,870],[576,3053],{"className":3054,"style":849},[646],[576,3056,803],{"className":3057},[853],[576,3059],{"className":3060,"style":849},[646],[576,3062,3064,3067,3071,3077,3081,3084,3087,3090,3093,3096,3099,3102,3105,3108],{"className":3063},[629],[576,3065],{"className":3066,"style":829},[633],[576,3068,3070],{"className":3069},[638],"3",[576,3072,3074],{"className":3073},[638],[576,3075,602],{"className":3076},[642],[576,3078,3080],{"className":3079},[638],"5",[576,3082,602],{"className":3083},[642],[576,3085],{"className":3086,"style":2959},[646],[576,3088],{"className":3089,"style":647},[646],[576,3091,1087],{"className":3092,"style":736},[638,673],[576,3094,794],{"className":3095},[837],[576,3097,797],{"className":3098,"style":841},[638,673],[576,3100,800],{"className":3101},[845],[576,3103],{"className":3104,"style":849},[646],[576,3106,803],{"className":3107},[853],[576,3109],{"className":3110,"style":849},[646],[576,3112,3114,3117,3179,3182,3185],{"className":3113},[629],[576,3115],{"className":3116,"style":1533},[633],[576,3118,3120,3123,3176],{"className":3119},[638],[576,3121],{"className":3122},[837,870],[576,3124,3126],{"className":3125},[805],[576,3127,3129,3168],{"className":3128},[877,878],[576,3130,3132,3165],{"className":3131},[882],[576,3133,3135,3146,3154],{"className":3134,"style":1552},[886],[576,3136,3137,3140],{"style":1555},[576,3138],{"className":3139,"style":895},[894],[576,3141,3143],{"className":3142},[638],[576,3144,2290],{"className":3145},[638],[576,3147,3148,3151],{"style":911},[576,3149],{"className":3150,"style":895},[894],[576,3152],{"className":3153,"style":919},[918],[576,3155,3156,3159],{"style":1575},[576,3157],{"className":3158,"style":895},[894],[576,3160,3162],{"className":3161},[638],[576,3163,2812],{"className":3164},[638],[576,3166,945],{"className":3167},[944],[576,3169,3171],{"className":3170},[882],[576,3172,3174],{"className":3173,"style":1594},[886],[576,3175],{},[576,3177],{"className":3178},[845,870],[576,3180],{"className":3181,"style":849},[646],[576,3183,2817],{"className":3184},[853],[576,3186],{"className":3187,"style":849},[646],[576,3189,3191,3194,3197,3203,3207,3210,3213,3216,3219,3222,3225],{"className":3190},[629],[576,3192],{"className":3193,"style":634},[633],[576,3195,605],{"className":3196},[638],[576,3198,3200],{"className":3199},[638],[576,3201,602],{"className":3202},[642],[576,3204,3206],{"className":3205},[638],"92",[576,3208,602],{"className":3209},[642],[576,3211],{"className":3212,"style":2959},[646],[576,3214],{"className":3215,"style":647},[646],[576,3217,1077],{"className":3218,"style":1109},[638,673],[576,3220],{"className":3221,"style":849},[646],[576,3223,2817],{"className":3224},[853],[576,3226],{"className":3227,"style":849},[646],[576,3229,3231,3234,3237,3243],{"className":3230},[629],[576,3232],{"className":3233,"style":634},[633],[576,3235,597],{"className":3236},[638],[576,3238,3240],{"className":3239},[638],[576,3241,602],{"className":3242},[642],[576,3244,3246],{"className":3245},[638],"71",[564,3248,3249,3250,3278,3279,1425],{},"Ein Programm zieht eine ganze Zufallszahl von ",[576,3251,3253,3266],{"className":3252},[579],[576,3254,3256],{"className":3255},[583],[585,3257,3258],{"xmlns":587},[589,3259,3260,3264],{},[592,3261,3262],{},[595,3263,597],{},[618,3265,597],{"encoding":620},[576,3267,3269],{"className":3268,"ariaHidden":601},[625],[576,3270,3272,3275],{"className":3271},[629],[576,3273],{"className":3274,"style":1055},[633],[576,3276,597],{"className":3277},[638]," bis ",[576,3280,3282,3296],{"className":3281},[579],[576,3283,3285],{"className":3284},[583],[585,3286,3287],{"xmlns":587},[589,3288,3289,3294],{},[592,3290,3291],{},[595,3292,3293],{},"10",[618,3295,3293],{"encoding":620},[576,3297,3299],{"className":3298,"ariaHidden":601},[625],[576,3300,3302,3305],{"className":3301},[629],[576,3303],{"className":3304,"style":1055},[633],[576,3306,3293],{"className":3307},[638],[576,3309,3311],{"className":3310},[1429],[576,3312,3314,3390],{"className":3313},[579],[576,3315,3317],{"className":3316},[583],[585,3318,3319],{"xmlns":587,"display":1438},[589,3320,3321,3387],{},[592,3322,3323,3325,3327,3329,3331,3333,3345,3347,3350,3352,3354,3356,3358,3360,3362,3364,3371,3373,3376,3378,3380,3382,3384],{},[614,3324,790],{},[599,3326,794],{"stretchy":793},[614,3328,797],{},[599,3330,800],{"stretchy":793},[599,3332,803],{},[805,3334,3335,3343],{},[592,3336,3337,3339,3341],{},[595,3338,3293],{},[599,3340,696],{},[595,3342,597],{},[595,3344,605],{},[599,3346,803],{},[595,3348,3349],{},"5,5",[599,3351,602],{"separator":601},[646,3353],{"width":2771},[614,3355,1087],{},[599,3357,794],{"stretchy":793},[614,3359,797],{},[599,3361,800],{"stretchy":793},[599,3363,803],{},[805,3365,3366,3369],{},[595,3367,3368],{},"99",[595,3370,2290],{},[599,3372,803],{},[595,3374,3375],{},"8,25",[599,3377,602],{"separator":601},[646,3379],{"width":2771},[614,3381,1077],{},[599,3383,2817],{},[595,3385,3386],{},"2,87",[618,3388,3389],{"encoding":620},"E(X) = \\frac{10 + 1}{2} = 5{,}5, \\qquad V(X) = \\frac{99}{12} = 8{,}25, \\qquad \\sigma \\approx 2{,}87",[576,3391,3393,3420,3509,3557,3634,3675],{"className":3392,"ariaHidden":601},[625],[576,3394,3396,3399,3402,3405,3408,3411,3414,3417],{"className":3395},[629],[576,3397],{"className":3398,"style":829},[633],[576,3400,790],{"className":3401,"style":833},[638,673],[576,3403,794],{"className":3404},[837],[576,3406,797],{"className":3407,"style":841},[638,673],[576,3409,800],{"className":3410},[845],[576,3412],{"className":3413,"style":849},[646],[576,3415,803],{"className":3416},[853],[576,3418],{"className":3419,"style":849},[646],[576,3421,3423,3426,3500,3503,3506],{"className":3422},[629],[576,3424],{"className":3425,"style":1533},[633],[576,3427,3429,3432,3497],{"className":3428},[638],[576,3430],{"className":3431},[837,870],[576,3433,3435],{"className":3434},[805],[576,3436,3438,3489],{"className":3437},[877,878],[576,3439,3441,3486],{"className":3440},[882],[576,3442,3444,3455,3463],{"className":3443,"style":1552},[886],[576,3445,3446,3449],{"style":1555},[576,3447],{"className":3448,"style":895},[894],[576,3450,3452],{"className":3451},[638],[576,3453,605],{"className":3454},[638],[576,3456,3457,3460],{"style":911},[576,3458],{"className":3459,"style":895},[894],[576,3461],{"className":3462,"style":919},[918],[576,3464,3465,3468],{"style":1575},[576,3466],{"className":3467,"style":895},[894],[576,3469,3471,3474,3477,3480,3483],{"className":3470},[638],[576,3472,3293],{"className":3473},[638],[576,3475],{"className":3476,"style":736},[646],[576,3478,696],{"className":3479},[740],[576,3481],{"className":3482,"style":736},[646],[576,3484,597],{"className":3485},[638],[576,3487,945],{"className":3488},[944],[576,3490,3492],{"className":3491},[882],[576,3493,3495],{"className":3494,"style":1594},[886],[576,3496],{},[576,3498],{"className":3499},[845,870],[576,3501],{"className":3502,"style":849},[646],[576,3504,803],{"className":3505},[853],[576,3507],{"className":3508,"style":849},[646],[576,3510,3512,3515,3518,3524,3527,3530,3533,3536,3539,3542,3545,3548,3551,3554],{"className":3511},[629],[576,3513],{"className":3514,"style":829},[633],[576,3516,3080],{"className":3517},[638],[576,3519,3521],{"className":3520},[638],[576,3522,602],{"className":3523},[642],[576,3525,3080],{"className":3526},[638],[576,3528,602],{"className":3529},[642],[576,3531],{"className":3532,"style":2959},[646],[576,3534],{"className":3535,"style":647},[646],[576,3537,1087],{"className":3538,"style":736},[638,673],[576,3540,794],{"className":3541},[837],[576,3543,797],{"className":3544,"style":841},[638,673],[576,3546,800],{"className":3547},[845],[576,3549],{"className":3550,"style":849},[646],[576,3552,803],{"className":3553},[853],[576,3555],{"className":3556,"style":849},[646],[576,3558,3560,3563,3625,3628,3631],{"className":3559},[629],[576,3561],{"className":3562,"style":1533},[633],[576,3564,3566,3569,3622],{"className":3565},[638],[576,3567],{"className":3568},[837,870],[576,3570,3572],{"className":3571},[805],[576,3573,3575,3614],{"className":3574},[877,878],[576,3576,3578,3611],{"className":3577},[882],[576,3579,3581,3592,3600],{"className":3580,"style":1552},[886],[576,3582,3583,3586],{"style":1555},[576,3584],{"className":3585,"style":895},[894],[576,3587,3589],{"className":3588},[638],[576,3590,2290],{"className":3591},[638],[576,3593,3594,3597],{"style":911},[576,3595],{"className":3596,"style":895},[894],[576,3598],{"className":3599,"style":919},[918],[576,3601,3602,3605],{"style":1575},[576,3603],{"className":3604,"style":895},[894],[576,3606,3608],{"className":3607},[638],[576,3609,3368],{"className":3610},[638],[576,3612,945],{"className":3613},[944],[576,3615,3617],{"className":3616},[882],[576,3618,3620],{"className":3619,"style":1594},[886],[576,3621],{},[576,3623],{"className":3624},[845,870],[576,3626],{"className":3627,"style":849},[646],[576,3629,803],{"className":3630},[853],[576,3632],{"className":3633,"style":849},[646],[576,3635,3637,3640,3644,3650,3654,3657,3660,3663,3666,3669,3672],{"className":3636},[629],[576,3638],{"className":3639,"style":634},[633],[576,3641,3643],{"className":3642},[638],"8",[576,3645,3647],{"className":3646},[638],[576,3648,602],{"className":3649},[642],[576,3651,3653],{"className":3652},[638],"25",[576,3655,602],{"className":3656},[642],[576,3658],{"className":3659,"style":2959},[646],[576,3661],{"className":3662,"style":647},[646],[576,3664,1077],{"className":3665,"style":1109},[638,673],[576,3667],{"className":3668,"style":849},[646],[576,3670,2817],{"className":3671},[853],[576,3673],{"className":3674,"style":849},[646],[576,3676,3678,3681,3684,3690],{"className":3677},[629],[576,3679],{"className":3680,"style":634},[633],[576,3682,605],{"className":3683},[638],[576,3685,3687],{"className":3686},[638],[576,3688,602],{"className":3689},[642],[576,3691,3693],{"className":3692},[638],"87",[559,3695,3697],{"id":3696},"typische-fehler","Typische Fehler",[3699,3700,3701,3908,4133],"ul",{},[3702,3703,3704,3705,3733,3734,3278,3763,3792,3793,3869,3870,1200],"li",{},"Die Formeln für Werte verwenden, die nicht bei ",[576,3706,3708,3721],{"className":3707},[579],[576,3709,3711],{"className":3710},[583],[585,3712,3713],{"xmlns":587},[589,3714,3715,3719],{},[592,3716,3717],{},[595,3718,597],{},[618,3720,597],{"encoding":620},[576,3722,3724],{"className":3723,"ariaHidden":601},[625],[576,3725,3727,3730],{"className":3726},[629],[576,3728],{"className":3729,"style":1055},[633],[576,3731,597],{"className":3732},[638]," beginnen. Für ",[576,3735,3737,3751],{"className":3736},[579],[576,3738,3740],{"className":3739},[583],[585,3741,3742],{"xmlns":587},[589,3743,3744,3749],{},[592,3745,3746],{},[595,3747,3748],{},"0",[618,3750,3748],{"encoding":620},[576,3752,3754],{"className":3753,"ariaHidden":601},[625],[576,3755,3757,3760],{"className":3756},[629],[576,3758],{"className":3759,"style":1055},[633],[576,3761,3748],{"className":3762},[638],[576,3764,3766,3780],{"className":3765},[579],[576,3767,3769],{"className":3768},[583],[585,3770,3771],{"xmlns":587},[589,3772,3773,3778],{},[592,3774,3775],{},[595,3776,3777],{},"9",[618,3779,3777],{"encoding":620},[576,3781,3783],{"className":3782,"ariaHidden":601},[625],[576,3784,3786,3789],{"className":3785},[629],[576,3787],{"className":3788,"style":1055},[633],[576,3790,3777],{"className":3791},[638]," ist ",[576,3794,3796,3821],{"className":3795},[579],[576,3797,3799],{"className":3798},[583],[585,3800,3801],{"xmlns":587},[589,3802,3803,3818],{},[592,3804,3805,3807,3809,3811,3813,3815],{},[614,3806,790],{},[599,3808,794],{"stretchy":793},[614,3810,797],{},[599,3812,800],{"stretchy":793},[599,3814,803],{},[595,3816,3817],{},"4,5",[618,3819,3820],{"encoding":620},"E(X) = 4{,}5",[576,3822,3824,3851],{"className":3823,"ariaHidden":601},[625],[576,3825,3827,3830,3833,3836,3839,3842,3845,3848],{"className":3826},[629],[576,3828],{"className":3829,"style":829},[633],[576,3831,790],{"className":3832,"style":833},[638,673],[576,3834,794],{"className":3835},[837],[576,3837,797],{"className":3838,"style":841},[638,673],[576,3840,800],{"className":3841},[845],[576,3843],{"className":3844,"style":849},[646],[576,3846,803],{"className":3847},[853],[576,3849],{"className":3850,"style":849},[646],[576,3852,3854,3857,3860,3866],{"className":3853},[629],[576,3855],{"className":3856,"style":634},[633],[576,3858,2271],{"className":3859},[638],[576,3861,3863],{"className":3862},[638],[576,3864,602],{"className":3865},[642],[576,3867,3080],{"className":3868},[638],", nicht ",[576,3871,3873,3887],{"className":3872},[579],[576,3874,3876],{"className":3875},[583],[585,3877,3878],{"xmlns":587},[589,3879,3880,3884],{},[592,3881,3882],{},[595,3883,3349],{},[618,3885,3886],{"encoding":620},"5{,}5",[576,3888,3890],{"className":3889,"ariaHidden":601},[625],[576,3891,3893,3896,3899,3905],{"className":3892},[629],[576,3894],{"className":3895,"style":634},[633],[576,3897,3080],{"className":3898},[638],[576,3900,3902],{"className":3901},[638],[576,3903,602],{"className":3904},[642],[576,3906,3080],{"className":3907},[638],[3702,3909,3910,3954,3955,3984,3985,4132],{},[576,3911,3913,3933],{"className":3912},[579],[576,3914,3916],{"className":3915},[583],[585,3917,3918],{"xmlns":587},[589,3919,3920,3930],{},[592,3921,3922,3924,3926,3928],{},[614,3923,1087],{},[599,3925,794],{"stretchy":793},[614,3927,797],{},[599,3929,800],{"stretchy":793},[618,3931,3932],{"encoding":620},"V(X)",[576,3934,3936],{"className":3935,"ariaHidden":601},[625],[576,3937,3939,3942,3945,3948,3951],{"className":3938},[629],[576,3940],{"className":3941,"style":829},[633],[576,3943,1087],{"className":3944,"style":736},[638,673],[576,3946,794],{"className":3947},[837],[576,3949,797],{"className":3950,"style":841},[638,673],[576,3952,800],{"className":3953},[845]," und ",[576,3956,3958,3972],{"className":3957},[579],[576,3959,3961],{"className":3960},[583],[585,3962,3963],{"xmlns":587},[589,3964,3965,3969],{},[592,3966,3967],{},[614,3968,1077],{},[618,3970,3971],{"encoding":620},"\\sigma",[576,3973,3975],{"className":3974,"ariaHidden":601},[625],[576,3976,3978,3981],{"className":3977},[629],[576,3979],{"className":3980,"style":998},[633],[576,3982,1077],{"className":3983,"style":1109},[638,673]," verwechseln. ",[576,3986,3988,4016],{"className":3987},[579],[576,3989,3991],{"className":3990},[583],[585,3992,3993],{"xmlns":587},[589,3994,3995,4013],{},[592,3996,3997],{},[805,3998,3999,4011],{},[592,4000,4001,4007,4009],{},[1809,4002,4003,4005],{},[614,4004,616],{},[595,4006,605],{},[599,4008,979],{},[595,4010,597],{},[595,4012,2290],{},[618,4014,4015],{"encoding":620},"\\frac{n^2-1}{12}",[576,4017,4019],{"className":4018,"ariaHidden":601},[625],[576,4020,4022,4026],{"className":4021},[629],[576,4023],{"className":4024,"style":4025},[633],"height:1.3629em;vertical-align:-0.345em;",[576,4027,4029,4032,4129],{"className":4028},[638],[576,4030],{"className":4031},[837,870],[576,4033,4035],{"className":4034},[805],[576,4036,4038,4121],{"className":4037},[877,878],[576,4039,4041,4118],{"className":4040},[882],[576,4042,4045,4059,4067],{"className":4043,"style":4044},[886],"height:1.0179em;",[576,4046,4047,4050],{"style":890},[576,4048],{"className":4049,"style":895},[894],[576,4051,4053],{"className":4052},[899,900,901,902],[576,4054,4056],{"className":4055},[638,902],[576,4057,2290],{"className":4058},[638,902],[576,4060,4061,4064],{"style":911},[576,4062],{"className":4063,"style":895},[894],[576,4065],{"className":4066,"style":919},[918],[576,4068,4069,4072],{"style":922},[576,4070],{"className":4071,"style":895},[894],[576,4073,4075],{"className":4074},[899,900,901,902],[576,4076,4078,4112,4115],{"className":4077},[638,902],[576,4079,4081,4084],{"className":4080},[638,902],[576,4082,616],{"className":4083},[638,673,902],[576,4085,4087],{"className":4086},[1876],[576,4088,4090],{"className":4089},[877],[576,4091,4093],{"className":4092},[882],[576,4094,4097],{"className":4095,"style":4096},[886],"height:0.8913em;",[576,4098,4100,4104],{"style":4099},"top:-2.931em;margin-right:0.0714em;",[576,4101],{"className":4102,"style":4103},[894],"height:2.5em;",[576,4105,4109],{"className":4106},[899,4107,4108,902],"reset-size3","size1",[576,4110,605],{"className":4111},[638,902],[576,4113,979],{"className":4114},[740,902],[576,4116,597],{"className":4117},[638,902],[576,4119,945],{"className":4120},[944],[576,4122,4124],{"className":4123},[882],[576,4125,4127],{"className":4126,"style":952},[886],[576,4128],{},[576,4130],{"className":4131},[845,870]," ist die Varianz, die Standardabweichung ist die Wurzel daraus.",[3702,4134,4135,4136,1200],{},"Den Erwartungswert als möglichen Wert ansehen. Ein Würfel zeigt nie ",[576,4137,4139,4153],{"className":4138},[579],[576,4140,4142],{"className":4141},[583],[585,4143,4144],{"xmlns":587},[589,4145,4146,4150],{},[592,4147,4148],{},[595,4149,2793],{},[618,4151,4152],{"encoding":620},"3{,}5",[576,4154,4156],{"className":4155,"ariaHidden":601},[625],[576,4157,4159,4162,4165,4171],{"className":4158},[629],[576,4160],{"className":4161,"style":634},[633],[576,4163,3070],{"className":4164},[638],[576,4166,4168],{"className":4167},[638],[576,4169,602],{"className":4170},[642],[576,4172,3080],{"className":4173},[638],{"title":4175,"searchDepth":4176,"depth":4176,"links":4177},"",2,[4178,4179,4180,4181],{"id":561,"depth":4176,"text":562},{"id":1203,"depth":4176,"text":1204},{"id":2674,"depth":4176,"text":2675},{"id":3696,"depth":4176,"text":3697},[4183,4186,4189,4192,4195,4197,4200,4203,4206,4209,4212],{"lhs":4184,"rhs":4185},"(n*(n+1)\u002F2) \u002F n","(n+1)\u002F2",{"lhs":4187,"rhs":4188},"(n+1)*(2*n+1)\u002F6 - ((n+1)\u002F2)^2","(n^2 - 1)\u002F12",{"lhs":4190,"rhs":4191},"sum(map(1:6, f(k) = k)) \u002F 6","3.5",{"lhs":4193,"rhs":4194},"sum(map(1:6, f(k) = (k - 3.5)^2)) \u002F 6","35\u002F12",{"lhs":4196,"rhs":4194},"(6^2 - 1)\u002F12",{"lhs":4198,"rhs":4199},"round(35\u002F12, 2)","2.92",{"lhs":4201,"rhs":4202},"round(sqrt(35\u002F12), 2)","1.71",{"lhs":4204,"rhs":4205},"(10 + 1)\u002F2","5.5",{"lhs":4207,"rhs":4208},"(10^2 - 1)\u002F12","8.25",{"lhs":4210,"rhs":4211},"round(sqrt(8.25), 2)","2.87",{"lhs":4213,"rhs":4214},"(0 + 9)\u002F2","4.5","X \\text{ nimmt die Werte } 1, 2, \\ldots, n \\text{ an},\\ n \\geq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">nimmt die Werte\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1,\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>\u003Cmn>2\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">2, \\ldots, n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">an\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","uniform-distribution-discrete","P(X = k) = \\frac{1}{n}, \\qquad E(X) = \\frac{n+1}{2}, \\qquad V(X) = \\frac{n^2 - 1}{12}","\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>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsup>\u003Cmi>n\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmn>12\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P(X = k) = \\frac{1}{n}, \\qquad E(X) = \\frac{n+1}{2}, \\qquad V(X) = \\frac{n^2 - 1}{12}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\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>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.1771em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">12\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\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=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdiskrete-gleichverteilung",[],[4228,4229,4230,4231],"laplace-probability","expected-value","variance-random-variable","uniform-distribution-continuous",{"title":548,"description":4175},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdiskrete-gleichverteilung","Nimmt X die Werte 1 bis n gleich wahrscheinlich an, gilt E(X) = (n+1)\u002F2 und V(X) = (n²−1)\u002F12.",[4236,4237,4238,4239,4240],"gleichverteilung","laplace-experiment","zufallsgröße","erwartungswert","varianz",[4242,4245,4248,4251,4255],{"symbol":797,"meaning":4243,"symbolHtml":4244},"Zufallsgröße, die jeden der Werte 1 bis n mit gleicher Wahrscheinlichkeit annimmt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2756,"meaning":4246,"symbolHtml":4247},"einer der möglichen Werte 1, 2, …, n","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":616,"meaning":4249,"symbolHtml":4250},"Anzahl der möglichen Werte","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4252,"meaning":4253,"symbolHtml":4254},"E(X)","Erwartungswert","\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>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(X)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3932,"meaning":4256,"symbolHtml":4257},"Varianz","\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>","svh8Bi9JBt8T9L450JCDfFFZxX1Ay4gTGQlm14acwKw",[4260,4262,4265,4268],{"stem":4261,"title":4253,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert",{"stem":4263,"title":4264,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Flaplace-wahrscheinlichkeit","Laplace-Wahrscheinlichkeit",{"stem":4266,"title":4267,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstetige-gleichverteilung","Stetige Gleichverteilung",{"stem":4269,"title":4270,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Varianz einer Zufallsgröße",1793824284996]