[{"data":1,"prerenderedAt":4096},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-naeherung":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-naeherung":4083},[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":4009,"conditions":4040,"conditionsHtml":4041,"deprecated":4042,"description":4003,"extension":4043,"figure":4042,"figureCaption":4042,"figureHtml":4042,"formulaId":4044,"latex":4045,"latexHtml":4046,"level":4047,"meta":4048,"navigation":4049,"path":4050,"redirectFrom":4051,"related":4052,"seo":4057,"stem":4058,"subject":578,"summary":4059,"tags":4060,"variables":4066,"__hash__":4082},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-naeherung.md","Poisson-Näherung der Binomialverteilung",[550,551,552,553,554,555],"Poisson-Approximation","Poissonscher Grenzwertsatz","Binomialverteilung durch Poisson nähern","Gesetz der seltenen Ereignisse","Poisson-Näherung Faustregel","n groß p klein",{"type":557,"value":558,"toc":4002},"minimark",[559,564,714,918,1358,1597,1938,1974,1978,2202,2205,2485,2488,2899,3089,3614,3618],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,614,615,644,645,649,650,713],"p",{},"Bei sehr vielen Versuchen (",[569,570,573,595],"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",[582,583,584,591],"semantics",{},[585,586,587],"mrow",{},[588,589,590],"mi",{},"n",[592,593,590],"annotation",{"encoding":594},"application\u002Fx-tex",[569,596,600],{"className":597,"ariaHidden":599},[598],"katex-html","true",[569,601,604,609],{"className":602},[603],"base",[569,605],{"className":606,"style":608},[607],"strut","height:0.4306em;",[569,610,590],{"className":611},[612,613],"mord","mathnormal"," groß) mit seltenen Treffern (",[569,616,618,631],{"className":617},[572],[569,619,621],{"className":620},[576],[578,622,623],{"xmlns":580},[582,624,625,629],{},[585,626,627],{},[588,628,565],{},[592,630,565],{"encoding":594},[569,632,634],{"className":633,"ariaHidden":599},[598],[569,635,637,641],{"className":636},[603],[569,638],{"className":639,"style":640},[607],"height:0.625em;vertical-align:-0.1944em;",[569,642,565],{"className":643},[612,613]," klein) ist die Binomialverteilung mühsam zu berechnen, weil große Binomialkoeffizienten und kleine Potenzen zusammenkommen. Die ",[646,647,648],"strong",{},"Poisson-Näherung"," ersetzt sie durch die Poisson-Verteilung mit demselben Erwartungswert ",[569,651,653,676],{"className":652},[572],[569,654,656],{"className":655},[576],[578,657,658],{"xmlns":580},[582,659,660,673],{},[585,661,662,665,669,671],{},[588,663,664],{},"λ",[666,667,668],"mo",{},"=",[588,670,590],{},[588,672,565],{},[592,674,675],{"encoding":594},"\\lambda = n p",[569,677,679,701],{"className":678,"ariaHidden":599},[598],[569,680,682,686,689,694,698],{"className":681},[603],[569,683],{"className":684,"style":685},[607],"height:0.6944em;",[569,687,664],{"className":688},[612,613],[569,690],{"className":691,"style":693},[692],"mspace","margin-right:0.2778em;",[569,695,668],{"className":696},[697],"mrel",[569,699],{"className":700,"style":693},[692],[569,702,704,707,710],{"className":703},[603],[569,705],{"className":706,"style":640},[607],[569,708,590],{"className":709},[612,613],[569,711,565],{"className":712},[612,613],".",[565,715,716,717,720,721,775,776,830,831,887,888],{},"Grundlage ist der ",[646,718,719],{},"Poissonsche Grenzwertsatz",": Lässt man ",[569,722,724,745],{"className":723},[572],[569,725,727],{"className":726},[576],[578,728,729],{"xmlns":580},[582,730,731,742],{},[585,732,733,735,738],{},[588,734,590],{},[666,736,737],{},"→",[588,739,741],{"mathvariant":740},"normal","∞",[592,743,744],{"encoding":594},"n \\to \\infty",[569,746,748,766],{"className":747,"ariaHidden":599},[598],[569,749,751,754,757,760,763],{"className":750},[603],[569,752],{"className":753,"style":608},[607],[569,755,590],{"className":756},[612,613],[569,758],{"className":759,"style":693},[692],[569,761,737],{"className":762},[697],[569,764],{"className":765,"style":693},[692],[569,767,769,772],{"className":768},[603],[569,770],{"className":771,"style":608},[607],[569,773,741],{"className":774},[612]," und ",[569,777,779,799],{"className":778},[572],[569,780,782],{"className":781},[576],[578,783,784],{"xmlns":580},[582,785,786,796],{},[585,787,788,790,792],{},[588,789,565],{},[666,791,737],{},[793,794,795],"mn",{},"0",[592,797,798],{"encoding":594},"p \\to 0",[569,800,802,820],{"className":801,"ariaHidden":599},[598],[569,803,805,808,811,814,817],{"className":804},[603],[569,806],{"className":807,"style":640},[607],[569,809,565],{"className":810},[612,613],[569,812],{"className":813,"style":693},[692],[569,815,737],{"className":816},[697],[569,818],{"className":819,"style":693},[692],[569,821,823,827],{"className":822},[603],[569,824],{"className":825,"style":826},[607],"height:0.6444em;",[569,828,795],{"className":829},[612]," so laufen, dass ",[569,832,834,854],{"className":833},[572],[569,835,837],{"className":836},[576],[578,838,839],{"xmlns":580},[582,840,841,851],{},[585,842,843,845,847,849],{},[588,844,590],{},[588,846,565],{},[666,848,668],{},[588,850,664],{},[592,852,853],{"encoding":594},"n p = \\lambda",[569,855,857,878],{"className":856,"ariaHidden":599},[598],[569,858,860,863,866,869,872,875],{"className":859},[603],[569,861],{"className":862,"style":640},[607],[569,864,590],{"className":865},[612,613],[569,867,565],{"className":868},[612,613],[569,870],{"className":871,"style":693},[692],[569,873,668],{"className":874},[697],[569,876],{"className":877,"style":693},[692],[569,879,881,884],{"className":880},[603],[569,882],{"className":883,"style":685},[607],[569,885,664],{"className":886},[612,613]," fest bleibt, dann gilt für jedes feste ",[569,889,891,905],{"className":890},[572],[569,892,894],{"className":893},[576],[578,895,896],{"xmlns":580},[582,897,898,903],{},[585,899,900],{},[588,901,902],{},"k",[592,904,902],{"encoding":594},[569,906,908],{"className":907,"ariaHidden":599},[598],[569,909,911,914],{"className":910},[603],[569,912],{"className":913,"style":685},[607],[569,915,902],{"className":916,"style":917},[612,613],"margin-right:0.0315em;",[569,919,922],{"className":920},[921],"katex-display",[569,923,925,1016],{"className":924},[572],[569,926,928],{"className":927},[576],[578,929,931],{"xmlns":580,"display":930},"block",[582,932,933,1013],{},[585,934,935,951,958,961,964,967,969,981,983,998,1002],{},[585,936,937,940,948],{},[666,938,939],{"fence":599},"(",[941,942,944,946],"mfrac",{"linethickness":943},"0px",[588,945,590],{},[588,947,902],{},[666,949,950],{"fence":599},")",[952,953,954,956],"msup",{},[588,955,565],{},[588,957,902],{},[666,959,939],{"stretchy":960},"false",[793,962,963],{},"1",[666,965,966],{},"−",[588,968,565],{},[952,970,971,973],{},[666,972,950],{"stretchy":960},[585,974,975,977,979],{},[588,976,590],{},[666,978,966],{},[588,980,902],{},[666,982,737],{},[941,984,985,991],{},[952,986,987,989],{},[588,988,664],{},[588,990,902],{},[585,992,993,995],{},[588,994,902],{},[666,996,997],{"stretchy":960},"!",[999,1000,1001],"mtext",{}," ",[952,1003,1004,1007],{},[588,1005,1006],{},"e",[585,1008,1009,1011],{},[666,1010,966],{},[588,1012,664],{},[592,1014,1015],{"encoding":594},"\\binom{n}{k} p^k (1 - p)^{n-k} \\to \\frac{\\lambda^k}{k!}\\, e^{-\\lambda}",[569,1017,1019,1157,1214],{"className":1018,"ariaHidden":599},[598],[569,1020,1022,1026,1104,1140,1143,1146,1150,1154],{"className":1021},[603],[569,1023],{"className":1024,"style":1025},[607],"height:2.4em;vertical-align:-0.95em;",[569,1027,1029,1040,1097],{"className":1028},[612],[569,1030,1035],{"className":1031,"style":1034},[1032,1033],"mopen","delimcenter","top:0em;",[569,1036,939],{"className":1037},[1038,1039],"delimsizing","size3",[569,1041,1043],{"className":1042},[941],[569,1044,1048,1088],{"className":1045},[1046,1047],"vlist-t","vlist-t2",[569,1049,1052,1083],{"className":1050},[1051],"vlist-r",[569,1053,1057,1071],{"className":1054,"style":1056},[1055],"vlist","height:1.1076em;",[569,1058,1060,1065],{"style":1059},"top:-2.314em;",[569,1061],{"className":1062,"style":1064},[1063],"pstrut","height:3em;",[569,1066,1068],{"className":1067},[612],[569,1069,902],{"className":1070,"style":917},[612,613],[569,1072,1074,1077],{"style":1073},"top:-3.677em;",[569,1075],{"className":1076,"style":1064},[1063],[569,1078,1080],{"className":1079},[612],[569,1081,590],{"className":1082},[612,613],[569,1084,1087],{"className":1085},[1086],"vlist-s","​",[569,1089,1091],{"className":1090},[1051],[569,1092,1095],{"className":1093,"style":1094},[1055],"height:0.686em;",[569,1096],{},[569,1098,1101],{"className":1099,"style":1034},[1100,1033],"mclose",[569,1102,950],{"className":1103},[1038,1039],[569,1105,1107,1110],{"className":1106},[612],[569,1108,565],{"className":1109},[612,613],[569,1111,1114],{"className":1112},[1113],"msupsub",[569,1115,1117],{"className":1116},[1046],[569,1118,1120],{"className":1119},[1051],[569,1121,1124],{"className":1122,"style":1123},[1055],"height:0.8991em;",[569,1125,1127,1131],{"style":1126},"top:-3.113em;margin-right:0.05em;",[569,1128],{"className":1129,"style":1130},[1063],"height:2.7em;",[569,1132,1137],{"className":1133},[1134,1135,1039,1136],"sizing","reset-size6","mtight",[569,1138,902],{"className":1139,"style":917},[612,613,1136],[569,1141,939],{"className":1142},[1032],[569,1144,963],{"className":1145},[612],[569,1147],{"className":1148,"style":1149},[692],"margin-right:0.2222em;",[569,1151,966],{"className":1152},[1153],"mbin",[569,1155],{"className":1156,"style":1149},[692],[569,1158,1160,1164,1167,1205,1208,1211],{"className":1159},[603],[569,1161],{"className":1162,"style":1163},[607],"height:1.1491em;vertical-align:-0.25em;",[569,1165,565],{"className":1166},[612,613],[569,1168,1170,1173],{"className":1169},[1100],[569,1171,950],{"className":1172},[1100],[569,1174,1176],{"className":1175},[1113],[569,1177,1179],{"className":1178},[1046],[569,1180,1182],{"className":1181},[1051],[569,1183,1185],{"className":1184,"style":1123},[1055],[569,1186,1187,1190],{"style":1126},[569,1188],{"className":1189,"style":1130},[1063],[569,1191,1193],{"className":1192},[1134,1135,1039,1136],[569,1194,1196,1199,1202],{"className":1195},[612,1136],[569,1197,590],{"className":1198},[612,613,1136],[569,1200,966],{"className":1201},[1153,1136],[569,1203,902],{"className":1204,"style":917},[612,613,1136],[569,1206],{"className":1207,"style":693},[692],[569,1209,737],{"className":1210},[697],[569,1212],{"className":1213,"style":693},[692],[569,1215,1217,1221,1319,1323],{"className":1216},[603],[569,1218],{"className":1219,"style":1220},[607],"height:2.2121em;vertical-align:-0.686em;",[569,1222,1224,1228,1316],{"className":1223},[612],[569,1225],{"className":1226},[1032,1227],"nulldelimiter",[569,1229,1231],{"className":1230},[941],[569,1232,1234,1308],{"className":1233},[1046,1047],[569,1235,1237,1305],{"className":1236},[1051],[569,1238,1241,1255,1266],{"className":1239,"style":1240},[1055],"height:1.5261em;",[569,1242,1243,1246],{"style":1059},[569,1244],{"className":1245,"style":1064},[1063],[569,1247,1249,1252],{"className":1248},[612],[569,1250,902],{"className":1251,"style":917},[612,613],[569,1253,997],{"className":1254},[1100],[569,1256,1258,1261],{"style":1257},"top:-3.23em;",[569,1259],{"className":1260,"style":1064},[1063],[569,1262],{"className":1263,"style":1265},[1264],"frac-line","border-bottom-width:0.04em;",[569,1267,1268,1271],{"style":1073},[569,1269],{"className":1270,"style":1064},[1063],[569,1272,1274],{"className":1273},[612],[569,1275,1277,1280],{"className":1276},[612],[569,1278,664],{"className":1279},[612,613],[569,1281,1283],{"className":1282},[1113],[569,1284,1286],{"className":1285},[1046],[569,1287,1289],{"className":1288},[1051],[569,1290,1293],{"className":1291,"style":1292},[1055],"height:0.8491em;",[569,1294,1296,1299],{"style":1295},"top:-3.063em;margin-right:0.05em;",[569,1297],{"className":1298,"style":1130},[1063],[569,1300,1302],{"className":1301},[1134,1135,1039,1136],[569,1303,902],{"className":1304,"style":917},[612,613,1136],[569,1306,1087],{"className":1307},[1086],[569,1309,1311],{"className":1310},[1051],[569,1312,1314],{"className":1313,"style":1094},[1055],[569,1315],{},[569,1317],{"className":1318},[1100,1227],[569,1320],{"className":1321,"style":1322},[692],"margin-right:0.1667em;",[569,1324,1326,1329],{"className":1325},[612],[569,1327,1006],{"className":1328},[612,613],[569,1330,1332],{"className":1331},[1113],[569,1333,1335],{"className":1334},[1046],[569,1336,1338],{"className":1337},[1051],[569,1339,1341],{"className":1340,"style":1123},[1055],[569,1342,1343,1346],{"style":1126},[569,1344],{"className":1345,"style":1130},[1063],[569,1347,1349],{"className":1348},[1134,1135,1039,1136],[569,1350,1352,1355],{"className":1351},[612,1136],[569,1353,966],{"className":1354},[612,1136],[569,1356,664],{"className":1357},[612,613,1136],[565,1359,1360,1361,713],{},"Der entscheidende Schritt ist ",[569,1362,1364,1408],{"className":1363},[572],[569,1365,1367],{"className":1366},[576],[578,1368,1369],{"xmlns":580},[582,1370,1371,1405],{},[585,1372,1373,1393,1395],{},[952,1374,1375,1391],{},[585,1376,1377,1379,1381,1383,1389],{},[666,1378,939],{"fence":599},[793,1380,963],{},[666,1382,966],{},[941,1384,1385,1387],{},[588,1386,664],{},[588,1388,590],{},[666,1390,950],{"fence":599},[588,1392,590],{},[666,1394,737],{},[952,1396,1397,1399],{},[588,1398,1006],{},[585,1400,1401,1403],{},[666,1402,966],{},[588,1404,664],{},[592,1406,1407],{"encoding":594},"\\left(1 - \\frac{\\lambda}{n}\\right)^n \\to e^{-\\lambda}",[569,1409,1411,1556],{"className":1410,"ariaHidden":599},[598],[569,1412,1414,1418,1547,1550,1553],{"className":1413},[603],[569,1415],{"className":1416,"style":1417},[607],"height:1.2844em;vertical-align:-0.35em;",[569,1419,1422,1522],{"className":1420},[1421],"minner",[569,1423,1425,1432,1435,1438,1441,1444,1516],{"className":1424},[1421],[569,1426,1428],{"className":1427,"style":1034},[1032,1033],[569,1429,939],{"className":1430},[1038,1431],"size1",[569,1433,963],{"className":1434},[612],[569,1436],{"className":1437,"style":1149},[692],[569,1439,966],{"className":1440},[1153],[569,1442],{"className":1443,"style":1149},[692],[569,1445,1447,1450,1513],{"className":1446},[612],[569,1448],{"className":1449},[1032,1227],[569,1451,1453],{"className":1452},[941],[569,1454,1456,1504],{"className":1455},[1046,1047],[569,1457,1459,1501],{"className":1458},[1051],[569,1460,1463,1478,1486],{"className":1461,"style":1462},[1055],"height:0.8801em;",[569,1464,1466,1469],{"style":1465},"top:-2.655em;",[569,1467],{"className":1468,"style":1064},[1063],[569,1470,1472],{"className":1471},[1134,1135,1039,1136],[569,1473,1475],{"className":1474},[612,1136],[569,1476,590],{"className":1477},[612,613,1136],[569,1479,1480,1483],{"style":1257},[569,1481],{"className":1482,"style":1064},[1063],[569,1484],{"className":1485,"style":1265},[1264],[569,1487,1489,1492],{"style":1488},"top:-3.394em;",[569,1490],{"className":1491,"style":1064},[1063],[569,1493,1495],{"className":1494},[1134,1135,1039,1136],[569,1496,1498],{"className":1497},[612,1136],[569,1499,664],{"className":1500},[612,613,1136],[569,1502,1087],{"className":1503},[1086],[569,1505,1507],{"className":1506},[1051],[569,1508,1511],{"className":1509,"style":1510},[1055],"height:0.345em;",[569,1512],{},[569,1514],{"className":1515},[1100,1227],[569,1517,1519],{"className":1518,"style":1034},[1100,1033],[569,1520,950],{"className":1521},[1038,1431],[569,1523,1525],{"className":1524},[1113],[569,1526,1528],{"className":1527},[1046],[569,1529,1531],{"className":1530},[1051],[569,1532,1535],{"className":1533,"style":1534},[1055],"height:0.9344em;",[569,1536,1538,1541],{"style":1537},"top:-3.333em;margin-right:0.05em;",[569,1539],{"className":1540,"style":1130},[1063],[569,1542,1544],{"className":1543},[1134,1135,1039,1136],[569,1545,590],{"className":1546},[612,613,1136],[569,1548],{"className":1549,"style":693},[692],[569,1551,737],{"className":1552},[697],[569,1554],{"className":1555,"style":693},[692],[569,1557,1559,1562],{"className":1558},[603],[569,1560],{"className":1561,"style":1292},[607],[569,1563,1565,1568],{"className":1564},[612],[569,1566,1006],{"className":1567},[612,613],[569,1569,1571],{"className":1570},[1113],[569,1572,1574],{"className":1573},[1046],[569,1575,1577],{"className":1576},[1051],[569,1578,1580],{"className":1579,"style":1292},[1055],[569,1581,1582,1585],{"style":1295},[569,1583],{"className":1584,"style":1130},[1063],[569,1586,1588],{"className":1587},[1134,1135,1039,1136],[569,1589,1591,1594],{"className":1590},[612,1136],[569,1592,966],{"className":1593},[612,1136],[569,1595,664],{"className":1596},[612,613,1136],[565,1598,1599,1600,775,1654,1720,1721,1778,1779,1807,1808,1880,1881,1909,1910,713],{},"Faustregel: ",[569,1601,1603,1623],{"className":1602},[572],[569,1604,1606],{"className":1605},[576],[578,1607,1608],{"xmlns":580},[582,1609,1610,1620],{},[585,1611,1612,1614,1617],{},[588,1613,590],{},[666,1615,1616],{},"≥",[793,1618,1619],{},"50",[592,1621,1622],{"encoding":594},"n \\geq 50",[569,1624,1626,1645],{"className":1625,"ariaHidden":599},[598],[569,1627,1629,1633,1636,1639,1642],{"className":1628},[603],[569,1630],{"className":1631,"style":1632},[607],"height:0.7719em;vertical-align:-0.136em;",[569,1634,590],{"className":1635},[612,613],[569,1637],{"className":1638,"style":693},[692],[569,1640,1616],{"className":1641},[697],[569,1643],{"className":1644,"style":693},[692],[569,1646,1648,1651],{"className":1647},[603],[569,1649],{"className":1650,"style":826},[607],[569,1652,1619],{"className":1653},[612],[569,1655,1657,1677],{"className":1656},[572],[569,1658,1660],{"className":1659},[576],[578,1661,1662],{"xmlns":580},[582,1663,1664,1674],{},[585,1665,1666,1668,1671],{},[588,1667,565],{},[666,1669,1670],{},"≤",[793,1672,1673],{},"0,1",[592,1675,1676],{"encoding":594},"p \\leq 0{,}1",[569,1678,1680,1699],{"className":1679,"ariaHidden":599},[598],[569,1681,1683,1687,1690,1693,1696],{"className":1682},[603],[569,1684],{"className":1685,"style":1686},[607],"height:0.8304em;vertical-align:-0.1944em;",[569,1688,565],{"className":1689},[612,613],[569,1691],{"className":1692,"style":693},[692],[569,1694,1670],{"className":1695},[697],[569,1697],{"className":1698,"style":693},[692],[569,1700,1702,1706,1709,1717],{"className":1701},[603],[569,1703],{"className":1704,"style":1705},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,1707,795],{"className":1708},[612],[569,1710,1712],{"className":1711},[612],[569,1713,1716],{"className":1714},[1715],"mpunct",",",[569,1718,963],{"className":1719},[612]," (manche Bücher verlangen zusätzlich ",[569,1722,1724,1745],{"className":1723},[572],[569,1725,1727],{"className":1726},[576],[578,1728,1729],{"xmlns":580},[582,1730,1731,1742],{},[585,1732,1733,1735,1737,1739],{},[588,1734,590],{},[588,1736,565],{},[666,1738,1670],{},[793,1740,1741],{},"10",[592,1743,1744],{"encoding":594},"n p \\leq 10",[569,1746,1748,1769],{"className":1747,"ariaHidden":599},[598],[569,1749,1751,1754,1757,1760,1763,1766],{"className":1750},[603],[569,1752],{"className":1753,"style":1686},[607],[569,1755,590],{"className":1756},[612,613],[569,1758,565],{"className":1759},[612,613],[569,1761],{"className":1762,"style":693},[692],[569,1764,1670],{"className":1765},[697],[569,1767],{"className":1768,"style":693},[692],[569,1770,1772,1775],{"className":1771},[603],[569,1773],{"className":1774,"style":826},[607],[569,1776,1741],{"className":1777},[612],"). Eine Fehlerschranke liefert die Ungleichung von Le Cam: Die Summe der Abweichungen über alle ",[569,1780,1782,1795],{"className":1781},[572],[569,1783,1785],{"className":1784},[576],[578,1786,1787],{"xmlns":580},[582,1788,1789,1793],{},[585,1790,1791],{},[588,1792,902],{},[592,1794,902],{"encoding":594},[569,1796,1798],{"className":1797,"ariaHidden":599},[598],[569,1799,1801,1804],{"className":1800},[603],[569,1802],{"className":1803,"style":685},[607],[569,1805,902],{"className":1806,"style":917},[612,613]," ist kleiner als ",[569,1809,1811,1834],{"className":1810},[572],[569,1812,1814],{"className":1813},[576],[578,1815,1816],{"xmlns":580},[582,1817,1818,1831],{},[585,1819,1820,1823,1825],{},[793,1821,1822],{},"2",[588,1824,590],{},[952,1826,1827,1829],{},[588,1828,565],{},[793,1830,1822],{},[592,1832,1833],{"encoding":594},"2 n p^2",[569,1835,1837],{"className":1836,"ariaHidden":599},[598],[569,1838,1840,1844,1847,1850],{"className":1839},[603],[569,1841],{"className":1842,"style":1843},[607],"height:1.0085em;vertical-align:-0.1944em;",[569,1845,1822],{"className":1846},[612],[569,1848,590],{"className":1849},[612,613],[569,1851,1853,1856],{"className":1852},[612],[569,1854,565],{"className":1855},[612,613],[569,1857,1859],{"className":1858},[1113],[569,1860,1862],{"className":1861},[1046],[569,1863,1865],{"className":1864},[1051],[569,1866,1869],{"className":1867,"style":1868},[1055],"height:0.8141em;",[569,1870,1871,1874],{"style":1295},[569,1872],{"className":1873,"style":1130},[1063],[569,1875,1877],{"className":1876},[1134,1135,1039,1136],[569,1878,1822],{"className":1879},[612,1136],". Die Näherung ist also gut, wenn ",[569,1882,1884,1897],{"className":1883},[572],[569,1885,1887],{"className":1886},[576],[578,1888,1889],{"xmlns":580},[582,1890,1891,1895],{},[585,1892,1893],{},[588,1894,565],{},[592,1896,565],{"encoding":594},[569,1898,1900],{"className":1899,"ariaHidden":599},[598],[569,1901,1903,1906],{"className":1902},[603],[569,1904],{"className":1905,"style":640},[607],[569,1907,565],{"className":1908},[612,613]," klein ist, auch bei mäßig großem ",[569,1911,1913,1926],{"className":1912},[572],[569,1914,1916],{"className":1915},[576],[578,1917,1918],{"xmlns":580},[582,1919,1920,1924],{},[585,1921,1922],{},[588,1923,590],{},[592,1925,590],{"encoding":594},[569,1927,1929],{"className":1928,"ariaHidden":599},[598],[569,1930,1932,1935],{"className":1931},[603],[569,1933],{"className":1934,"style":608},[607],[569,1936,590],{"className":1937},[612,613],[565,1939,1940,1941,1969,1970,1973],{},"Im Gegensatz zur Näherung von Moivre-Laplace (große Varianz, beliebiges ",[569,1942,1944,1957],{"className":1943},[572],[569,1945,1947],{"className":1946},[576],[578,1948,1949],{"xmlns":580},[582,1950,1951,1955],{},[585,1952,1953],{},[588,1954,565],{},[592,1956,565],{"encoding":594},[569,1958,1960],{"className":1959,"ariaHidden":599},[598],[569,1961,1963,1966],{"className":1962},[603],[569,1964],{"className":1965,"style":640},[607],[569,1967,565],{"className":1968},[612,613],") ist die Poisson-Näherung für den Fall ",[646,1971,1972],{},"seltener Ereignisse"," gedacht.",[560,1975,1977],{"id":1976},"beispiele","Beispiele",[565,1979,1980,1981,2033,2034,2096,2097,713],{},"Ein Online-Shop verschickt ",[569,1982,1984,2003],{"className":1983},[572],[569,1985,1987],{"className":1986},[576],[578,1988,1989],{"xmlns":580},[582,1990,1991,2000],{},[585,1992,1993,1995,1997],{},[588,1994,590],{},[666,1996,668],{},[793,1998,1999],{},"200",[592,2001,2002],{"encoding":594},"n = 200",[569,2004,2006,2024],{"className":2005,"ariaHidden":599},[598],[569,2007,2009,2012,2015,2018,2021],{"className":2008},[603],[569,2010],{"className":2011,"style":608},[607],[569,2013,590],{"className":2014},[612,613],[569,2016],{"className":2017,"style":693},[692],[569,2019,668],{"className":2020},[697],[569,2022],{"className":2023,"style":693},[692],[569,2025,2027,2030],{"className":2026},[603],[569,2028],{"className":2029,"style":826},[607],[569,2031,1999],{"className":2032},[612]," Pakete, jedes geht mit ",[569,2035,2037,2056],{"className":2036},[572],[569,2038,2040],{"className":2039},[576],[578,2041,2042],{"xmlns":580},[582,2043,2044,2053],{},[585,2045,2046,2048,2050],{},[588,2047,565],{},[666,2049,668],{},[793,2051,2052],{},"0,01",[592,2054,2055],{"encoding":594},"p = 0{,}01",[569,2057,2059,2077],{"className":2058,"ariaHidden":599},[598],[569,2060,2062,2065,2068,2071,2074],{"className":2061},[603],[569,2063],{"className":2064,"style":640},[607],[569,2066,565],{"className":2067},[612,613],[569,2069],{"className":2070,"style":693},[692],[569,2072,668],{"className":2073},[697],[569,2075],{"className":2076,"style":693},[692],[569,2078,2080,2083,2086,2092],{"className":2079},[603],[569,2081],{"className":2082,"style":1705},[607],[569,2084,795],{"className":2085},[612],[569,2087,2089],{"className":2088},[612],[569,2090,1716],{"className":2091},[1715],[569,2093,2095],{"className":2094},[612],"01"," verloren. Es ist ",[569,2098,2100,2127],{"className":2099},[572],[569,2101,2103],{"className":2102},[576],[578,2104,2105],{"xmlns":580},[582,2106,2107,2124],{},[585,2108,2109,2111,2113,2115,2118,2120,2122],{},[588,2110,664],{},[666,2112,668],{},[793,2114,1999],{},[666,2116,2117],{},"⋅",[793,2119,2052],{},[666,2121,668],{},[793,2123,1822],{},[592,2125,2126],{"encoding":594},"\\lambda = 200 \\cdot 0{,}01 = 2",[569,2128,2130,2148,2166,2193],{"className":2129,"ariaHidden":599},[598],[569,2131,2133,2136,2139,2142,2145],{"className":2132},[603],[569,2134],{"className":2135,"style":685},[607],[569,2137,664],{"className":2138},[612,613],[569,2140],{"className":2141,"style":693},[692],[569,2143,668],{"className":2144},[697],[569,2146],{"className":2147,"style":693},[692],[569,2149,2151,2154,2157,2160,2163],{"className":2150},[603],[569,2152],{"className":2153,"style":826},[607],[569,2155,1999],{"className":2156},[612],[569,2158],{"className":2159,"style":1149},[692],[569,2161,2117],{"className":2162},[1153],[569,2164],{"className":2165,"style":1149},[692],[569,2167,2169,2172,2175,2181,2184,2187,2190],{"className":2168},[603],[569,2170],{"className":2171,"style":1705},[607],[569,2173,795],{"className":2174},[612],[569,2176,2178],{"className":2177},[612],[569,2179,1716],{"className":2180},[1715],[569,2182,2095],{"className":2183},[612],[569,2185],{"className":2186,"style":693},[692],[569,2188,668],{"className":2189},[697],[569,2191],{"className":2192,"style":693},[692],[569,2194,2196,2199],{"className":2195},[603],[569,2197],{"className":2198,"style":826},[607],[569,2200,1822],{"className":2201},[612],[565,2203,2204],{},"Kein Paket geht verloren:",[569,2206,2208],{"className":2207},[921],[569,2209,2211,2276],{"className":2210},[572],[569,2212,2214],{"className":2213},[576],[578,2215,2216],{"xmlns":580,"display":930},[582,2217,2218,2273],{},[585,2219,2220,2223,2230,2233,2236,2238,2241,2258,2268,2270],{},[999,2221,2222],{},"exakt: ",[952,2224,2225,2228],{},[793,2226,2227],{},"0,99",[793,2229,1999],{},[666,2231,2232],{},"≈",[793,2234,2235],{},"0,1340",[666,2237,1716],{"separator":599},[692,2239],{"width":2240},"2em",[585,2242,2243,2246,2255],{},[999,2244,2245],{},"N",[2247,2248,2249,2252],"mover",{"accent":599},[999,2250,2251],{},"a",[666,2253,2254],{},"¨",[999,2256,2257],{},"herung: ",[952,2259,2260,2262],{},[588,2261,1006],{},[585,2263,2264,2266],{},[666,2265,966],{},[793,2267,1822],{},[666,2269,2232],{},[793,2271,2272],{},"0,1353",[592,2274,2275],{"encoding":594},"\\text{exakt: } 0{,}99^{200} \\approx 0{,}1340, \\qquad \\text{Näherung: } e^{-2} \\approx 0{,}1353",[569,2277,2279,2348,2466],{"className":2278,"ariaHidden":599},[598],[569,2280,2282,2286,2293,2296,2302,2306,2339,2342,2345],{"className":2281},[603],[569,2283],{"className":2284,"style":2285},[607],"height:1.0585em;vertical-align:-0.1944em;",[569,2287,2290],{"className":2288},[612,2289],"text",[569,2291,2222],{"className":2292},[612],[569,2294,795],{"className":2295},[612],[569,2297,2299],{"className":2298},[612],[569,2300,1716],{"className":2301},[1715],[569,2303,2305],{"className":2304},[612],"9",[569,2307,2309,2312],{"className":2308},[612],[569,2310,2305],{"className":2311},[612],[569,2313,2315],{"className":2314},[1113],[569,2316,2318],{"className":2317},[1046],[569,2319,2321],{"className":2320},[1051],[569,2322,2325],{"className":2323,"style":2324},[1055],"height:0.8641em;",[569,2326,2327,2330],{"style":1126},[569,2328],{"className":2329,"style":1130},[1063],[569,2331,2333],{"className":2332},[1134,1135,1039,1136],[569,2334,2336],{"className":2335},[612,1136],[569,2337,1999],{"className":2338},[612,1136],[569,2340],{"className":2341,"style":693},[692],[569,2343,2232],{"className":2344},[697],[569,2346],{"className":2347,"style":693},[692],[569,2349,2351,2354,2357,2363,2367,2370,2374,2377,2422,2457,2460,2463],{"className":2350},[603],[569,2352],{"className":2353,"style":2285},[607],[569,2355,795],{"className":2356},[612],[569,2358,2360],{"className":2359},[612],[569,2361,1716],{"className":2362},[1715],[569,2364,2366],{"className":2365},[612],"1340",[569,2368,1716],{"className":2369},[1715],[569,2371],{"className":2372,"style":2373},[692],"margin-right:2em;",[569,2375],{"className":2376,"style":1322},[692],[569,2378,2380,2383,2419],{"className":2379},[612,2289],[569,2381,2245],{"className":2382},[612],[569,2384,2387],{"className":2385},[612,2386],"accent",[569,2388,2390],{"className":2389},[1046],[569,2391,2393],{"className":2392},[1051],[569,2394,2397,2406],{"className":2395,"style":2396},[1055],"height:0.6679em;",[569,2398,2400,2403],{"style":2399},"top:-3em;",[569,2401],{"className":2402,"style":1064},[1063],[569,2404,2251],{"className":2405},[612],[569,2407,2408,2411],{"style":2399},[569,2409],{"className":2410,"style":1064},[1063],[569,2412,2416],{"className":2413,"style":2415},[2414],"accent-body","left:-0.25em;",[569,2417,2254],{"className":2418},[612],[569,2420,2257],{"className":2421},[612],[569,2423,2425,2428],{"className":2424},[612],[569,2426,1006],{"className":2427},[612,613],[569,2429,2431],{"className":2430},[1113],[569,2432,2434],{"className":2433},[1046],[569,2435,2437],{"className":2436},[1051],[569,2438,2440],{"className":2439,"style":2324},[1055],[569,2441,2442,2445],{"style":1126},[569,2443],{"className":2444,"style":1130},[1063],[569,2446,2448],{"className":2447},[1134,1135,1039,1136],[569,2449,2451,2454],{"className":2450},[612,1136],[569,2452,966],{"className":2453},[612,1136],[569,2455,1822],{"className":2456},[612,1136],[569,2458],{"className":2459,"style":693},[692],[569,2461,2232],{"className":2462},[697],[569,2464],{"className":2465,"style":693},[692],[569,2467,2469,2472,2475,2481],{"className":2468},[603],[569,2470],{"className":2471,"style":1705},[607],[569,2473,795],{"className":2474},[612],[569,2476,2478],{"className":2477},[612],[569,2479,1716],{"className":2480},[1715],[569,2482,2484],{"className":2483},[612],"1353",[565,2486,2487],{},"Höchstens zwei Pakete gehen verloren:",[569,2489,2491],{"className":2490},[921],[569,2492,2494,2579],{"className":2493},[572],[569,2495,2497],{"className":2496},[576],[578,2498,2499],{"xmlns":580,"display":930},[582,2500,2501,2576],{},[585,2502,2503,2506,2508,2511,2513,2515,2517,2519,2529,2554,2556,2559,2561,2571,2573],{},[588,2504,2505],{},"P",[666,2507,939],{"stretchy":960},[588,2509,2510],{},"X",[666,2512,1670],{},[793,2514,1822],{},[666,2516,950],{"stretchy":960},[666,2518,2232],{},[952,2520,2521,2523],{},[588,2522,1006],{},[585,2524,2525,2527],{},[666,2526,966],{},[793,2528,1822],{},[585,2530,2531,2533,2535,2538,2540,2542,2552],{},[666,2532,939],{"fence":599},[793,2534,963],{},[666,2536,2537],{},"+",[793,2539,1822],{},[666,2541,2537],{},[941,2543,2544,2550],{},[952,2545,2546,2548],{},[793,2547,1822],{},[793,2549,1822],{},[793,2551,1822],{},[666,2553,950],{"fence":599},[666,2555,668],{},[793,2557,2558],{},"5",[666,2560,2117],{},[952,2562,2563,2565],{},[588,2564,1006],{},[585,2566,2567,2569],{},[666,2568,966],{},[793,2570,1822],{},[666,2572,2232],{},[793,2574,2575],{},"0,6767",[592,2577,2578],{"encoding":594},"P(X \\leq 2) \\approx e^{-2} \\left(1 + 2 + \\frac{2^2}{2}\\right) = 5 \\cdot e^{-2} \\approx 0{,}6767",[569,2580,2582,2609,2630,2812,2830,2880],{"className":2581,"ariaHidden":599},[598],[569,2583,2585,2589,2593,2596,2600,2603,2606],{"className":2584},[603],[569,2586],{"className":2587,"style":2588},[607],"height:1em;vertical-align:-0.25em;",[569,2590,2505],{"className":2591,"style":2592},[612,613],"margin-right:0.1389em;",[569,2594,939],{"className":2595},[1032],[569,2597,2510],{"className":2598,"style":2599},[612,613],"margin-right:0.0785em;",[569,2601],{"className":2602,"style":693},[692],[569,2604,1670],{"className":2605},[697],[569,2607],{"className":2608,"style":693},[692],[569,2610,2612,2615,2618,2621,2624,2627],{"className":2611},[603],[569,2613],{"className":2614,"style":2588},[607],[569,2616,1822],{"className":2617},[612],[569,2619,950],{"className":2620},[1100],[569,2622],{"className":2623,"style":693},[692],[569,2625,2232],{"className":2626},[697],[569,2628],{"className":2629,"style":693},[692],[569,2631,2633,2637,2672,2675,2803,2806,2809],{"className":2632},[603],[569,2634],{"className":2635,"style":2636},[607],"height:2.4411em;vertical-align:-0.95em;",[569,2638,2640,2643],{"className":2639},[612],[569,2641,1006],{"className":2642},[612,613],[569,2644,2646],{"className":2645},[1113],[569,2647,2649],{"className":2648},[1046],[569,2650,2652],{"className":2651},[1051],[569,2653,2655],{"className":2654,"style":2324},[1055],[569,2656,2657,2660],{"style":1126},[569,2658],{"className":2659,"style":1130},[1063],[569,2661,2663],{"className":2662},[1134,1135,1039,1136],[569,2664,2666,2669],{"className":2665},[612,1136],[569,2667,966],{"className":2668},[612,1136],[569,2670,1822],{"className":2671},[612,1136],[569,2673],{"className":2674,"style":1322},[692],[569,2676,2678,2684,2687,2690,2693,2696,2699,2702,2705,2708,2797],{"className":2677},[1421],[569,2679,2681],{"className":2680,"style":1034},[1032,1033],[569,2682,939],{"className":2683},[1038,1039],[569,2685,963],{"className":2686},[612],[569,2688],{"className":2689,"style":1149},[692],[569,2691,2537],{"className":2692},[1153],[569,2694],{"className":2695,"style":1149},[692],[569,2697,1822],{"className":2698},[612],[569,2700],{"className":2701,"style":1149},[692],[569,2703,2537],{"className":2704},[1153],[569,2706],{"className":2707,"style":1149},[692],[569,2709,2711,2714,2794],{"className":2710},[612],[569,2712],{"className":2713},[1032,1227],[569,2715,2717],{"className":2716},[941],[569,2718,2720,2786],{"className":2719},[1046,1047],[569,2721,2723,2783],{"className":2722},[1051],[569,2724,2727,2738,2746],{"className":2725,"style":2726},[1055],"height:1.4911em;",[569,2728,2729,2732],{"style":1059},[569,2730],{"className":2731,"style":1064},[1063],[569,2733,2735],{"className":2734},[612],[569,2736,1822],{"className":2737},[612],[569,2739,2740,2743],{"style":1257},[569,2741],{"className":2742,"style":1064},[1063],[569,2744],{"className":2745,"style":1265},[1264],[569,2747,2748,2751],{"style":1073},[569,2749],{"className":2750,"style":1064},[1063],[569,2752,2754],{"className":2753},[612],[569,2755,2757,2760],{"className":2756},[612],[569,2758,1822],{"className":2759},[612],[569,2761,2763],{"className":2762},[1113],[569,2764,2766],{"className":2765},[1046],[569,2767,2769],{"className":2768},[1051],[569,2770,2772],{"className":2771,"style":1868},[1055],[569,2773,2774,2777],{"style":1295},[569,2775],{"className":2776,"style":1130},[1063],[569,2778,2780],{"className":2779},[1134,1135,1039,1136],[569,2781,1822],{"className":2782},[612,1136],[569,2784,1087],{"className":2785},[1086],[569,2787,2789],{"className":2788},[1051],[569,2790,2792],{"className":2791,"style":1094},[1055],[569,2793],{},[569,2795],{"className":2796},[1100,1227],[569,2798,2800],{"className":2799,"style":1034},[1100,1033],[569,2801,950],{"className":2802},[1038,1039],[569,2804],{"className":2805,"style":693},[692],[569,2807,668],{"className":2808},[697],[569,2810],{"className":2811,"style":693},[692],[569,2813,2815,2818,2821,2824,2827],{"className":2814},[603],[569,2816],{"className":2817,"style":826},[607],[569,2819,2558],{"className":2820},[612],[569,2822],{"className":2823,"style":1149},[692],[569,2825,2117],{"className":2826},[1153],[569,2828],{"className":2829,"style":1149},[692],[569,2831,2833,2836,2871,2874,2877],{"className":2832},[603],[569,2834],{"className":2835,"style":2324},[607],[569,2837,2839,2842],{"className":2838},[612],[569,2840,1006],{"className":2841},[612,613],[569,2843,2845],{"className":2844},[1113],[569,2846,2848],{"className":2847},[1046],[569,2849,2851],{"className":2850},[1051],[569,2852,2854],{"className":2853,"style":2324},[1055],[569,2855,2856,2859],{"style":1126},[569,2857],{"className":2858,"style":1130},[1063],[569,2860,2862],{"className":2861},[1134,1135,1039,1136],[569,2863,2865,2868],{"className":2864},[612,1136],[569,2866,966],{"className":2867},[612,1136],[569,2869,1822],{"className":2870},[612,1136],[569,2872],{"className":2873,"style":693},[692],[569,2875,2232],{"className":2876},[697],[569,2878],{"className":2879,"style":693},[692],[569,2881,2883,2886,2889,2895],{"className":2882},[603],[569,2884],{"className":2885,"style":1705},[607],[569,2887,795],{"className":2888},[612],[569,2890,2892],{"className":2891},[612],[569,2893,1716],{"className":2894},[1715],[569,2896,2898],{"className":2897},[612],"6767",[565,2900,2901,2902,2940,2941,713],{},"Die exakte Binomialrechnung liefert auf vier Stellen ebenfalls ",[569,2903,2905,2919],{"className":2904},[572],[569,2906,2908],{"className":2907},[576],[578,2909,2910],{"xmlns":580},[582,2911,2912,2916],{},[585,2913,2914],{},[793,2915,2575],{},[592,2917,2918],{"encoding":594},"0{,}6767",[569,2920,2922],{"className":2921,"ariaHidden":599},[598],[569,2923,2925,2928,2931,2937],{"className":2924},[603],[569,2926],{"className":2927,"style":1705},[607],[569,2929,795],{"className":2930},[612],[569,2932,2934],{"className":2933},[612],[569,2935,1716],{"className":2936},[1715],[569,2938,2898],{"className":2939},[612],". Die Schranke von Le Cam ist ",[569,2942,2944,2975],{"className":2943},[572],[569,2945,2947],{"className":2946},[576],[578,2948,2949],{"xmlns":580},[582,2950,2951,2972],{},[585,2952,2953,2955,2957,2959,2961,2967,2969],{},[793,2954,1822],{},[666,2956,2117],{},[793,2958,1999],{},[666,2960,2117],{},[952,2962,2963,2965],{},[793,2964,2052],{},[793,2966,1822],{},[666,2968,668],{},[793,2970,2971],{},"0,04",[592,2973,2974],{"encoding":594},"2 \\cdot 200 \\cdot 0{,}01^2 = 0{,}04",[569,2976,2978,2996,3014,3070],{"className":2977,"ariaHidden":599},[598],[569,2979,2981,2984,2987,2990,2993],{"className":2980},[603],[569,2982],{"className":2983,"style":826},[607],[569,2985,1822],{"className":2986},[612],[569,2988],{"className":2989,"style":1149},[692],[569,2991,2117],{"className":2992},[1153],[569,2994],{"className":2995,"style":1149},[692],[569,2997,2999,3002,3005,3008,3011],{"className":2998},[603],[569,3000],{"className":3001,"style":826},[607],[569,3003,1999],{"className":3004},[612],[569,3006],{"className":3007,"style":1149},[692],[569,3009,2117],{"className":3010},[1153],[569,3012],{"className":3013,"style":1149},[692],[569,3015,3017,3020,3023,3029,3032,3061,3064,3067],{"className":3016},[603],[569,3018],{"className":3019,"style":1843},[607],[569,3021,795],{"className":3022},[612],[569,3024,3026],{"className":3025},[612],[569,3027,1716],{"className":3028},[1715],[569,3030,795],{"className":3031},[612],[569,3033,3035,3038],{"className":3034},[612],[569,3036,963],{"className":3037},[612],[569,3039,3041],{"className":3040},[1113],[569,3042,3044],{"className":3043},[1046],[569,3045,3047],{"className":3046},[1051],[569,3048,3050],{"className":3049,"style":1868},[1055],[569,3051,3052,3055],{"style":1295},[569,3053],{"className":3054,"style":1130},[1063],[569,3056,3058],{"className":3057},[1134,1135,1039,1136],[569,3059,1822],{"className":3060},[612,1136],[569,3062],{"className":3063,"style":693},[692],[569,3065,668],{"className":3066},[697],[569,3068],{"className":3069,"style":693},[692],[569,3071,3073,3076,3079,3085],{"className":3072},[603],[569,3074],{"className":3075,"style":1705},[607],[569,3077,795],{"className":3078},[612],[569,3080,3082],{"className":3081},[612],[569,3083,1716],{"className":3084},[1715],[569,3086,3088],{"className":3087},[612],"04",[565,3090,3091,3092,775,3144,3206,3207,3259,3260,3359,3360,3584,3585,3613],{},"Gegenbeispiel: Für ",[569,3093,3095,3114],{"className":3094},[572],[569,3096,3098],{"className":3097},[576],[578,3099,3100],{"xmlns":580},[582,3101,3102,3111],{},[585,3103,3104,3106,3108],{},[588,3105,590],{},[666,3107,668],{},[793,3109,3110],{},"20",[592,3112,3113],{"encoding":594},"n = 20",[569,3115,3117,3135],{"className":3116,"ariaHidden":599},[598],[569,3118,3120,3123,3126,3129,3132],{"className":3119},[603],[569,3121],{"className":3122,"style":608},[607],[569,3124,590],{"className":3125},[612,613],[569,3127],{"className":3128,"style":693},[692],[569,3130,668],{"className":3131},[697],[569,3133],{"className":3134,"style":693},[692],[569,3136,3138,3141],{"className":3137},[603],[569,3139],{"className":3140,"style":826},[607],[569,3142,3110],{"className":3143},[612],[569,3145,3147,3166],{"className":3146},[572],[569,3148,3150],{"className":3149},[576],[578,3151,3152],{"xmlns":580},[582,3153,3154,3163],{},[585,3155,3156,3158,3160],{},[588,3157,565],{},[666,3159,668],{},[793,3161,3162],{},"0,3",[592,3164,3165],{"encoding":594},"p = 0{,}3",[569,3167,3169,3187],{"className":3168,"ariaHidden":599},[598],[569,3170,3172,3175,3178,3181,3184],{"className":3171},[603],[569,3173],{"className":3174,"style":640},[607],[569,3176,565],{"className":3177},[612,613],[569,3179],{"className":3180,"style":693},[692],[569,3182,668],{"className":3183},[697],[569,3185],{"className":3186,"style":693},[692],[569,3188,3190,3193,3196,3202],{"className":3189},[603],[569,3191],{"className":3192,"style":1705},[607],[569,3194,795],{"className":3195},[612],[569,3197,3199],{"className":3198},[612],[569,3200,1716],{"className":3201},[1715],[569,3203,3205],{"className":3204},[612],"3"," (also ",[569,3208,3210,3229],{"className":3209},[572],[569,3211,3213],{"className":3212},[576],[578,3214,3215],{"xmlns":580},[582,3216,3217,3226],{},[585,3218,3219,3221,3223],{},[588,3220,664],{},[666,3222,668],{},[793,3224,3225],{},"6",[592,3227,3228],{"encoding":594},"\\lambda = 6",[569,3230,3232,3250],{"className":3231,"ariaHidden":599},[598],[569,3233,3235,3238,3241,3244,3247],{"className":3234},[603],[569,3236],{"className":3237,"style":685},[607],[569,3239,664],{"className":3240},[612,613],[569,3242],{"className":3243,"style":693},[692],[569,3245,668],{"className":3246},[697],[569,3248],{"className":3249,"style":693},[692],[569,3251,3253,3256],{"className":3252},[603],[569,3254],{"className":3255,"style":826},[607],[569,3257,3225],{"className":3258},[612],") ist exakt ",[569,3261,3263,3292],{"className":3262},[572],[569,3264,3266],{"className":3265},[576],[578,3267,3268],{"xmlns":580},[582,3269,3270,3289],{},[585,3271,3272,3274,3276,3278,3280,3282,3284,3286],{},[588,3273,2505],{},[666,3275,939],{"stretchy":960},[588,3277,2510],{},[666,3279,668],{},[793,3281,3225],{},[666,3283,950],{"stretchy":960},[666,3285,2232],{},[793,3287,3288],{},"0,1916",[592,3290,3291],{"encoding":594},"P(X = 6) \\approx 0{,}1916",[569,3293,3295,3319,3340],{"className":3294,"ariaHidden":599},[598],[569,3296,3298,3301,3304,3307,3310,3313,3316],{"className":3297},[603],[569,3299],{"className":3300,"style":2588},[607],[569,3302,2505],{"className":3303,"style":2592},[612,613],[569,3305,939],{"className":3306},[1032],[569,3308,2510],{"className":3309,"style":2599},[612,613],[569,3311],{"className":3312,"style":693},[692],[569,3314,668],{"className":3315},[697],[569,3317],{"className":3318,"style":693},[692],[569,3320,3322,3325,3328,3331,3334,3337],{"className":3321},[603],[569,3323],{"className":3324,"style":2588},[607],[569,3326,3225],{"className":3327},[612],[569,3329,950],{"className":3330},[1100],[569,3332],{"className":3333,"style":693},[692],[569,3335,2232],{"className":3336},[697],[569,3338],{"className":3339,"style":693},[692],[569,3341,3343,3346,3349,3355],{"className":3342},[603],[569,3344],{"className":3345,"style":1705},[607],[569,3347,795],{"className":3348},[612],[569,3350,3352],{"className":3351},[612],[569,3353,1716],{"className":3354},[1715],[569,3356,3358],{"className":3357},[612],"1916",", die Poisson-Näherung ",[569,3361,3363,3406],{"className":3362},[572],[569,3364,3366],{"className":3365},[576],[578,3367,3368],{"xmlns":580},[582,3369,3370,3403],{},[585,3371,3372,3386,3388,3398,3400],{},[941,3373,3374,3380],{},[952,3375,3376,3378],{},[793,3377,3225],{},[793,3379,3225],{},[585,3381,3382,3384],{},[793,3383,3225],{},[666,3385,997],{"stretchy":960},[999,3387,1001],{},[952,3389,3390,3392],{},[588,3391,1006],{},[585,3393,3394,3396],{},[666,3395,966],{},[793,3397,3225],{},[666,3399,2232],{},[793,3401,3402],{},"0,1606",[592,3404,3405],{"encoding":594},"\\frac{6^6}{6!}\\,e^{-6} \\approx 0{,}1606",[569,3407,3409,3565],{"className":3408,"ariaHidden":599},[598],[569,3410,3412,3416,3518,3521,3556,3559,3562],{"className":3411},[603],[569,3413],{"className":3414,"style":3415},[607],"height:1.3629em;vertical-align:-0.345em;",[569,3417,3419,3422,3515],{"className":3418},[612],[569,3420],{"className":3421},[1032,1227],[569,3423,3425],{"className":3424},[941],[569,3426,3428,3507],{"className":3427},[1046,1047],[569,3429,3431,3504],{"className":3430},[1051],[569,3432,3435,3452,3460],{"className":3433,"style":3434},[1055],"height:1.0179em;",[569,3436,3437,3440],{"style":1465},[569,3438],{"className":3439,"style":1064},[1063],[569,3441,3443],{"className":3442},[1134,1135,1039,1136],[569,3444,3446,3449],{"className":3445},[612,1136],[569,3447,3225],{"className":3448},[612,1136],[569,3450,997],{"className":3451},[1100,1136],[569,3453,3454,3457],{"style":1257},[569,3455],{"className":3456,"style":1064},[1063],[569,3458],{"className":3459,"style":1265},[1264],[569,3461,3462,3465],{"style":1488},[569,3463],{"className":3464,"style":1064},[1063],[569,3466,3468],{"className":3467},[1134,1135,1039,1136],[569,3469,3471],{"className":3470},[612,1136],[569,3472,3474,3477],{"className":3473},[612,1136],[569,3475,3225],{"className":3476},[612,1136],[569,3478,3480],{"className":3479},[1113],[569,3481,3483],{"className":3482},[1046],[569,3484,3486],{"className":3485},[1051],[569,3487,3490],{"className":3488,"style":3489},[1055],"height:0.8913em;",[569,3491,3493,3497],{"style":3492},"top:-2.931em;margin-right:0.0714em;",[569,3494],{"className":3495,"style":3496},[1063],"height:2.5em;",[569,3498,3501],{"className":3499},[1134,3500,1431,1136],"reset-size3",[569,3502,3225],{"className":3503},[612,1136],[569,3505,1087],{"className":3506},[1086],[569,3508,3510],{"className":3509},[1051],[569,3511,3513],{"className":3512,"style":1510},[1055],[569,3514],{},[569,3516],{"className":3517},[1100,1227],[569,3519],{"className":3520,"style":1322},[692],[569,3522,3524,3527],{"className":3523},[612],[569,3525,1006],{"className":3526},[612,613],[569,3528,3530],{"className":3529},[1113],[569,3531,3533],{"className":3532},[1046],[569,3534,3536],{"className":3535},[1051],[569,3537,3539],{"className":3538,"style":1868},[1055],[569,3540,3541,3544],{"style":1295},[569,3542],{"className":3543,"style":1130},[1063],[569,3545,3547],{"className":3546},[1134,1135,1039,1136],[569,3548,3550,3553],{"className":3549},[612,1136],[569,3551,966],{"className":3552},[612,1136],[569,3554,3225],{"className":3555},[612,1136],[569,3557],{"className":3558,"style":693},[692],[569,3560,2232],{"className":3561},[697],[569,3563],{"className":3564,"style":693},[692],[569,3566,3568,3571,3574,3580],{"className":3567},[603],[569,3569],{"className":3570,"style":1705},[607],[569,3572,795],{"className":3573},[612],[569,3575,3577],{"className":3576},[612],[569,3578,1716],{"className":3579},[1715],[569,3581,3583],{"className":3582},[612],"1606"," liegt deutlich daneben. Hier ist ",[569,3586,3588,3601],{"className":3587},[572],[569,3589,3591],{"className":3590},[576],[578,3592,3593],{"xmlns":580},[582,3594,3595,3599],{},[585,3596,3597],{},[588,3598,565],{},[592,3600,565],{"encoding":594},[569,3602,3604],{"className":3603,"ariaHidden":599},[598],[569,3605,3607,3610],{"className":3606},[603],[569,3608],{"className":3609,"style":640},[607],[569,3611,565],{"className":3612},[612,613]," zu groß.",[560,3615,3617],{"id":3616},"typische-fehler","Typische Fehler",[3619,3620,3621,3756,3970],"ul",{},[3622,3623,3624,3625,3653,3654,3725,3726,3755],"li",{},"Die Näherung bei großem ",[569,3626,3628,3641],{"className":3627},[572],[569,3629,3631],{"className":3630},[576],[578,3632,3633],{"xmlns":580},[582,3634,3635,3639],{},[585,3636,3637],{},[588,3638,565],{},[592,3640,565],{"encoding":594},[569,3642,3644],{"className":3643,"ariaHidden":599},[598],[569,3645,3647,3650],{"className":3646},[603],[569,3648],{"className":3649,"style":640},[607],[569,3651,565],{"className":3652},[612,613]," verwenden. Dann ist die Varianz ",[569,3655,3657,3683],{"className":3656},[572],[569,3658,3660],{"className":3659},[576],[578,3661,3662],{"xmlns":580},[582,3663,3664,3680],{},[585,3665,3666,3668,3670,3672,3674,3676,3678],{},[588,3667,590],{},[588,3669,565],{},[666,3671,939],{"stretchy":960},[793,3673,963],{},[666,3675,966],{},[588,3677,565],{},[666,3679,950],{"stretchy":960},[592,3681,3682],{"encoding":594},"n p (1 - p)",[569,3684,3686,3713],{"className":3685,"ariaHidden":599},[598],[569,3687,3689,3692,3695,3698,3701,3704,3707,3710],{"className":3688},[603],[569,3690],{"className":3691,"style":2588},[607],[569,3693,590],{"className":3694},[612,613],[569,3696,565],{"className":3697},[612,613],[569,3699,939],{"className":3700},[1032],[569,3702,963],{"className":3703},[612],[569,3705],{"className":3706,"style":1149},[692],[569,3708,966],{"className":3709},[1153],[569,3711],{"className":3712,"style":1149},[692],[569,3714,3716,3719,3722],{"className":3715},[603],[569,3717],{"className":3718,"style":2588},[607],[569,3720,565],{"className":3721},[612,613],[569,3723,950],{"className":3724},[1100]," deutlich kleiner als ",[569,3727,3729,3743],{"className":3728},[572],[569,3730,3732],{"className":3731},[576],[578,3733,3734],{"xmlns":580},[582,3735,3736,3740],{},[585,3737,3738],{},[588,3739,664],{},[592,3741,3742],{"encoding":594},"\\lambda",[569,3744,3746],{"className":3745,"ariaHidden":599},[598],[569,3747,3749,3752],{"className":3748},[603],[569,3750],{"className":3751,"style":685},[607],[569,3753,664],{"className":3754},[612,613],", und die Poisson-Verteilung streut zu stark.",[3622,3757,3758,3786,3787,3888,3889,3917,3918,713],{},[569,3759,3761,3774],{"className":3760},[572],[569,3762,3764],{"className":3763},[576],[578,3765,3766],{"xmlns":580},[582,3767,3768,3772],{},[585,3769,3770],{},[588,3771,664],{},[592,3773,3742],{"encoding":594},[569,3775,3777],{"className":3776,"ariaHidden":599},[598],[569,3778,3780,3783],{"className":3779},[603],[569,3781],{"className":3782,"style":685},[607],[569,3784,664],{"className":3785},[612,613]," falsch bilden, z.B. als ",[569,3788,3790,3808],{"className":3789},[572],[569,3791,3793],{"className":3792},[576],[578,3794,3795],{"xmlns":580},[582,3796,3797,3805],{},[585,3798,3799],{},[941,3800,3801,3803],{},[588,3802,590],{},[588,3804,565],{},[592,3806,3807],{"encoding":594},"\\frac{n}{p}",[569,3809,3811],{"className":3810,"ariaHidden":599},[598],[569,3812,3814,3818],{"className":3813},[603],[569,3815],{"className":3816,"style":3817},[607],"height:1.1765em;vertical-align:-0.4811em;",[569,3819,3821,3824,3885],{"className":3820},[612],[569,3822],{"className":3823},[1032,1227],[569,3825,3827],{"className":3826},[941],[569,3828,3830,3876],{"className":3829},[1046,1047],[569,3831,3833,3873],{"className":3832},[1051],[569,3834,3837,3851,3859],{"className":3835,"style":3836},[1055],"height:0.6954em;",[569,3838,3839,3842],{"style":1465},[569,3840],{"className":3841,"style":1064},[1063],[569,3843,3845],{"className":3844},[1134,1135,1039,1136],[569,3846,3848],{"className":3847},[612,1136],[569,3849,565],{"className":3850},[612,613,1136],[569,3852,3853,3856],{"style":1257},[569,3854],{"className":3855,"style":1064},[1063],[569,3857],{"className":3858,"style":1265},[1264],[569,3860,3861,3864],{"style":1488},[569,3862],{"className":3863,"style":1064},[1063],[569,3865,3867],{"className":3866},[1134,1135,1039,1136],[569,3868,3870],{"className":3869},[612,1136],[569,3871,590],{"className":3872},[612,613,1136],[569,3874,1087],{"className":3875},[1086],[569,3877,3879],{"className":3878},[1051],[569,3880,3883],{"className":3881,"style":3882},[1055],"height:0.4811em;",[569,3884],{},[569,3886],{"className":3887},[1100,1227]," oder ",[569,3890,3892,3905],{"className":3891},[572],[569,3893,3895],{"className":3894},[576],[578,3896,3897],{"xmlns":580},[582,3898,3899,3903],{},[585,3900,3901],{},[588,3902,565],{},[592,3904,565],{"encoding":594},[569,3906,3908],{"className":3907,"ariaHidden":599},[598],[569,3909,3911,3914],{"className":3910},[603],[569,3912],{"className":3913,"style":640},[607],[569,3915,565],{"className":3916},[612,613]," statt ",[569,3919,3921,3939],{"className":3920},[572],[569,3922,3924],{"className":3923},[576],[578,3925,3926],{"xmlns":580},[582,3927,3928,3936],{},[585,3929,3930,3932,3934],{},[588,3931,590],{},[666,3933,2117],{},[588,3935,565],{},[592,3937,3938],{"encoding":594},"n \\cdot p",[569,3940,3942,3961],{"className":3941,"ariaHidden":599},[598],[569,3943,3945,3949,3952,3955,3958],{"className":3944},[603],[569,3946],{"className":3947,"style":3948},[607],"height:0.4445em;",[569,3950,590],{"className":3951},[612,613],[569,3953],{"className":3954,"style":1149},[692],[569,3956,2117],{"className":3957},[1153],[569,3959],{"className":3960,"style":1149},[692],[569,3962,3964,3967],{"className":3963},[603],[569,3965],{"className":3966,"style":640},[607],[569,3968,565],{"className":3969},[612,613],[3622,3971,3972,3973,4001],{},"Die Poisson-Näherung mit der Normalverteilungsnäherung verwechseln. Bei kleinem ",[569,3974,3976,3989],{"className":3975},[572],[569,3977,3979],{"className":3978},[576],[578,3980,3981],{"xmlns":580},[582,3982,3983,3987],{},[585,3984,3985],{},[588,3986,664],{},[592,3988,3742],{"encoding":594},[569,3990,3992],{"className":3991,"ariaHidden":599},[598],[569,3993,3995,3998],{"className":3994},[603],[569,3996],{"className":3997,"style":685},[607],[569,3999,664],{"className":4000},[612,613]," ist die Verteilung stark schief, die Normalverteilung passt dann schlecht.",{"title":4003,"searchDepth":4004,"depth":4004,"links":4005},"",2,[4006,4007,4008],{"id":562,"depth":4004,"text":563},{"id":1976,"depth":4004,"text":1977},{"id":3616,"depth":4004,"text":3617},[4010,4013,4015,4018,4021,4024,4026,4029,4031,4034,4037],{"lhs":4011,"rhs":4012},"round((1 - 2\u002F1000000)^1000000, 5)","round(exp(-2), 5)",{"lhs":4014,"rhs":1822},"200 * 0.01",{"lhs":4016,"rhs":4017},"round(0.99^200, 4)","0.134",{"lhs":4019,"rhs":4020},"round(exp(-2), 4)","0.1353",{"lhs":4022,"rhs":4023},"round(sum(map(0:2, f(k) = combinations(200, k) * 0.01^k * 0.99^(200 - k))), 4)","0.6767",{"lhs":4025,"rhs":4023},"round(exp(-2) * (1 + 2 + 2^2\u002F2), 4)",{"lhs":4027,"rhs":4028},"exp(-2) * (1 + 2 + 2)","5 * exp(-2)",{"lhs":4030,"rhs":3225},"20 * 0.3",{"lhs":4032,"rhs":4033},"round(combinations(20, 6) * 0.3^6 * 0.7^14, 4)","0.1916",{"lhs":4035,"rhs":4036},"round(6^6 \u002F 6! * exp(-6), 4)","0.1606",{"lhs":4038,"rhs":4039},"2 * 200 * 0.01^2","0.04","n \\text{ groß},\\ p \\text{ klein (Faustregel: } n \\geq 50,\\ p \\leq 0{,}1),\\ k \\in \\{0, 1, \\ldots, n\\}","\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> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">groß\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>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">klein (Faustregel:\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>50\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmn>0,1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 50,\\ p \\leq 0{,}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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">50\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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\">0\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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>k\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmo stretchy=\"false\">{\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">}\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\in \\{0, 1, \\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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=\"mopen\">{\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>\u003Cspan class=\"mclose\">}\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","poisson-approximation","\\binom{n}{k} p^k (1 - p)^{n-k} \\approx \\frac{\\lambda^k}{k!}\\, e^{-\\lambda}, \\qquad \\lambda = n p","\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>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>n\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmsup>\u003Cmi>p\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>≈\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>λ\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>λ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\binom{n}{k} p^k (1 - p)^{n-k} \\approx \\frac{\\lambda^k}{k!}\\, e^{-\\lambda}, \\qquad \\lambda = n p\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:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\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>\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 delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\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 mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1491em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\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\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:2.2121em;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:1.5261em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\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\">λ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8491em;\">\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 mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8991em;\">\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\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">λ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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\">λ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-naeherung",[],[4053,4054,4055,4056],"poisson-distribution","binomial-distribution","euler-number-limit","moivre-laplace",{"title":548,"description":4003},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-naeherung","Bei vielen Versuchen mit kleiner Trefferwahrscheinlichkeit lässt sich die Binomialverteilung durch die Poisson-Verteilung mit λ = n·p ersetzen.",[4061,4062,4063,4064,4065],"poisson-verteilung","binomialverteilung","näherung","seltene ereignisse","grenzwertsatz",[4067,4070,4073,4076,4079],{"symbol":590,"meaning":4068,"symbolHtml":4069},"Anzahl der unabhängigen Versuche","\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":565,"meaning":4071,"symbolHtml":4072},"Trefferwahrscheinlichkeit pro Versuch","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":902,"meaning":4074,"symbolHtml":4075},"Anzahl der Treffer","\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":3742,"meaning":4077,"symbolHtml":4078},"Erwartungswert der Trefferzahl, λ = n·p","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>λ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lambda\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\">λ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1006,"meaning":4080,"symbolHtml":4081},"Eulersche Zahl, etwa 2,718","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e\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\">e\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","eim4c_V5MzjBuRtpivo-REyMChhNBy2L568vZcwdzbA",[4084,4087,4090,4093],{"stem":4085,"title":4086,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert","Eulersche Zahl als Grenzwert",{"stem":4088,"title":4089,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":4091,"title":4092,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fnaeherung-von-moivre-laplace","Näherung von Moivre-Laplace",{"stem":4094,"title":4095,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fpoisson-verteilung","Poisson-Verteilung",1793824287161]