[{"data":1,"prerenderedAt":4106},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation":4093},[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":4030,"conditions":4054,"conditionsHtml":4055,"deprecated":4056,"description":4024,"extension":4057,"figure":4056,"figureCaption":4056,"figureHtml":4056,"formulaId":4058,"latex":4059,"latexHtml":4060,"level":4061,"meta":4062,"navigation":4063,"path":4064,"redirectFrom":4065,"related":4066,"seo":4071,"stem":4072,"subject":578,"summary":4073,"tags":4074,"variables":4079,"__hash__":4092},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation.md","Varianz bei linearer Transformation",[550,551,552,553,554,555],"Var(aX+b)","Varianz aX+b","Rechenregeln Varianz","Varianz mal Konstante","Standardabweichung linear transformiert","Varianz Umrechnung Einheiten",{"type":557,"value":558,"toc":4023},"minimark",[559,564,679,760,763,919,1379,1663,1667,1904,2299,2337,2578,2919,2923],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,678],"p",{},"Wird eine Zufallsgröße linear umgerechnet, ",[569,570,573,612],"span",{"className":571},[572],"katex",[569,574,577],{"className":575},[576],"katex-mathml",[578,579,581],"math",{"xmlns":580},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[582,583,584,607],"semantics",{},[585,586,587,591,595,598,601,604],"mrow",{},[588,589,590],"mi",{},"Y",[592,593,594],"mo",{},"=",[588,596,597],{},"a",[588,599,600],{},"X",[592,602,603],{},"+",[588,605,606],{},"b",[608,609,611],"annotation",{"encoding":610},"application\u002Fx-tex","Y = aX + b",[569,613,617,644,668],{"className":614,"ariaHidden":616},[615],"katex-html","true",[569,618,621,626,632,637,641],{"className":619},[620],"base",[569,622],{"className":623,"style":625},[624],"strut","height:0.6833em;",[569,627,590],{"className":628,"style":631},[629,630],"mord","mathnormal","margin-right:0.2222em;",[569,633],{"className":634,"style":636},[635],"mspace","margin-right:0.2778em;",[569,638,594],{"className":639},[640],"mrel",[569,642],{"className":643,"style":636},[635],[569,645,647,651,654,658,661,665],{"className":646},[620],[569,648],{"className":649,"style":650},[624],"height:0.7667em;vertical-align:-0.0833em;",[569,652,597],{"className":653},[629,630],[569,655,600],{"className":656,"style":657},[629,630],"margin-right:0.0785em;",[569,659],{"className":660,"style":631},[635],[569,662,603],{"className":663},[664],"mbin",[569,666],{"className":667,"style":631},[635],[569,669,671,675],{"className":670},[620],[569,672],{"className":673,"style":674},[624],"height:0.6944em;",[569,676,606],{"className":677},[629,630],", dann gilt:",[680,681,682,720],"ul",{},[683,684,685,686,690,691,719],"li",{},"Die ",[687,688,689],"strong",{},"Verschiebung"," ",[569,692,694,707],{"className":693},[572],[569,695,697],{"className":696},[576],[578,698,699],{"xmlns":580},[582,700,701,705],{},[585,702,703],{},[588,704,606],{},[608,706,606],{"encoding":610},[569,708,710],{"className":709,"ariaHidden":616},[615],[569,711,713,716],{"className":712},[620],[569,714],{"className":715,"style":674},[624],[569,717,606],{"className":718},[629,630]," ändert die Varianz nicht. Alle Werte und der Erwartungswert verschieben sich gleich, die Abweichungen bleiben.",[683,721,722,723,690,726,755,756,759],{},"Der ",[687,724,725],{},"Faktor",[569,727,729,742],{"className":728},[572],[569,730,732],{"className":731},[576],[578,733,734],{"xmlns":580},[582,735,736,740],{},[585,737,738],{},[588,739,597],{},[608,741,597],{"encoding":610},[569,743,745],{"className":744,"ariaHidden":616},[615],[569,746,748,752],{"className":747},[620],[569,749],{"className":750,"style":751},[624],"height:0.4306em;",[569,753,597],{"className":754},[629,630]," geht ",[687,757,758],{},"quadriert"," ein, weil die Varianz aus quadrierten Abweichungen besteht.",[565,761,762],{},"Für die Standardabweichung folgt",[569,764,767],{"className":765},[766],"katex-display",[569,768,770,822],{"className":769},[572],[569,771,773],{"className":772},[576],[578,774,776],{"xmlns":580,"display":775},"block",[582,777,778,819],{},[585,779,780,783,787,789,791,793,795,798,800,804,806,808,811,813,815,817],{},[588,781,782],{},"σ",[592,784,786],{"stretchy":785},"false","(",[588,788,597],{},[588,790,600],{},[592,792,603],{},[588,794,606],{},[592,796,797],{"stretchy":785},")",[592,799,594],{},[588,801,803],{"mathvariant":802},"normal","∣",[588,805,597],{},[588,807,803],{"mathvariant":802},[592,809,810],{},"⋅",[588,812,782],{},[592,814,786],{"stretchy":785},[588,816,600],{},[592,818,797],{"stretchy":785},[608,820,821],{"encoding":610},"\\sigma(aX + b) = |a| \\cdot \\sigma(X)",[569,823,825,855,877,901],{"className":824,"ariaHidden":616},[615],[569,826,828,832,836,840,843,846,849,852],{"className":827},[620],[569,829],{"className":830,"style":831},[624],"height:1em;vertical-align:-0.25em;",[569,833,782],{"className":834,"style":835},[629,630],"margin-right:0.0359em;",[569,837,786],{"className":838},[839],"mopen",[569,841,597],{"className":842},[629,630],[569,844,600],{"className":845,"style":657},[629,630],[569,847],{"className":848,"style":631},[635],[569,850,603],{"className":851},[664],[569,853],{"className":854,"style":631},[635],[569,856,858,861,864,868,871,874],{"className":857},[620],[569,859],{"className":860,"style":831},[624],[569,862,606],{"className":863},[629,630],[569,865,797],{"className":866},[867],"mclose",[569,869],{"className":870,"style":636},[635],[569,872,594],{"className":873},[640],[569,875],{"className":876,"style":636},[635],[569,878,880,883,886,889,892,895,898],{"className":879},[620],[569,881],{"className":882,"style":831},[624],[569,884,803],{"className":885},[629],[569,887,597],{"className":888},[629,630],[569,890,803],{"className":891},[629],[569,893],{"className":894,"style":631},[635],[569,896,810],{"className":897},[664],[569,899],{"className":900,"style":631},[635],[569,902,904,907,910,913,916],{"className":903},[620],[569,905],{"className":906,"style":831},[624],[569,908,782],{"className":909,"style":835},[629,630],[569,911,786],{"className":912},[839],[569,914,600],{"className":915,"style":657},[629,630],[569,917,797],{"className":918},[867],[565,920,921,924,925,1070,1071,1270,1271,1378],{},[687,922,923],{},"Herleitung:"," Mit ",[569,926,928,975],{"className":927},[572],[569,929,931],{"className":930},[576],[578,932,933],{"xmlns":580},[582,934,935,972],{},[585,936,937,940,942,944,946,948,950,952,954,956,960,962,964,966,968,970],{},[588,938,939],{},"E",[592,941,786],{"stretchy":785},[588,943,597],{},[588,945,600],{},[592,947,603],{},[588,949,606],{},[592,951,797],{"stretchy":785},[592,953,594],{},[588,955,597],{},[957,958,959],"mtext",{}," ",[588,961,939],{},[592,963,786],{"stretchy":785},[588,965,600],{},[592,967,797],{"stretchy":785},[592,969,603],{},[588,971,606],{},[608,973,974],{"encoding":610},"E(aX + b) = a\\,E(X) + b",[569,976,978,1006,1027,1061],{"className":977,"ariaHidden":616},[615],[569,979,981,984,988,991,994,997,1000,1003],{"className":980},[620],[569,982],{"className":983,"style":831},[624],[569,985,939],{"className":986,"style":987},[629,630],"margin-right:0.0576em;",[569,989,786],{"className":990},[839],[569,992,597],{"className":993},[629,630],[569,995,600],{"className":996,"style":657},[629,630],[569,998],{"className":999,"style":631},[635],[569,1001,603],{"className":1002},[664],[569,1004],{"className":1005,"style":631},[635],[569,1007,1009,1012,1015,1018,1021,1024],{"className":1008},[620],[569,1010],{"className":1011,"style":831},[624],[569,1013,606],{"className":1014},[629,630],[569,1016,797],{"className":1017},[867],[569,1019],{"className":1020,"style":636},[635],[569,1022,594],{"className":1023},[640],[569,1025],{"className":1026,"style":636},[635],[569,1028,1030,1033,1036,1040,1043,1046,1049,1052,1055,1058],{"className":1029},[620],[569,1031],{"className":1032,"style":831},[624],[569,1034,597],{"className":1035},[629,630],[569,1037],{"className":1038,"style":1039},[635],"margin-right:0.1667em;",[569,1041,939],{"className":1042,"style":987},[629,630],[569,1044,786],{"className":1045},[839],[569,1047,600],{"className":1048,"style":657},[629,630],[569,1050,797],{"className":1051},[867],[569,1053],{"className":1054,"style":631},[635],[569,1056,603],{"className":1057},[664],[569,1059],{"className":1060,"style":631},[635],[569,1062,1064,1067],{"className":1063},[620],[569,1065],{"className":1066,"style":674},[624],[569,1068,606],{"className":1069},[629,630]," ist ",[569,1072,1074,1133],{"className":1073},[572],[569,1075,1077],{"className":1076},[576],[578,1078,1079],{"xmlns":580},[582,1080,1081,1130],{},[585,1082,1083,1085,1087,1089,1091,1094,1096,1098,1100,1102,1104,1106,1108,1110,1112,1114,1116,1118,1120,1122,1124,1126,1128],{},[588,1084,597],{},[588,1086,600],{},[592,1088,603],{},[588,1090,606],{},[592,1092,1093],{},"−",[588,1095,939],{},[592,1097,786],{"stretchy":785},[588,1099,597],{},[588,1101,600],{},[592,1103,603],{},[588,1105,606],{},[592,1107,797],{"stretchy":785},[592,1109,594],{},[588,1111,597],{},[957,1113,959],{},[592,1115,786],{"stretchy":785},[588,1117,600],{},[592,1119,1093],{},[588,1121,939],{},[592,1123,786],{"stretchy":785},[588,1125,600],{},[592,1127,797],{"stretchy":785},[592,1129,797],{"stretchy":785},[608,1131,1132],{"encoding":610},"aX + b - E(aX + b) = a\\,(X - E(X))",[569,1134,1136,1157,1176,1203,1224,1251],{"className":1135,"ariaHidden":616},[615],[569,1137,1139,1142,1145,1148,1151,1154],{"className":1138},[620],[569,1140],{"className":1141,"style":650},[624],[569,1143,597],{"className":1144},[629,630],[569,1146,600],{"className":1147,"style":657},[629,630],[569,1149],{"className":1150,"style":631},[635],[569,1152,603],{"className":1153},[664],[569,1155],{"className":1156,"style":631},[635],[569,1158,1160,1164,1167,1170,1173],{"className":1159},[620],[569,1161],{"className":1162,"style":1163},[624],"height:0.7778em;vertical-align:-0.0833em;",[569,1165,606],{"className":1166},[629,630],[569,1168],{"className":1169,"style":631},[635],[569,1171,1093],{"className":1172},[664],[569,1174],{"className":1175,"style":631},[635],[569,1177,1179,1182,1185,1188,1191,1194,1197,1200],{"className":1178},[620],[569,1180],{"className":1181,"style":831},[624],[569,1183,939],{"className":1184,"style":987},[629,630],[569,1186,786],{"className":1187},[839],[569,1189,597],{"className":1190},[629,630],[569,1192,600],{"className":1193,"style":657},[629,630],[569,1195],{"className":1196,"style":631},[635],[569,1198,603],{"className":1199},[664],[569,1201],{"className":1202,"style":631},[635],[569,1204,1206,1209,1212,1215,1218,1221],{"className":1205},[620],[569,1207],{"className":1208,"style":831},[624],[569,1210,606],{"className":1211},[629,630],[569,1213,797],{"className":1214},[867],[569,1216],{"className":1217,"style":636},[635],[569,1219,594],{"className":1220},[640],[569,1222],{"className":1223,"style":636},[635],[569,1225,1227,1230,1233,1236,1239,1242,1245,1248],{"className":1226},[620],[569,1228],{"className":1229,"style":831},[624],[569,1231,597],{"className":1232},[629,630],[569,1234],{"className":1235,"style":1039},[635],[569,1237,786],{"className":1238},[839],[569,1240,600],{"className":1241,"style":657},[629,630],[569,1243],{"className":1244,"style":631},[635],[569,1246,1093],{"className":1247},[664],[569,1249],{"className":1250,"style":631},[635],[569,1252,1254,1257,1260,1263,1266],{"className":1253},[620],[569,1255],{"className":1256,"style":831},[624],[569,1258,939],{"className":1259,"style":987},[629,630],[569,1261,786],{"className":1262},[839],[569,1264,600],{"className":1265,"style":657},[629,630],[569,1267,1269],{"className":1268},[867],"))",". Quadrieren und Erwartungswert bilden liefert ",[569,1272,1274,1307],{"className":1273},[572],[569,1275,1277],{"className":1276},[576],[578,1278,1279],{"xmlns":580},[582,1280,1281,1304],{},[585,1282,1283,1292,1295,1298,1300,1302],{},[1284,1285,1286,1288],"msup",{},[588,1287,597],{},[1289,1290,1291],"mn",{},"2",[588,1293,1294],{"mathvariant":802},"Var",[592,1296,1297],{},"⁡",[592,1299,786],{"stretchy":785},[588,1301,600],{},[592,1303,797],{"stretchy":785},[608,1305,1306],{"encoding":610},"a^2 \\operatorname{Var}(X)",[569,1308,1310],{"className":1309,"ariaHidden":616},[615],[569,1311,1313,1317,1358,1361,1369,1372,1375],{"className":1312},[620],[569,1314],{"className":1315,"style":1316},[624],"height:1.0641em;vertical-align:-0.25em;",[569,1318,1320,1323],{"className":1319},[629],[569,1321,597],{"className":1322},[629,630],[569,1324,1327],{"className":1325},[1326],"msupsub",[569,1328,1331],{"className":1329},[1330],"vlist-t",[569,1332,1335],{"className":1333},[1334],"vlist-r",[569,1336,1340],{"className":1337,"style":1339},[1338],"vlist","height:0.8141em;",[569,1341,1343,1348],{"style":1342},"top:-3.063em;margin-right:0.05em;",[569,1344],{"className":1345,"style":1347},[1346],"pstrut","height:2.7em;",[569,1349,1355],{"className":1350},[1351,1352,1353,1354],"sizing","reset-size6","size3","mtight",[569,1356,1291],{"className":1357},[629,1354],[569,1359],{"className":1360,"style":1039},[635],[569,1362,1365],{"className":1363},[1364],"mop",[569,1366,1294],{"className":1367},[629,1368],"mathrm",[569,1370,786],{"className":1371},[839],[569,1373,600],{"className":1374,"style":657},[629,630],[569,1376,797],{"className":1377},[867],".",[565,1380,1381,1382,1604,1605,1633,1634,1662],{},"Für eine Summe zweier Zufallsgrößen gilt allgemein ",[569,1383,1385,1455],{"className":1384},[572],[569,1386,1388],{"className":1387},[576],[578,1389,1390],{"xmlns":580},[582,1391,1392,1452],{},[585,1393,1394,1396,1398,1400,1402,1404,1406,1408,1410,1412,1414,1416,1418,1420,1422,1424,1426,1428,1430,1432,1434,1436,1439,1441,1443,1445,1448,1450],{},[588,1395,1294],{"mathvariant":802},[592,1397,1297],{},[592,1399,786],{"stretchy":785},[588,1401,600],{},[592,1403,603],{},[588,1405,590],{},[592,1407,797],{"stretchy":785},[592,1409,594],{},[588,1411,1294],{"mathvariant":802},[592,1413,1297],{},[592,1415,786],{"stretchy":785},[588,1417,600],{},[592,1419,797],{"stretchy":785},[592,1421,603],{},[588,1423,1294],{"mathvariant":802},[592,1425,1297],{},[592,1427,786],{"stretchy":785},[588,1429,590],{},[592,1431,797],{"stretchy":785},[592,1433,603],{},[1289,1435,1291],{},[588,1437,1438],{"mathvariant":802},"Cov",[592,1440,1297],{},[592,1442,786],{"stretchy":785},[588,1444,600],{},[592,1446,1447],{"separator":616},",",[588,1449,590],{},[592,1451,797],{"stretchy":785},[608,1453,1454],{"encoding":610},"\\operatorname{Var}(X + Y) = \\operatorname{Var}(X) + \\operatorname{Var}(Y) + 2\\operatorname{Cov}(X, Y)",[569,1456,1458,1485,1506,1536,1566],{"className":1457,"ariaHidden":616},[615],[569,1459,1461,1464,1470,1473,1476,1479,1482],{"className":1460},[620],[569,1462],{"className":1463,"style":831},[624],[569,1465,1467],{"className":1466},[1364],[569,1468,1294],{"className":1469},[629,1368],[569,1471,786],{"className":1472},[839],[569,1474,600],{"className":1475,"style":657},[629,630],[569,1477],{"className":1478,"style":631},[635],[569,1480,603],{"className":1481},[664],[569,1483],{"className":1484,"style":631},[635],[569,1486,1488,1491,1494,1497,1500,1503],{"className":1487},[620],[569,1489],{"className":1490,"style":831},[624],[569,1492,590],{"className":1493,"style":631},[629,630],[569,1495,797],{"className":1496},[867],[569,1498],{"className":1499,"style":636},[635],[569,1501,594],{"className":1502},[640],[569,1504],{"className":1505,"style":636},[635],[569,1507,1509,1512,1518,1521,1524,1527,1530,1533],{"className":1508},[620],[569,1510],{"className":1511,"style":831},[624],[569,1513,1515],{"className":1514},[1364],[569,1516,1294],{"className":1517},[629,1368],[569,1519,786],{"className":1520},[839],[569,1522,600],{"className":1523,"style":657},[629,630],[569,1525,797],{"className":1526},[867],[569,1528],{"className":1529,"style":631},[635],[569,1531,603],{"className":1532},[664],[569,1534],{"className":1535,"style":631},[635],[569,1537,1539,1542,1548,1551,1554,1557,1560,1563],{"className":1538},[620],[569,1540],{"className":1541,"style":831},[624],[569,1543,1545],{"className":1544},[1364],[569,1546,1294],{"className":1547},[629,1368],[569,1549,786],{"className":1550},[839],[569,1552,590],{"className":1553,"style":631},[629,630],[569,1555,797],{"className":1556},[867],[569,1558],{"className":1559,"style":631},[635],[569,1561,603],{"className":1562},[664],[569,1564],{"className":1565,"style":631},[635],[569,1567,1569,1572,1575,1578,1585,1588,1591,1595,1598,1601],{"className":1568},[620],[569,1570],{"className":1571,"style":831},[624],[569,1573,1291],{"className":1574},[629],[569,1576],{"className":1577,"style":1039},[635],[569,1579,1581],{"className":1580},[1364],[569,1582,1438],{"className":1583,"style":1584},[629,1368],"margin-right:0.0139em;",[569,1586,786],{"className":1587},[839],[569,1589,600],{"className":1590,"style":657},[629,630],[569,1592,1447],{"className":1593},[1594],"mpunct",[569,1596],{"className":1597,"style":1039},[635],[569,1599,590],{"className":1600,"style":631},[629,630],[569,1602,797],{"className":1603},[867],". Nur bei unkorrelierten (z.B. unabhängigen) ",[569,1606,1608,1621],{"className":1607},[572],[569,1609,1611],{"className":1610},[576],[578,1612,1613],{"xmlns":580},[582,1614,1615,1619],{},[585,1616,1617],{},[588,1618,600],{},[608,1620,600],{"encoding":610},[569,1622,1624],{"className":1623,"ariaHidden":616},[615],[569,1625,1627,1630],{"className":1626},[620],[569,1628],{"className":1629,"style":625},[624],[569,1631,600],{"className":1632,"style":657},[629,630]," und ",[569,1635,1637,1650],{"className":1636},[572],[569,1638,1640],{"className":1639},[576],[578,1641,1642],{"xmlns":580},[582,1643,1644,1648],{},[585,1645,1646],{},[588,1647,590],{},[608,1649,590],{"encoding":610},[569,1651,1653],{"className":1652,"ariaHidden":616},[615],[569,1654,1656,1659],{"className":1655},[620],[569,1657],{"className":1658,"style":625},[624],[569,1660,590],{"className":1661,"style":631},[629,630]," fällt der letzte Summand weg.",[560,1664,1666],{"id":1665},"beispiele","Beispiele",[565,1668,1669,1670,1700,1701,1730,1731,1803,1804,1903],{},"Die Tagestemperatur ",[569,1671,1673,1687],{"className":1672},[572],[569,1674,1676],{"className":1675},[576],[578,1677,1678],{"xmlns":580},[582,1679,1680,1685],{},[585,1681,1682],{},[588,1683,1684],{},"C",[608,1686,1684],{"encoding":610},[569,1688,1690],{"className":1689,"ariaHidden":616},[615],[569,1691,1693,1696],{"className":1692},[620],[569,1694],{"className":1695,"style":625},[624],[569,1697,1684],{"className":1698,"style":1699},[629,630],"margin-right:0.0715em;"," in Grad Celsius hat die Standardabweichung ",[569,1702,1704,1717],{"className":1703},[572],[569,1705,1707],{"className":1706},[576],[578,1708,1709],{"xmlns":580},[582,1710,1711,1715],{},[585,1712,1713],{},[1289,1714,1291],{},[608,1716,1291],{"encoding":610},[569,1718,1720],{"className":1719,"ariaHidden":616},[615],[569,1721,1723,1727],{"className":1722},[620],[569,1724],{"className":1725,"style":1726},[624],"height:0.6444em;",[569,1728,1291],{"className":1729},[629],", also ",[569,1732,1734,1761],{"className":1733},[572],[569,1735,1737],{"className":1736},[576],[578,1738,1739],{"xmlns":580},[582,1740,1741,1758],{},[585,1742,1743,1745,1747,1749,1751,1753,1755],{},[588,1744,1294],{"mathvariant":802},[592,1746,1297],{},[592,1748,786],{"stretchy":785},[588,1750,1684],{},[592,1752,797],{"stretchy":785},[592,1754,594],{},[1289,1756,1757],{},"4",[608,1759,1760],{"encoding":610},"\\operatorname{Var}(C) = 4",[569,1762,1764,1794],{"className":1763,"ariaHidden":616},[615],[569,1765,1767,1770,1776,1779,1782,1785,1788,1791],{"className":1766},[620],[569,1768],{"className":1769,"style":831},[624],[569,1771,1773],{"className":1772},[1364],[569,1774,1294],{"className":1775},[629,1368],[569,1777,786],{"className":1778},[839],[569,1780,1684],{"className":1781,"style":1699},[629,630],[569,1783,797],{"className":1784},[867],[569,1786],{"className":1787,"style":636},[635],[569,1789,594],{"className":1790},[640],[569,1792],{"className":1793,"style":636},[635],[569,1795,1797,1800],{"className":1796},[620],[569,1798],{"className":1799,"style":1726},[624],[569,1801,1757],{"className":1802},[629],". In Fahrenheit ist ",[569,1805,1807,1836],{"className":1806},[572],[569,1808,1810],{"className":1809},[576],[578,1811,1812],{"xmlns":580},[582,1813,1814,1833],{},[585,1815,1816,1819,1821,1824,1826,1828,1830],{},[588,1817,1818],{},"F",[592,1820,594],{},[1289,1822,1823],{},"1,8",[957,1825,959],{},[588,1827,1684],{},[592,1829,603],{},[1289,1831,1832],{},"32",[608,1834,1835],{"encoding":610},"F = 1{,}8\\,C + 32",[569,1837,1839,1858,1894],{"className":1838,"ariaHidden":616},[615],[569,1840,1842,1845,1849,1852,1855],{"className":1841},[620],[569,1843],{"className":1844,"style":625},[624],[569,1846,1818],{"className":1847,"style":1848},[629,630],"margin-right:0.1389em;",[569,1850],{"className":1851,"style":636},[635],[569,1853,594],{"className":1854},[640],[569,1856],{"className":1857,"style":636},[635],[569,1859,1861,1865,1869,1875,1879,1882,1885,1888,1891],{"className":1860},[620],[569,1862],{"className":1863,"style":1864},[624],"height:0.8778em;vertical-align:-0.1944em;",[569,1866,1868],{"className":1867},[629],"1",[569,1870,1872],{"className":1871},[629],[569,1873,1447],{"className":1874},[1594],[569,1876,1878],{"className":1877},[629],"8",[569,1880],{"className":1881,"style":1039},[635],[569,1883,1684],{"className":1884,"style":1699},[629,630],[569,1886],{"className":1887,"style":631},[635],[569,1889,603],{"className":1890},[664],[569,1892],{"className":1893,"style":631},[635],[569,1895,1897,1900],{"className":1896},[620],[569,1898],{"className":1899,"style":1726},[624],[569,1901,1832],{"className":1902},[629],":",[569,1905,1907],{"className":1906},[766],[569,1908,1910,1982],{"className":1909},[572],[569,1911,1913],{"className":1912},[576],[578,1914,1915],{"xmlns":580,"display":775},[582,1916,1917,1979],{},[585,1918,1919,1921,1923,1925,1927,1929,1931,1937,1939,1941,1943,1946,1948,1951,1953,1955,1957,1959,1961,1966,1968,1970,1972,1974,1976],{},[588,1920,1294],{"mathvariant":802},[592,1922,1297],{},[592,1924,786],{"stretchy":785},[588,1926,1818],{},[592,1928,797],{"stretchy":785},[592,1930,594],{},[1284,1932,1933,1935],{},[1289,1934,1823],{},[1289,1936,1291],{},[592,1938,810],{},[1289,1940,1757],{},[592,1942,594],{},[1289,1944,1945],{},"12,96",[592,1947,1447],{"separator":616},[635,1949],{"width":1950},"2em",[588,1952,782],{},[592,1954,786],{"stretchy":785},[588,1956,1818],{},[592,1958,797],{"stretchy":785},[592,1960,594],{},[1962,1963,1964],"msqrt",{},[1289,1965,1945],{},[592,1967,594],{},[1289,1969,1823],{},[592,1971,810],{},[1289,1973,1291],{},[592,1975,594],{},[1289,1977,1978],{},"3,6",[608,1980,1981],{"encoding":610},"\\operatorname{Var}(F) = 1{,}8^2 \\cdot 4 = 12{,}96, \\qquad \\sigma(F) = \\sqrt{12{,}96} = 1{,}8 \\cdot 2 = 3{,}6",[569,1983,1985,2015,2071,2089,2140,2233,2261,2279],{"className":1984,"ariaHidden":616},[615],[569,1986,1988,1991,1997,2000,2003,2006,2009,2012],{"className":1987},[620],[569,1989],{"className":1990,"style":831},[624],[569,1992,1994],{"className":1993},[1364],[569,1995,1294],{"className":1996},[629,1368],[569,1998,786],{"className":1999},[839],[569,2001,1818],{"className":2002,"style":1848},[629,630],[569,2004,797],{"className":2005},[867],[569,2007],{"className":2008,"style":636},[635],[569,2010,594],{"className":2011},[640],[569,2013],{"className":2014,"style":636},[635],[569,2016,2018,2022,2025,2031,2062,2065,2068],{"className":2017},[620],[569,2019],{"className":2020,"style":2021},[624],"height:1.0585em;vertical-align:-0.1944em;",[569,2023,1868],{"className":2024},[629],[569,2026,2028],{"className":2027},[629],[569,2029,1447],{"className":2030},[1594],[569,2032,2034,2037],{"className":2033},[629],[569,2035,1878],{"className":2036},[629],[569,2038,2040],{"className":2039},[1326],[569,2041,2043],{"className":2042},[1330],[569,2044,2046],{"className":2045},[1334],[569,2047,2050],{"className":2048,"style":2049},[1338],"height:0.8641em;",[569,2051,2053,2056],{"style":2052},"top:-3.113em;margin-right:0.05em;",[569,2054],{"className":2055,"style":1347},[1346],[569,2057,2059],{"className":2058},[1351,1352,1353,1354],[569,2060,1291],{"className":2061},[629,1354],[569,2063],{"className":2064,"style":631},[635],[569,2066,810],{"className":2067},[664],[569,2069],{"className":2070,"style":631},[635],[569,2072,2074,2077,2080,2083,2086],{"className":2073},[620],[569,2075],{"className":2076,"style":1726},[624],[569,2078,1757],{"className":2079},[629],[569,2081],{"className":2082,"style":636},[635],[569,2084,594],{"className":2085},[640],[569,2087],{"className":2088,"style":636},[635],[569,2090,2092,2095,2099,2105,2109,2112,2116,2119,2122,2125,2128,2131,2134,2137],{"className":2091},[620],[569,2093],{"className":2094,"style":831},[624],[569,2096,2098],{"className":2097},[629],"12",[569,2100,2102],{"className":2101},[629],[569,2103,1447],{"className":2104},[1594],[569,2106,2108],{"className":2107},[629],"96",[569,2110,1447],{"className":2111},[1594],[569,2113],{"className":2114,"style":2115},[635],"margin-right:2em;",[569,2117],{"className":2118,"style":1039},[635],[569,2120,782],{"className":2121,"style":835},[629,630],[569,2123,786],{"className":2124},[839],[569,2126,1818],{"className":2127,"style":1848},[629,630],[569,2129,797],{"className":2130},[867],[569,2132],{"className":2133,"style":636},[635],[569,2135,594],{"className":2136},[640],[569,2138],{"className":2139,"style":636},[635],[569,2141,2143,2147,2224,2227,2230],{"className":2142},[620],[569,2144],{"className":2145,"style":2146},[624],"height:1.24em;vertical-align:-0.2811em;",[569,2148,2151],{"className":2149},[629,2150],"sqrt",[569,2152,2155,2215],{"className":2153},[1330,2154],"vlist-t2",[569,2156,2158,2210],{"className":2157},[1334],[569,2159,2162,2187],{"className":2160,"style":2161},[1338],"height:0.9589em;",[569,2163,2167,2171],{"className":2164,"style":2166},[2165],"svg-align","top:-3.2em;",[569,2168],{"className":2169,"style":2170},[1346],"height:3.2em;",[569,2172,2175,2178,2184],{"className":2173,"style":2174},[629],"padding-left:1em;",[569,2176,2098],{"className":2177},[629],[569,2179,2181],{"className":2180},[629],[569,2182,1447],{"className":2183},[1594],[569,2185,2108],{"className":2186},[629],[569,2188,2190,2193],{"style":2189},"top:-2.9189em;",[569,2191],{"className":2192,"style":2170},[1346],[569,2194,2198],{"className":2195,"style":2197},[2196],"hide-tail","min-width:1.02em;height:1.28em;",[2199,2200,2206],"svg",{"xmlns":2201,"width":2202,"height":2203,"viewBox":2204,"preserveAspectRatio":2205},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.28em","0 0 400000 1296","xMinYMin slice",[2207,2208],"path",{"d":2209},"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",[569,2211,2214],{"className":2212},[2213],"vlist-s","​",[569,2216,2218],{"className":2217},[1334],[569,2219,2222],{"className":2220,"style":2221},[1338],"height:0.2811em;",[569,2223],{},[569,2225],{"className":2226,"style":636},[635],[569,2228,594],{"className":2229},[640],[569,2231],{"className":2232,"style":636},[635],[569,2234,2236,2240,2243,2249,2252,2255,2258],{"className":2235},[620],[569,2237],{"className":2238,"style":2239},[624],"height:0.8389em;vertical-align:-0.1944em;",[569,2241,1868],{"className":2242},[629],[569,2244,2246],{"className":2245},[629],[569,2247,1447],{"className":2248},[1594],[569,2250,1878],{"className":2251},[629],[569,2253],{"className":2254,"style":631},[635],[569,2256,810],{"className":2257},[664],[569,2259],{"className":2260,"style":631},[635],[569,2262,2264,2267,2270,2273,2276],{"className":2263},[620],[569,2265],{"className":2266,"style":1726},[624],[569,2268,1291],{"className":2269},[629],[569,2271],{"className":2272,"style":636},[635],[569,2274,594],{"className":2275},[640],[569,2277],{"className":2278,"style":636},[635],[569,2280,2282,2285,2289,2295],{"className":2281},[620],[569,2283],{"className":2284,"style":2239},[624],[569,2286,2288],{"className":2287},[629],"3",[569,2290,2292],{"className":2291},[629],[569,2293,1447],{"className":2294},[1594],[569,2296,2298],{"className":2297},[629],"6",[565,2300,685,2301,2336],{},[569,2302,2304,2320],{"className":2303},[572],[569,2305,2307],{"className":2306},[576],[578,2308,2309],{"xmlns":580},[582,2310,2311,2317],{},[585,2312,2313,2315],{},[592,2314,603],{},[1289,2316,1832],{},[608,2318,2319],{"encoding":610},"+32",[569,2321,2323],{"className":2322,"ariaHidden":616},[615],[569,2324,2326,2330,2333],{"className":2325},[620],[569,2327],{"className":2328,"style":2329},[624],"height:0.7278em;vertical-align:-0.0833em;",[569,2331,603],{"className":2332},[629],[569,2334,1832],{"className":2335},[629]," spielt keine Rolle.",[565,2338,2339,2340,2368,2369,2521,2522,1903],{},"Augenzahl ",[569,2341,2343,2356],{"className":2342},[572],[569,2344,2346],{"className":2345},[576],[578,2347,2348],{"xmlns":580},[582,2349,2350,2354],{},[585,2351,2352],{},[588,2353,600],{},[608,2355,600],{"encoding":610},[569,2357,2359],{"className":2358,"ariaHidden":616},[615],[569,2360,2362,2365],{"className":2361},[620],[569,2363],{"className":2364,"style":625},[624],[569,2366,600],{"className":2367,"style":657},[629,630]," eines Würfels mit ",[569,2370,2372,2404],{"className":2371},[572],[569,2373,2375],{"className":2374},[576],[578,2376,2377],{"xmlns":580},[582,2378,2379,2401],{},[585,2380,2381,2383,2385,2387,2389,2391,2393],{},[588,2382,1294],{"mathvariant":802},[592,2384,1297],{},[592,2386,786],{"stretchy":785},[588,2388,600],{},[592,2390,797],{"stretchy":785},[592,2392,594],{},[2394,2395,2396,2399],"mfrac",{},[1289,2397,2398],{},"35",[1289,2400,2098],{},[608,2402,2403],{"encoding":610},"\\operatorname{Var}(X) = \\frac{35}{12}",[569,2405,2407,2437],{"className":2406,"ariaHidden":616},[615],[569,2408,2410,2413,2419,2422,2425,2428,2431,2434],{"className":2409},[620],[569,2411],{"className":2412,"style":831},[624],[569,2414,2416],{"className":2415},[1364],[569,2417,1294],{"className":2418},[629,1368],[569,2420,786],{"className":2421},[839],[569,2423,600],{"className":2424,"style":657},[629,630],[569,2426,797],{"className":2427},[867],[569,2429],{"className":2430,"style":636},[635],[569,2432,594],{"className":2433},[640],[569,2435],{"className":2436,"style":636},[635],[569,2438,2440,2444],{"className":2439},[620],[569,2441],{"className":2442,"style":2443},[624],"height:1.1901em;vertical-align:-0.345em;",[569,2445,2447,2451,2518],{"className":2446},[629],[569,2448],{"className":2449},[839,2450],"nulldelimiter",[569,2452,2454],{"className":2453},[2394],[569,2455,2457,2509],{"className":2456},[1330,2154],[569,2458,2460,2506],{"className":2459},[1334],[569,2461,2464,2480,2491],{"className":2462,"style":2463},[1338],"height:0.8451em;",[569,2465,2467,2471],{"style":2466},"top:-2.655em;",[569,2468],{"className":2469,"style":2470},[1346],"height:3em;",[569,2472,2474],{"className":2473},[1351,1352,1353,1354],[569,2475,2477],{"className":2476},[629,1354],[569,2478,2098],{"className":2479},[629,1354],[569,2481,2483,2486],{"style":2482},"top:-3.23em;",[569,2484],{"className":2485,"style":2470},[1346],[569,2487],{"className":2488,"style":2490},[2489],"frac-line","border-bottom-width:0.04em;",[569,2492,2494,2497],{"style":2493},"top:-3.394em;",[569,2495],{"className":2496,"style":2470},[1346],[569,2498,2500],{"className":2499},[1351,1352,1353,1354],[569,2501,2503],{"className":2502},[629,1354],[569,2504,2398],{"className":2505},[629,1354],[569,2507,2214],{"className":2508},[2213],[569,2510,2512],{"className":2511},[1334],[569,2513,2516],{"className":2514,"style":2515},[1338],"height:0.345em;",[569,2517],{},[569,2519],{"className":2520},[867,2450],". Für den Gewinn ",[569,2523,2525,2545],{"className":2524},[572],[569,2526,2528],{"className":2527},[576],[578,2529,2530],{"xmlns":580},[582,2531,2532,2542],{},[585,2533,2534,2536,2538,2540],{},[1289,2535,1291],{},[588,2537,600],{},[592,2539,1093],{},[1289,2541,2288],{},[608,2543,2544],{"encoding":610},"2X - 3",[569,2546,2548,2569],{"className":2547,"ariaHidden":616},[615],[569,2549,2551,2554,2557,2560,2563,2566],{"className":2550},[620],[569,2552],{"className":2553,"style":650},[624],[569,2555,1291],{"className":2556},[629],[569,2558,600],{"className":2559,"style":657},[629,630],[569,2561],{"className":2562,"style":631},[635],[569,2564,1093],{"className":2565},[664],[569,2567],{"className":2568,"style":631},[635],[569,2570,2572,2575],{"className":2571},[620],[569,2573],{"className":2574,"style":1726},[624],[569,2576,2288],{"className":2577},[629],[569,2579,2581],{"className":2580},[766],[569,2582,2584,2642],{"className":2583},[572],[569,2585,2587],{"className":2586},[576],[578,2588,2589],{"xmlns":580,"display":775},[582,2590,2591,2639],{},[585,2592,2593,2595,2597,2599,2601,2603,2605,2607,2609,2611,2617,2619,2625,2627,2633,2636],{},[588,2594,1294],{"mathvariant":802},[592,2596,1297],{},[592,2598,786],{"stretchy":785},[1289,2600,1291],{},[588,2602,600],{},[592,2604,1093],{},[1289,2606,2288],{},[592,2608,797],{"stretchy":785},[592,2610,594],{},[1284,2612,2613,2615],{},[1289,2614,1291],{},[1289,2616,1291],{},[592,2618,810],{},[2394,2620,2621,2623],{},[1289,2622,2398],{},[1289,2624,2098],{},[592,2626,594],{},[2394,2628,2629,2631],{},[1289,2630,2398],{},[1289,2632,2288],{},[592,2634,2635],{},"≈",[1289,2637,2638],{},"11,67",[608,2640,2641],{"encoding":610},"\\operatorname{Var}(2X - 3) = 2^2 \\cdot \\frac{35}{12} = \\frac{35}{3} \\approx 11{,}67",[569,2643,2645,2675,2696,2740,2822,2899],{"className":2644,"ariaHidden":616},[615],[569,2646,2648,2651,2657,2660,2663,2666,2669,2672],{"className":2647},[620],[569,2649],{"className":2650,"style":831},[624],[569,2652,2654],{"className":2653},[1364],[569,2655,1294],{"className":2656},[629,1368],[569,2658,786],{"className":2659},[839],[569,2661,1291],{"className":2662},[629],[569,2664,600],{"className":2665,"style":657},[629,630],[569,2667],{"className":2668,"style":631},[635],[569,2670,1093],{"className":2671},[664],[569,2673],{"className":2674,"style":631},[635],[569,2676,2678,2681,2684,2687,2690,2693],{"className":2677},[620],[569,2679],{"className":2680,"style":831},[624],[569,2682,2288],{"className":2683},[629],[569,2685,797],{"className":2686},[867],[569,2688],{"className":2689,"style":636},[635],[569,2691,594],{"className":2692},[640],[569,2694],{"className":2695,"style":636},[635],[569,2697,2699,2702,2731,2734,2737],{"className":2698},[620],[569,2700],{"className":2701,"style":2049},[624],[569,2703,2705,2708],{"className":2704},[629],[569,2706,1291],{"className":2707},[629],[569,2709,2711],{"className":2710},[1326],[569,2712,2714],{"className":2713},[1330],[569,2715,2717],{"className":2716},[1334],[569,2718,2720],{"className":2719,"style":2049},[1338],[569,2721,2722,2725],{"style":2052},[569,2723],{"className":2724,"style":1347},[1346],[569,2726,2728],{"className":2727},[1351,1352,1353,1354],[569,2729,1291],{"className":2730},[629,1354],[569,2732],{"className":2733,"style":631},[635],[569,2735,810],{"className":2736},[664],[569,2738],{"className":2739,"style":631},[635],[569,2741,2743,2747,2813,2816,2819],{"className":2742},[620],[569,2744],{"className":2745,"style":2746},[624],"height:2.0074em;vertical-align:-0.686em;",[569,2748,2750,2753,2810],{"className":2749},[629],[569,2751],{"className":2752},[839,2450],[569,2754,2756],{"className":2755},[2394],[569,2757,2759,2801],{"className":2758},[1330,2154],[569,2760,2762,2798],{"className":2761},[1334],[569,2763,2766,2778,2786],{"className":2764,"style":2765},[1338],"height:1.3214em;",[569,2767,2769,2772],{"style":2768},"top:-2.314em;",[569,2770],{"className":2771,"style":2470},[1346],[569,2773,2775],{"className":2774},[629],[569,2776,2098],{"className":2777},[629],[569,2779,2780,2783],{"style":2482},[569,2781],{"className":2782,"style":2470},[1346],[569,2784],{"className":2785,"style":2490},[2489],[569,2787,2789,2792],{"style":2788},"top:-3.677em;",[569,2790],{"className":2791,"style":2470},[1346],[569,2793,2795],{"className":2794},[629],[569,2796,2398],{"className":2797},[629],[569,2799,2214],{"className":2800},[2213],[569,2802,2804],{"className":2803},[1334],[569,2805,2808],{"className":2806,"style":2807},[1338],"height:0.686em;",[569,2809],{},[569,2811],{"className":2812},[867,2450],[569,2814],{"className":2815,"style":636},[635],[569,2817,594],{"className":2818},[640],[569,2820],{"className":2821,"style":636},[635],[569,2823,2825,2828,2890,2893,2896],{"className":2824},[620],[569,2826],{"className":2827,"style":2746},[624],[569,2829,2831,2834,2887],{"className":2830},[629],[569,2832],{"className":2833},[839,2450],[569,2835,2837],{"className":2836},[2394],[569,2838,2840,2879],{"className":2839},[1330,2154],[569,2841,2843,2876],{"className":2842},[1334],[569,2844,2846,2857,2865],{"className":2845,"style":2765},[1338],[569,2847,2848,2851],{"style":2768},[569,2849],{"className":2850,"style":2470},[1346],[569,2852,2854],{"className":2853},[629],[569,2855,2288],{"className":2856},[629],[569,2858,2859,2862],{"style":2482},[569,2860],{"className":2861,"style":2470},[1346],[569,2863],{"className":2864,"style":2490},[2489],[569,2866,2867,2870],{"style":2788},[569,2868],{"className":2869,"style":2470},[1346],[569,2871,2873],{"className":2872},[629],[569,2874,2398],{"className":2875},[629],[569,2877,2214],{"className":2878},[2213],[569,2880,2882],{"className":2881},[1334],[569,2883,2885],{"className":2884,"style":2807},[1338],[569,2886],{},[569,2888],{"className":2889},[867,2450],[569,2891],{"className":2892,"style":636},[635],[569,2894,2635],{"className":2895},[640],[569,2897],{"className":2898,"style":636},[635],[569,2900,2902,2905,2909,2915],{"className":2901},[620],[569,2903],{"className":2904,"style":2239},[624],[569,2906,2908],{"className":2907},[629],"11",[569,2910,2912],{"className":2911},[629],[569,2913,1447],{"className":2914},[1594],[569,2916,2918],{"className":2917},[629],"67",[560,2920,2922],{"id":2921},"typische-fehler","Typische Fehler",[680,2924,2925,3209,3457,3766],{},[683,2926,2927,2928,3208],{},"Den Faktor nicht quadrieren. ",[569,2929,2931,2979],{"className":2930},[572],[569,2932,2934],{"className":2933},[576],[578,2935,2936],{"xmlns":580},[582,2937,2938,2976],{},[585,2939,2940,2942,2944,2946,2948,2950,2952,2954,2956,2958,2960,2962,2968,2970],{},[588,2941,1294],{"mathvariant":802},[592,2943,1297],{},[592,2945,786],{"stretchy":785},[1289,2947,1291],{},[588,2949,600],{},[592,2951,1093],{},[1289,2953,2288],{},[592,2955,797],{"stretchy":785},[592,2957,594],{},[1289,2959,1291],{},[592,2961,810],{},[2394,2963,2964,2966],{},[1289,2965,2398],{},[1289,2967,2098],{},[592,2969,594],{},[2394,2971,2972,2974],{},[1289,2973,2398],{},[1289,2975,2298],{},[608,2977,2978],{"encoding":610},"\\operatorname{Var}(2X - 3) = 2 \\cdot \\frac{35}{12} = \\frac{35}{6}",[569,2980,2982,3012,3033,3051,3134],{"className":2981,"ariaHidden":616},[615],[569,2983,2985,2988,2994,2997,3000,3003,3006,3009],{"className":2984},[620],[569,2986],{"className":2987,"style":831},[624],[569,2989,2991],{"className":2990},[1364],[569,2992,1294],{"className":2993},[629,1368],[569,2995,786],{"className":2996},[839],[569,2998,1291],{"className":2999},[629],[569,3001,600],{"className":3002,"style":657},[629,630],[569,3004],{"className":3005,"style":631},[635],[569,3007,1093],{"className":3008},[664],[569,3010],{"className":3011,"style":631},[635],[569,3013,3015,3018,3021,3024,3027,3030],{"className":3014},[620],[569,3016],{"className":3017,"style":831},[624],[569,3019,2288],{"className":3020},[629],[569,3022,797],{"className":3023},[867],[569,3025],{"className":3026,"style":636},[635],[569,3028,594],{"className":3029},[640],[569,3031],{"className":3032,"style":636},[635],[569,3034,3036,3039,3042,3045,3048],{"className":3035},[620],[569,3037],{"className":3038,"style":1726},[624],[569,3040,1291],{"className":3041},[629],[569,3043],{"className":3044,"style":631},[635],[569,3046,810],{"className":3047},[664],[569,3049],{"className":3050,"style":631},[635],[569,3052,3054,3057,3125,3128,3131],{"className":3053},[620],[569,3055],{"className":3056,"style":2443},[624],[569,3058,3060,3063,3122],{"className":3059},[629],[569,3061],{"className":3062},[839,2450],[569,3064,3066],{"className":3065},[2394],[569,3067,3069,3114],{"className":3068},[1330,2154],[569,3070,3072,3111],{"className":3071},[1334],[569,3073,3075,3089,3097],{"className":3074,"style":2463},[1338],[569,3076,3077,3080],{"style":2466},[569,3078],{"className":3079,"style":2470},[1346],[569,3081,3083],{"className":3082},[1351,1352,1353,1354],[569,3084,3086],{"className":3085},[629,1354],[569,3087,2098],{"className":3088},[629,1354],[569,3090,3091,3094],{"style":2482},[569,3092],{"className":3093,"style":2470},[1346],[569,3095],{"className":3096,"style":2490},[2489],[569,3098,3099,3102],{"style":2493},[569,3100],{"className":3101,"style":2470},[1346],[569,3103,3105],{"className":3104},[1351,1352,1353,1354],[569,3106,3108],{"className":3107},[629,1354],[569,3109,2398],{"className":3110},[629,1354],[569,3112,2214],{"className":3113},[2213],[569,3115,3117],{"className":3116},[1334],[569,3118,3120],{"className":3119,"style":2515},[1338],[569,3121],{},[569,3123],{"className":3124},[867,2450],[569,3126],{"className":3127,"style":636},[635],[569,3129,594],{"className":3130},[640],[569,3132],{"className":3133,"style":636},[635],[569,3135,3137,3140],{"className":3136},[620],[569,3138],{"className":3139,"style":2443},[624],[569,3141,3143,3146,3205],{"className":3142},[629],[569,3144],{"className":3145},[839,2450],[569,3147,3149],{"className":3148},[2394],[569,3150,3152,3197],{"className":3151},[1330,2154],[569,3153,3155,3194],{"className":3154},[1334],[569,3156,3158,3172,3180],{"className":3157,"style":2463},[1338],[569,3159,3160,3163],{"style":2466},[569,3161],{"className":3162,"style":2470},[1346],[569,3164,3166],{"className":3165},[1351,1352,1353,1354],[569,3167,3169],{"className":3168},[629,1354],[569,3170,2298],{"className":3171},[629,1354],[569,3173,3174,3177],{"style":2482},[569,3175],{"className":3176,"style":2470},[1346],[569,3178],{"className":3179,"style":2490},[2489],[569,3181,3182,3185],{"style":2493},[569,3183],{"className":3184,"style":2470},[1346],[569,3186,3188],{"className":3187},[1351,1352,1353,1354],[569,3189,3191],{"className":3190},[629,1354],[569,3192,2398],{"className":3193},[629,1354],[569,3195,2214],{"className":3196},[2213],[569,3198,3200],{"className":3199},[1334],[569,3201,3203],{"className":3202,"style":2515},[1338],[569,3204],{},[569,3206],{"className":3207},[867,2450]," ist falsch.",[683,3210,3211,3212,3390,3391,3456],{},"Die Verschiebung mitnehmen, also ",[569,3213,3215,3265],{"className":3214},[572],[569,3216,3218],{"className":3217},[576],[578,3219,3220],{"xmlns":580},[582,3221,3222,3262],{},[585,3223,3224,3226,3228,3230,3232,3234,3236,3238,3240,3242,3248,3250,3252,3254,3256,3258,3260],{},[588,3225,1294],{"mathvariant":802},[592,3227,1297],{},[592,3229,786],{"stretchy":785},[588,3231,597],{},[588,3233,600],{},[592,3235,603],{},[588,3237,606],{},[592,3239,797],{"stretchy":785},[592,3241,594],{},[1284,3243,3244,3246],{},[588,3245,597],{},[1289,3247,1291],{},[588,3249,1294],{"mathvariant":802},[592,3251,1297],{},[592,3253,786],{"stretchy":785},[588,3255,600],{},[592,3257,797],{"stretchy":785},[592,3259,603],{},[588,3261,606],{},[608,3263,3264],{"encoding":610},"\\operatorname{Var}(aX + b) = a^2 \\operatorname{Var}(X) + b",[569,3266,3268,3298,3319,3381],{"className":3267,"ariaHidden":616},[615],[569,3269,3271,3274,3280,3283,3286,3289,3292,3295],{"className":3270},[620],[569,3272],{"className":3273,"style":831},[624],[569,3275,3277],{"className":3276},[1364],[569,3278,1294],{"className":3279},[629,1368],[569,3281,786],{"className":3282},[839],[569,3284,597],{"className":3285},[629,630],[569,3287,600],{"className":3288,"style":657},[629,630],[569,3290],{"className":3291,"style":631},[635],[569,3293,603],{"className":3294},[664],[569,3296],{"className":3297,"style":631},[635],[569,3299,3301,3304,3307,3310,3313,3316],{"className":3300},[620],[569,3302],{"className":3303,"style":831},[624],[569,3305,606],{"className":3306},[629,630],[569,3308,797],{"className":3309},[867],[569,3311],{"className":3312,"style":636},[635],[569,3314,594],{"className":3315},[640],[569,3317],{"className":3318,"style":636},[635],[569,3320,3322,3325,3354,3357,3363,3366,3369,3372,3375,3378],{"className":3321},[620],[569,3323],{"className":3324,"style":1316},[624],[569,3326,3328,3331],{"className":3327},[629],[569,3329,597],{"className":3330},[629,630],[569,3332,3334],{"className":3333},[1326],[569,3335,3337],{"className":3336},[1330],[569,3338,3340],{"className":3339},[1334],[569,3341,3343],{"className":3342,"style":1339},[1338],[569,3344,3345,3348],{"style":1342},[569,3346],{"className":3347,"style":1347},[1346],[569,3349,3351],{"className":3350},[1351,1352,1353,1354],[569,3352,1291],{"className":3353},[629,1354],[569,3355],{"className":3356,"style":1039},[635],[569,3358,3360],{"className":3359},[1364],[569,3361,1294],{"className":3362},[629,1368],[569,3364,786],{"className":3365},[839],[569,3367,600],{"className":3368,"style":657},[629,630],[569,3370,797],{"className":3371},[867],[569,3373],{"className":3374,"style":631},[635],[569,3376,603],{"className":3377},[664],[569,3379],{"className":3380,"style":631},[635],[569,3382,3384,3387],{"className":3383},[620],[569,3385],{"className":3386,"style":674},[624],[569,3388,606],{"className":3389},[629,630]," oder ",[569,3392,3394,3414],{"className":3393},[572],[569,3395,3397],{"className":3396},[576],[578,3398,3399],{"xmlns":580},[582,3400,3401,3411],{},[585,3402,3403,3405],{},[592,3404,603],{},[1284,3406,3407,3409],{},[588,3408,606],{},[1289,3410,1291],{},[608,3412,3413],{"encoding":610},"+ b^2",[569,3415,3417],{"className":3416,"ariaHidden":616},[615],[569,3418,3420,3424,3427],{"className":3419},[620],[569,3421],{"className":3422,"style":3423},[624],"height:0.8974em;vertical-align:-0.0833em;",[569,3425,603],{"className":3426},[629],[569,3428,3430,3433],{"className":3429},[629],[569,3431,606],{"className":3432},[629,630],[569,3434,3436],{"className":3435},[1326],[569,3437,3439],{"className":3438},[1330],[569,3440,3442],{"className":3441},[1334],[569,3443,3445],{"className":3444,"style":1339},[1338],[569,3446,3447,3450],{"style":1342},[569,3448],{"className":3449,"style":1347},[1346],[569,3451,3453],{"className":3452},[1351,1352,1353,1354],[569,3454,1291],{"className":3455},[629,1354]," schreiben.",[683,3458,3459,3460,3488,3489,1633,3680,1378],{},"Bei negativem ",[569,3461,3463,3476],{"className":3462},[572],[569,3464,3466],{"className":3465},[576],[578,3467,3468],{"xmlns":580},[582,3469,3470,3474],{},[585,3471,3472],{},[588,3473,597],{},[608,3475,597],{"encoding":610},[569,3477,3479],{"className":3478,"ariaHidden":616},[615],[569,3480,3482,3485],{"className":3481},[620],[569,3483],{"className":3484,"style":751},[624],[569,3486,597],{"className":3487},[629,630]," eine negative Varianz oder Standardabweichung angeben. Es ist ",[569,3490,3492,3552],{"className":3491},[572],[569,3493,3495],{"className":3494},[576],[578,3496,3497],{"xmlns":580},[582,3498,3499,3549],{},[585,3500,3501,3503,3505,3507,3509,3511,3513,3515,3517,3519,3521,3527,3529,3531,3533,3535,3537,3539,3541,3543,3545,3547],{},[588,3502,1294],{"mathvariant":802},[592,3504,1297],{},[592,3506,786],{"stretchy":785},[592,3508,1093],{},[588,3510,600],{},[592,3512,797],{"stretchy":785},[592,3514,594],{},[592,3516,786],{"stretchy":785},[592,3518,1093],{},[1289,3520,1868],{},[1284,3522,3523,3525],{},[592,3524,797],{"stretchy":785},[1289,3526,1291],{},[588,3528,1294],{"mathvariant":802},[592,3530,1297],{},[592,3532,786],{"stretchy":785},[588,3534,600],{},[592,3536,797],{"stretchy":785},[592,3538,594],{},[588,3540,1294],{"mathvariant":802},[592,3542,1297],{},[592,3544,786],{"stretchy":785},[588,3546,600],{},[592,3548,797],{"stretchy":785},[608,3550,3551],{"encoding":610},"\\operatorname{Var}(-X) = (-1)^2 \\operatorname{Var}(X) = \\operatorname{Var}(X)",[569,3553,3555,3588,3659],{"className":3554,"ariaHidden":616},[615],[569,3556,3558,3561,3567,3570,3573,3576,3579,3582,3585],{"className":3557},[620],[569,3559],{"className":3560,"style":831},[624],[569,3562,3564],{"className":3563},[1364],[569,3565,1294],{"className":3566},[629,1368],[569,3568,786],{"className":3569},[839],[569,3571,1093],{"className":3572},[629],[569,3574,600],{"className":3575,"style":657},[629,630],[569,3577,797],{"className":3578},[867],[569,3580],{"className":3581,"style":636},[635],[569,3583,594],{"className":3584},[640],[569,3586],{"className":3587,"style":636},[635],[569,3589,3591,3594,3597,3600,3603,3632,3635,3641,3644,3647,3650,3653,3656],{"className":3590},[620],[569,3592],{"className":3593,"style":1316},[624],[569,3595,786],{"className":3596},[839],[569,3598,1093],{"className":3599},[629],[569,3601,1868],{"className":3602},[629],[569,3604,3606,3609],{"className":3605},[867],[569,3607,797],{"className":3608},[867],[569,3610,3612],{"className":3611},[1326],[569,3613,3615],{"className":3614},[1330],[569,3616,3618],{"className":3617},[1334],[569,3619,3621],{"className":3620,"style":1339},[1338],[569,3622,3623,3626],{"style":1342},[569,3624],{"className":3625,"style":1347},[1346],[569,3627,3629],{"className":3628},[1351,1352,1353,1354],[569,3630,1291],{"className":3631},[629,1354],[569,3633],{"className":3634,"style":1039},[635],[569,3636,3638],{"className":3637},[1364],[569,3639,1294],{"className":3640},[629,1368],[569,3642,786],{"className":3643},[839],[569,3645,600],{"className":3646,"style":657},[629,630],[569,3648,797],{"className":3649},[867],[569,3651],{"className":3652,"style":636},[635],[569,3654,594],{"className":3655},[640],[569,3657],{"className":3658,"style":636},[635],[569,3660,3662,3665,3671,3674,3677],{"className":3661},[620],[569,3663],{"className":3664,"style":831},[624],[569,3666,3668],{"className":3667},[1364],[569,3669,1294],{"className":3670},[629,1368],[569,3672,786],{"className":3673},[839],[569,3675,600],{"className":3676,"style":657},[629,630],[569,3678,797],{"className":3679},[867],[569,3681,3683,3715],{"className":3682},[572],[569,3684,3686],{"className":3685},[576],[578,3687,3688],{"xmlns":580},[582,3689,3690,3712],{},[585,3691,3692,3694,3696,3698,3700,3702,3704,3706,3708,3710],{},[588,3693,782],{},[592,3695,786],{"stretchy":785},[592,3697,1093],{},[588,3699,600],{},[592,3701,797],{"stretchy":785},[592,3703,594],{},[588,3705,782],{},[592,3707,786],{"stretchy":785},[588,3709,600],{},[592,3711,797],{"stretchy":785},[608,3713,3714],{"encoding":610},"\\sigma(-X) = \\sigma(X)",[569,3716,3718,3748],{"className":3717,"ariaHidden":616},[615],[569,3719,3721,3724,3727,3730,3733,3736,3739,3742,3745],{"className":3720},[620],[569,3722],{"className":3723,"style":831},[624],[569,3725,782],{"className":3726,"style":835},[629,630],[569,3728,786],{"className":3729},[839],[569,3731,1093],{"className":3732},[629],[569,3734,600],{"className":3735,"style":657},[629,630],[569,3737,797],{"className":3738},[867],[569,3740],{"className":3741,"style":636},[635],[569,3743,594],{"className":3744},[640],[569,3746],{"className":3747,"style":636},[635],[569,3749,3751,3754,3757,3760,3763],{"className":3750},[620],[569,3752],{"className":3753,"style":831},[624],[569,3755,782],{"className":3756,"style":835},[629,630],[569,3758,786],{"className":3759},[839],[569,3761,600],{"className":3762,"style":657},[629,630],[569,3764,797],{"className":3765},[867],[683,3767,3768,3889,3890,3918,3919,1378],{},[569,3769,3771,3811],{"className":3770},[572],[569,3772,3774],{"className":3773},[576],[578,3775,3776],{"xmlns":580},[582,3777,3778,3808],{},[585,3779,3780,3782,3784,3786,3788,3790,3792,3794,3796,3798,3800,3802,3804,3806],{},[588,3781,1294],{"mathvariant":802},[592,3783,1297],{},[592,3785,786],{"stretchy":785},[588,3787,600],{},[592,3789,603],{},[588,3791,600],{},[592,3793,797],{"stretchy":785},[592,3795,594],{},[1289,3797,1291],{},[588,3799,1294],{"mathvariant":802},[592,3801,1297],{},[592,3803,786],{"stretchy":785},[588,3805,600],{},[592,3807,797],{"stretchy":785},[608,3809,3810],{"encoding":610},"\\operatorname{Var}(X + X) = 2\\operatorname{Var}(X)",[569,3812,3814,3841,3862],{"className":3813,"ariaHidden":616},[615],[569,3815,3817,3820,3826,3829,3832,3835,3838],{"className":3816},[620],[569,3818],{"className":3819,"style":831},[624],[569,3821,3823],{"className":3822},[1364],[569,3824,1294],{"className":3825},[629,1368],[569,3827,786],{"className":3828},[839],[569,3830,600],{"className":3831,"style":657},[629,630],[569,3833],{"className":3834,"style":631},[635],[569,3836,603],{"className":3837},[664],[569,3839],{"className":3840,"style":631},[635],[569,3842,3844,3847,3850,3853,3856,3859],{"className":3843},[620],[569,3845],{"className":3846,"style":831},[624],[569,3848,600],{"className":3849,"style":657},[629,630],[569,3851,797],{"className":3852},[867],[569,3854],{"className":3855,"style":636},[635],[569,3857,594],{"className":3858},[640],[569,3860],{"className":3861,"style":636},[635],[569,3863,3865,3868,3871,3874,3880,3883,3886],{"className":3864},[620],[569,3866],{"className":3867,"style":831},[624],[569,3869,1291],{"className":3870},[629],[569,3872],{"className":3873,"style":1039},[635],[569,3875,3877],{"className":3876},[1364],[569,3878,1294],{"className":3879},[629,1368],[569,3881,786],{"className":3882},[839],[569,3884,600],{"className":3885,"style":657},[629,630],[569,3887,797],{"className":3888},[867]," annehmen. Da ",[569,3891,3893,3906],{"className":3892},[572],[569,3894,3896],{"className":3895},[576],[578,3897,3898],{"xmlns":580},[582,3899,3900,3904],{},[585,3901,3902],{},[588,3903,600],{},[608,3905,600],{"encoding":610},[569,3907,3909],{"className":3908,"ariaHidden":616},[615],[569,3910,3912,3915],{"className":3911},[620],[569,3913],{"className":3914,"style":625},[624],[569,3916,600],{"className":3917,"style":657},[629,630]," mit sich selbst vollständig korreliert ist, gilt ",[569,3920,3922,3960],{"className":3921},[572],[569,3923,3925],{"className":3924},[576],[578,3926,3927],{"xmlns":580},[582,3928,3929,3957],{},[585,3930,3931,3933,3935,3937,3939,3941,3943,3945,3947,3949,3951,3953,3955],{},[588,3932,1294],{"mathvariant":802},[592,3934,1297],{},[592,3936,786],{"stretchy":785},[1289,3938,1291],{},[588,3940,600],{},[592,3942,797],{"stretchy":785},[592,3944,594],{},[1289,3946,1757],{},[588,3948,1294],{"mathvariant":802},[592,3950,1297],{},[592,3952,786],{"stretchy":785},[588,3954,600],{},[592,3956,797],{"stretchy":785},[608,3958,3959],{"encoding":610},"\\operatorname{Var}(2X) = 4\\operatorname{Var}(X)",[569,3961,3963,3996],{"className":3962,"ariaHidden":616},[615],[569,3964,3966,3969,3975,3978,3981,3984,3987,3990,3993],{"className":3965},[620],[569,3967],{"className":3968,"style":831},[624],[569,3970,3972],{"className":3971},[1364],[569,3973,1294],{"className":3974},[629,1368],[569,3976,786],{"className":3977},[839],[569,3979,1291],{"className":3980},[629],[569,3982,600],{"className":3983,"style":657},[629,630],[569,3985,797],{"className":3986},[867],[569,3988],{"className":3989,"style":636},[635],[569,3991,594],{"className":3992},[640],[569,3994],{"className":3995,"style":636},[635],[569,3997,3999,4002,4005,4008,4014,4017,4020],{"className":3998},[620],[569,4000],{"className":4001,"style":831},[624],[569,4003,1757],{"className":4004},[629],[569,4006],{"className":4007,"style":1039},[635],[569,4009,4011],{"className":4010},[1364],[569,4012,1294],{"className":4013},[629,1368],[569,4015,786],{"className":4016},[839],[569,4018,600],{"className":4019,"style":657},[629,630],[569,4021,797],{"className":4022},[867],{"title":4024,"searchDepth":4025,"depth":4025,"links":4026},"",2,[4027,4028,4029],{"id":562,"depth":4025,"text":563},{"id":1665,"depth":4025,"text":1666},{"id":2921,"depth":4025,"text":2922},[4031,4034,4037,4040,4042,4045,4048,4051],{"lhs":4032,"rhs":4033},"((a*x1 + b) - (a*(x1*p + x2*(1-p)) + b))^2 * p + ((a*x2 + b) - (a*(x1*p + x2*(1-p)) + b))^2 * (1-p)","a^2 * ((x1 - (x1*p + x2*(1-p)))^2 * p + (x2 - (x1*p + x2*(1-p)))^2 * (1-p))",{"lhs":4035,"rhs":4036},"1.8^2 * 4","12.96",{"lhs":4038,"rhs":4039},"sqrt(12.96)","3.6",{"lhs":4041,"rhs":4039},"1.8 * 2",{"lhs":4043,"rhs":4044},"2^2 * 35\u002F12","35\u002F3",{"lhs":4046,"rhs":4047},"round(35\u002F3, 2)","11.67",{"lhs":4049,"rhs":4050},"(-1)^2 * 35\u002F12","35\u002F12",{"lhs":4052,"rhs":4053},"2 * 35\u002F12","35\u002F6","a, b \\in \\mathbb{R},\\ \\operatorname{Var}(X) \\text{ existiert}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\in \\mathbb{R},\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\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 mathvariant=\"normal\">Var\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Var}(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=\"mop\">\u003Cspan class=\"mord mathrm\">Var\u003C\u002Fspan>\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> \u003Cspan class=\"katex\">existiert\u003C\u002Fspan>",null,"md","variance-linear-transformation","\\operatorname{Var}(aX + b) = a^2 \\operatorname{Var}(X)","\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 mathvariant=\"normal\">Var\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmi mathvariant=\"normal\">Var\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Var}(aX + b) = a^2 \\operatorname{Var}(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=\"mop\">\u003Cspan class=\"mord mathrm\">Var\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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\">b\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:1.1141em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">Var\u003C\u002Fspan>\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>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation",[],[4067,4068,4069,4070],"variance-random-variable","expectation-linearity","standard-deviation","covariance",{"title":548,"description":4024},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-lineare-transformation","Eine Verschiebung um b ändert die Varianz nicht, ein Faktor a geht quadriert ein.",[4075,4076,4077,4078],"varianz","lineare transformation","standardabweichung","rechenregeln",[4080,4084,4087,4090],{"symbol":4081,"meaning":4082,"symbolHtml":4083},"\\operatorname{Var}(X)","Varianz der Zufallsgröße X, in der Schule oft V(X)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Var\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Var}(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=\"mop\">\u003Cspan class=\"mord mathrm\">Var\u003C\u002Fspan>\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":600,"meaning":4085,"symbolHtml":4086},"Zufallsgröße","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":597,"meaning":4088,"symbolHtml":4089},"Streckfaktor","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\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\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":606,"meaning":689,"symbolHtml":4091},"\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\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\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","Pr74JarsbqSjtdxPBdw8jFBf2RhCen20Z2oJPRfVEho",[4094,4097,4100,4103],{"stem":4095,"title":4096,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fkovarianz","Kovarianz",{"stem":4098,"title":4099,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Flinearitaet-des-erwartungswerts","Linearität des Erwartungswerts",{"stem":4101,"title":4102,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstandardabweichung","Standardabweichung",{"stem":4104,"title":4105,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Varianz einer Zufallsgröße",1793824288211]