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\\mu| \\geq k\\sigma\\big) \\leq \\frac{1}{k^2}",[573,895,897,934,956,983],{"className":896,"ariaHidden":604},[603],[573,898,900,904,908,916,919,923,927,931],{"className":899},[608],[573,901],{"className":902,"style":903},[612],"height:1.2em;vertical-align:-0.35em;",[573,905,846],{"className":906,"style":907},[617,618],"margin-right:0.1389em;",[573,909,911],{"className":910},[617],[573,912,851],{"className":913},[914,915],"delimsizing","size1",[573,917,855],{"className":918},[617],[573,920,858],{"className":921,"style":922},[617,618],"margin-right:0.0785em;",[573,924],{"className":925,"style":926},[747],"margin-right:0.2222em;",[573,928,861],{"className":929},[930],"mbin",[573,932],{"className":933,"style":926},[747],[573,935,937,941,944,947,950,953],{"className":936},[608],[573,938],{"className":939,"style":940},[612],"height:1em;vertical-align:-0.25em;",[573,942,594],{"className":943},[617,618],[573,945,855],{"className":946},[617],[573,948],{"className":949,"style":748},[747],[573,951,868],{"className":952},[752],[573,954],{"className":955,"style":748},[747],[573,957,959,962,965,968,974,977,980],{"className":958},[608],[573,960],{"className":961,"style":903},[612],[573,963,725],{"className":964,"style":766},[617,618],[573,966,637],{"className":967,"style":661},[617,618],[573,969,971],{"className":970},[617],[573,972,875],{"className":973},[914,915],[573,975],{"className":976,"style":748},[747],[573,978,878],{"className":979},[752],[573,981],{"className":982,"style":748},[747],[573,984,986,990],{"className":985},[608],[573,987],{"className":988,"style":989},[612],"height:2.0074em;vertical-align:-0.686em;",[573,991,993,998,1090],{"className":992},[617],[573,994],{"className":995},[996,997],"mopen","nulldelimiter",[573,999,1001],{"className":1000},[880],[573,1002,1005,1081],{"className":1003},[669,1004],"vlist-t2",[573,1006,1008,1076],{"className":1007},[673],[573,1009,1012,1053,1064],{"className":1010,"style":1011},[677],"height:1.3214em;",[573,1013,1015,1019],{"style":1014},"top:-2.314em;",[573,1016],{"className":1017,"style":1018},[684],"height:3em;",[573,1020,1022],{"className":1021},[617],[573,1023,1025,1028],{"className":1024},[617],[573,1026,725],{"className":1027,"style":766},[617,618],[573,1029,1031],{"className":1030},[665],[573,1032,1034],{"className":1033},[669],[573,1035,1037],{"className":1036},[673],[573,1038,1041],{"className":1039,"style":1040},[677],"height:0.7401em;",[573,1042,1044,1047],{"style":1043},"top:-2.989em;margin-right:0.05em;",[573,1045],{"className":1046,"style":685},[684],[573,1048,1050],{"className":1049},[689,690,691,692],[573,1051,641],{"className":1052},[617,692],[573,1054,1056,1059],{"style":1055},"top:-3.23em;",[573,1057],{"className":1058,"style":1018},[684],[573,1060],{"className":1061,"style":1063},[1062],"frac-line","border-bottom-width:0.04em;",[573,1065,1067,1070],{"style":1066},"top:-3.677em;",[573,1068],{"className":1069,"style":1018},[684],[573,1071,1073],{"className":1072},[617],[573,1074,884],{"className":1075},[617],[573,1077,1080],{"className":1078},[1079],"vlist-s","​",[573,1082,1084],{"className":1083},[673],[573,1085,1088],{"className":1086,"style":1087},[677],"height:0.686em;",[573,1089],{},[573,1091],{"className":1092},[1093,997],"mclose",[565,1095,1096,1097,1149,1150,1178,1179,1463],{},"Für ",[573,1098,1100,1118],{"className":1099},[576],[573,1101,1103],{"className":1102},[580],[582,1104,1105],{"xmlns":584},[586,1106,1107,1115],{},[589,1108,1109,1111,1113],{},[592,1110,725],{},[720,1112,878],{},[639,1114,884],{},[596,1116,1117],{"encoding":598},"k \\leq 1",[573,1119,1121,1140],{"className":1120,"ariaHidden":604},[603],[573,1122,1124,1128,1131,1134,1137],{"className":1123},[608],[573,1125],{"className":1126,"style":1127},[612],"height:0.8304em;vertical-align:-0.136em;",[573,1129,725],{"className":1130,"style":766},[617,618],[573,1132],{"className":1133,"style":748},[747],[573,1135,878],{"className":1136},[752],[573,1138],{"className":1139,"style":748},[747],[573,1141,1143,1146],{"className":1142},[608],[573,1144],{"className":1145,"style":822},[612],[573,1147,884],{"className":1148},[617]," ist die Schranke mindestens ",[573,1151,1153,1166],{"className":1152},[576],[573,1154,1156],{"className":1155},[580],[582,1157,1158],{"xmlns":584},[586,1159,1160,1164],{},[589,1161,1162],{},[639,1163,884],{},[596,1165,884],{"encoding":598},[573,1167,1169],{"className":1168,"ariaHidden":604},[603],[573,1170,1172,1175],{"className":1171},[608],[573,1173],{"className":1174,"style":822},[612],[573,1176,884],{"className":1177},[617]," und sagt nichts aus. Gleichwertig ist ",[573,1180,1182,1235],{"className":1181},[576],[573,1183,1185],{"className":1184},[580],[582,1186,1187],{"xmlns":584},[586,1188,1189,1232],{},[589,1190,1191,1193,1195,1197,1199,1201,1203,1205,1208,1210,1212,1214,1216,1218],{},[592,1192,846],{},[720,1194,851],{"stretchy":849},[592,1196,855],{"mathvariant":854},[592,1198,858],{},[720,1200,861],{},[592,1202,594],{},[592,1204,855],{"mathvariant":854},[720,1206,1207],{},"\u003C",[592,1209,718],{},[720,1211,875],{"stretchy":849},[720,1213,868],{},[639,1215,884],{},[720,1217,861],{},[880,1219,1220,1226],{},[633,1221,1222,1224],{},[592,1223,637],{},[639,1225,641],{},[633,1227,1228,1230],{},[592,1229,718],{},[639,1231,641],{},[596,1233,1234],{"encoding":598},"P(|X - \\mu| \u003C c) \\geq 1 - \\frac{\\sigma^2}{c^2}",[573,1236,1238,1265,1286,1307,1326],{"className":1237,"ariaHidden":604},[603],[573,1239,1241,1244,1247,1250,1253,1256,1259,1262],{"className":1240},[608],[573,1242],{"className":1243,"style":940},[612],[573,1245,846],{"className":1246,"style":907},[617,618],[573,1248,851],{"className":1249},[996],[573,1251,855],{"className":1252},[617],[573,1254,858],{"className":1255,"style":922},[617,618],[573,1257],{"className":1258,"style":926},[747],[573,1260,861],{"className":1261},[930],[573,1263],{"className":1264,"style":926},[747],[573,1266,1268,1271,1274,1277,1280,1283],{"className":1267},[608],[573,1269],{"className":1270,"style":940},[612],[573,1272,594],{"className":1273},[617,618],[573,1275,855],{"className":1276},[617],[573,1278],{"className":1279,"style":748},[747],[573,1281,1207],{"className":1282},[752],[573,1284],{"className":1285,"style":748},[747],[573,1287,1289,1292,1295,1298,1301,1304],{"className":1288},[608],[573,1290],{"className":1291,"style":940},[612],[573,1293,718],{"className":1294},[617,618],[573,1296,875],{"className":1297},[1093],[573,1299],{"className":1300,"style":748},[747],[573,1302,868],{"className":1303},[752],[573,1305],{"className":1306,"style":748},[747],[573,1308,1310,1314,1317,1320,1323],{"className":1309},[608],[573,1311],{"className":1312,"style":1313},[612],"height:0.7278em;vertical-align:-0.0833em;",[573,1315,884],{"className":1316},[617],[573,1318],{"className":1319,"style":926},[747],[573,1321,861],{"className":1322},[930],[573,1324],{"className":1325,"style":926},[747],[573,1327,1329,1333],{"className":1328},[608],[573,1330],{"className":1331,"style":1332},[612],"height:1.3629em;vertical-align:-0.345em;",[573,1334,1336,1339,1460],{"className":1335},[617],[573,1337],{"className":1338},[996,997],[573,1340,1342],{"className":1341},[880],[573,1343,1345,1451],{"className":1344},[669,1004],[573,1346,1348,1448],{"className":1347},[673],[573,1349,1352,1397,1405],{"className":1350,"style":1351},[677],"height:1.0179em;",[573,1353,1355,1358],{"style":1354},"top:-2.655em;",[573,1356],{"className":1357,"style":1018},[684],[573,1359,1361],{"className":1360},[689,690,691,692],[573,1362,1364],{"className":1363},[617,692],[573,1365,1367,1370],{"className":1366},[617,692],[573,1368,718],{"className":1369},[617,618,692],[573,1371,1373],{"className":1372},[665],[573,1374,1376],{"className":1375},[669],[573,1377,1379],{"className":1378},[673],[573,1380,1383],{"className":1381,"style":1382},[677],"height:0.7463em;",[573,1384,1386,1390],{"style":1385},"top:-2.786em;margin-right:0.0714em;",[573,1387],{"className":1388,"style":1389},[684],"height:2.5em;",[573,1391,1394],{"className":1392},[689,1393,915,692],"reset-size3",[573,1395,641],{"className":1396},[617,692],[573,1398,1399,1402],{"style":1055},[573,1400],{"className":1401,"style":1018},[684],[573,1403],{"className":1404,"style":1063},[1062],[573,1406,1408,1411],{"style":1407},"top:-3.394em;",[573,1409],{"className":1410,"style":1018},[684],[573,1412,1414],{"className":1413},[689,690,691,692],[573,1415,1417],{"className":1416},[617,692],[573,1418,1420,1423],{"className":1419},[617,692],[573,1421,637],{"className":1422,"style":661},[617,618,692],[573,1424,1426],{"className":1425},[665],[573,1427,1429],{"className":1428},[669],[573,1430,1432],{"className":1431},[673],[573,1433,1436],{"className":1434,"style":1435},[677],"height:0.8913em;",[573,1437,1439,1442],{"style":1438},"top:-2.931em;margin-right:0.0714em;",[573,1440],{"className":1441,"style":1389},[684],[573,1443,1445],{"className":1444},[689,1393,915,692],[573,1446,641],{"className":1447},[617,692],[573,1449,1080],{"className":1450},[1079],[573,1452,1454],{"className":1453},[673],[573,1455,1458],{"className":1456,"style":1457},[677],"height:0.345em;",[573,1459],{},[573,1461],{"className":1462},[1093,997],".",[565,1465,1466,1469,1470,1553,1554,1816,1817,1463],{},[569,1467,1468],{},"Herleitung:"," Mit dem Indikator des Ereignisses ",[573,1471,1473,1499],{"className":1472},[576],[573,1474,1476],{"className":1475},[580],[582,1477,1478],{"xmlns":584},[586,1479,1480,1496],{},[589,1481,1482,1484,1486,1488,1490,1492,1494],{},[592,1483,855],{"mathvariant":854},[592,1485,858],{},[720,1487,861],{},[592,1489,594],{},[592,1491,855],{"mathvariant":854},[720,1493,868],{},[592,1495,718],{},[596,1497,1498],{"encoding":598},"|X - \\mu| \\geq c",[573,1500,1502,1523,1544],{"className":1501,"ariaHidden":604},[603],[573,1503,1505,1508,1511,1514,1517,1520],{"className":1504},[608],[573,1506],{"className":1507,"style":940},[612],[573,1509,855],{"className":1510},[617],[573,1512,858],{"className":1513,"style":922},[617,618],[573,1515],{"className":1516,"style":926},[747],[573,1518,861],{"className":1519},[930],[573,1521],{"className":1522,"style":926},[747],[573,1524,1526,1529,1532,1535,1538,1541],{"className":1525},[608],[573,1527],{"className":1528,"style":940},[612],[573,1530,594],{"className":1531},[617,618],[573,1533,855],{"className":1534},[617],[573,1536],{"className":1537,"style":748},[747],[573,1539,868],{"className":1540},[752],[573,1542],{"className":1543,"style":748},[747],[573,1545,1547,1550],{"className":1546},[608],[573,1548],{"className":1549,"style":740},[612],[573,1551,718],{"className":1552},[617,618]," gilt ",[573,1555,1557,1622],{"className":1556},[576],[573,1558,1560],{"className":1559},[580],[582,1561,1562],{"xmlns":584},[586,1563,1564,1619],{},[589,1565,1566,1572,1575,1603,1605,1607,1609,1611,1613],{},[633,1567,1568,1570],{},[592,1569,718],{},[639,1571,641],{},[720,1573,1574],{},"⋅",[1576,1577,1578,1581],"msub",{},[639,1579,884],{"mathvariant":1580},"bold",[589,1582,1583,1586,1588,1590,1592,1594,1596,1598,1600],{},[720,1584,1585],{"stretchy":849},"{",[592,1587,855],{"mathvariant":854},[592,1589,858],{},[720,1591,861],{},[592,1593,594],{},[592,1595,855],{"mathvariant":854},[720,1597,868],{},[592,1599,718],{},[720,1601,1602],{"stretchy":849},"}",[720,1604,878],{},[720,1606,851],{"stretchy":849},[592,1608,858],{},[720,1610,861],{},[592,1612,594],{},[633,1614,1615,1617],{},[720,1616,875],{"stretchy":849},[639,1618,641],{},[596,1620,1621],{"encoding":598},"c^2 \\cdot \\mathbf{1}_{\\{|X - \\mu| \\geq c\\}} \\leq (X - 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Erwartungswert bilden liefert ",[573,1818,1820,1868],{"className":1819},[576],[573,1821,1823],{"className":1822},[580],[582,1824,1825],{"xmlns":584},[586,1826,1827,1865],{},[589,1828,1829,1835,1837,1839,1841,1843,1845,1847,1849,1851,1853,1855,1857,1859],{},[633,1830,1831,1833],{},[592,1832,718],{},[639,1834,641],{},[720,1836,1574],{},[592,1838,846],{},[720,1840,851],{"stretchy":849},[592,1842,855],{"mathvariant":854},[592,1844,858],{},[720,1846,861],{},[592,1848,594],{},[592,1850,855],{"mathvariant":854},[720,1852,868],{},[592,1854,718],{},[720,1856,875],{"stretchy":849},[720,1858,878],{},[633,1860,1861,1863],{},[592,1862,637],{},[639,1864,641],{},[596,1866,1867],{"encoding":598},"c^2 \\cdot P(|X - \\mu| \\geq c) \\leq \\sigma^2",[573,1869,1871,1915,1942,1963,1984],{"className":1870,"ariaHidden":604},[603],[573,1872,1874,1877,1906,1909,1912],{"className":1873},[608],[573,1875],{"className":1876,"style":654},[612],[573,1878,1880,1883],{"className":1879},[617],[573,1881,718],{"className":1882},[617,618],[573,1884,1886],{"className":1885},[665],[573,1887,1889],{"className":1888},[669],[573,1890,1892],{"className":1891},[673],[573,1893,1895],{"className":1894,"style":654},[677],[573,1896,1897,1900],{"style":680},[573,1898],{"className":1899,"style":685},[684],[573,1901,1903],{"className":1902},[689,690,691,692],[573,1904,641],{"className":1905},[617,692],[573,1907],{"className":1908,"style":926},[747],[573,1910,1574],{"className":1911},[930],[573,1913],{"className":1914,"style":926},[747],[573,1916,1918,1921,1924,1927,1930,1933,1936,1939],{"className":1917},[608],[573,1919],{"className":1920,"style":940},[612],[573,1922,846],{"className":1923,"style":907},[617,618],[573,1925,851],{"className":1926},[996],[573,1928,855],{"className":1929},[617],[573,1931,858],{"className":1932,"style":922},[617,618],[573,1934],{"className":1935,"style":926},[747],[573,1937,861],{"className":1938},[930],[573,1940],{"className":1941,"style":926},[747],[573,1943,1945,1948,1951,1954,1957,1960],{"className":1944},[608],[573,1946],{"className":1947,"style":940},[612],[573,1949,594],{"className":1950},[617,618],[573,1952,855],{"className":1953},[617],[573,1955],{"className":1956,"style":748},[747],[573,1958,868],{"className":1959},[752],[573,1961],{"className":1962,"style":748},[747],[573,1964,1966,1969,1972,1975,1978,1981],{"className":1965},[608],[573,1967],{"className":1968,"style":940},[612],[573,1970,718],{"className":1971},[617,618],[573,1973,875],{"className":1974},[1093],[573,1976],{"className":1977,"style":748},[747],[573,1979,878],{"className":1980},[752],[573,1982],{"className":1983,"style":748},[747],[573,1985,1987,1990],{"className":1986},[608],[573,1988],{"className":1989,"style":654},[612],[573,1991,1993,1996],{"className":1992},[617],[573,1994,637],{"className":1995,"style":661},[617,618],[573,1997,1999],{"className":1998},[665],[573,2000,2002],{"className":2001},[669],[573,2003,2005],{"className":2004},[673],[573,2006,2008],{"className":2007,"style":654},[677],[573,2009,2010,2013],{"style":680},[573,2011],{"className":2012,"style":685},[684],[573,2014,2016],{"className":2015},[689,690,691,692],[573,2017,641],{"className":2018},[617,692],[565,2020,2021,2022,2025,2026,2102,2103,2131,2132,2160,2161,2376],{},"Wichtigste Anwendung ist das ",[569,2023,2024],{},"schwache Gesetz der großen Zahlen",": Für die relative Häufigkeit 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in ",[573,2104,2106,2119],{"className":2105},[576],[573,2107,2109],{"className":2108},[580],[582,2110,2111],{"xmlns":584},[586,2112,2113,2117],{},[589,2114,2115],{},[592,2116,2045],{},[596,2118,2045],{"encoding":598},[573,2120,2122],{"className":2121,"ariaHidden":604},[603],[573,2123,2125,2128],{"className":2124},[608],[573,2126],{"className":2127,"style":740},[612],[573,2129,2045],{"className":2130},[617,618]," unabhängigen Versuchen mit Trefferwahrscheinlichkeit ",[573,2133,2135,2148],{"className":2134},[576],[573,2136,2138],{"className":2137},[580],[582,2139,2140],{"xmlns":584},[586,2141,2142,2146],{},[589,2143,2144],{},[592,2145,565],{},[596,2147,565],{"encoding":598},[573,2149,2151],{"className":2150,"ariaHidden":604},[603],[573,2152,2154,2157],{"className":2153},[608],[573,2155],{"className":2156,"style":613},[612],[573,2158,565],{"className":2159},[617,618]," ist 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Abweichung um mindestens ",[573,3234,3236,3255],{"className":3235},[576],[573,3237,3239],{"className":3238},[580],[582,3240,3241],{"xmlns":584},[586,3242,3243,3252],{},[589,3244,3245,3248,3250],{},[639,3246,3247],{},"10",[3118,3249,3120],{},[3118,3251,3123],{},[596,3253,3254],{"encoding":598},"10\\,\\text{g}",[573,3256,3258],{"className":3257,"ariaHidden":604},[603],[573,3259,3261,3264,3267,3270],{"className":3260},[608],[573,3262],{"className":3263,"style":3019},[612],[573,3265,3247],{"className":3266},[617],[573,3268],{"className":3269,"style":3160},[747],[573,3271,3273],{"className":3272},[617,3164],[573,3274,3123],{"className":3275},[617],":",[573,3278,3280],{"className":3279},[830],[573,3281,3283,3336],{"className":3282},[576],[573,3284,3286],{"className":3285},[580],[582,3287,3288],{"xmlns":584,"display":839},[586,3289,3290,3333],{},[589,3291,3292,3294,3296,3298,3300,3302,3304,3306,3308,3310,3312,3314,3328,3330],{},[592,3293,846],{},[720,3295,851],{"fence":849,"stretchy":604,"minsize":850,"maxsize":850},[592,3297,855],{"mathvariant":854},[592,3299,858],{},[720,3301,861],{},[639,3303,3116],{},[592,3305,855],{"mathvariant":854},[720,3307,868],{},[639,3309,3247],{},[720,3311,875],{"fence":849,"stretchy":604,"minsize":850,"maxsize":850},[720,3313,878],{},[880,3315,3316,3322],{},[633,3317,3318,3320],{},[639,3319,2454],{},[639,3321,641],{},[633,3323,3324,3326],{},[639,3325,3247],{},[639,3327,641],{},[720,3329,722],{},[639,3331,3332],{},"0,16",[596,3334,3335],{"encoding":598},"P\\big(|X - 500| \\geq 10\\big) \\leq \\frac{4^2}{10^2} = 0{,}16",[573,3337,3339,3369,3388,3412,3546],{"className":3338,"ariaHidden":604},[603],[573,3340,3342,3345,3348,3354,3357,3360,3363,3366],{"className":3341},[608],[573,3343],{"className":3344,"style":903},[612],[573,3346,846],{"className":3347,"style":907},[617,618],[573,3349,3351],{"className":3350},[617],[573,3352,851],{"className":3353},[914,915],[573,3355,855],{"className":3356},[617],[573,3358,858],{"className":3359,"style":922},[617,618],[573,3361],{"className":3362,"style":926},[747],[573,3364,861],{"className":3365},[930],[573,3367],{"className":3368,"style":926},[747],[573,3370,3372,3375,3379,3382,3385],{"className":3371},[608],[573,3373],{"className":3374,"style":940},[612],[573,3376,3378],{"className":3377},[617],"500∣",[573,3380],{"className":3381,"style":748},[747],[573,3383,868],{"className":3384},[752],[573,3386],{"className":3387,"style":748},[747],[573,3389,3391,3394,3397,3403,3406,3409],{"className":3390},[608],[573,3392],{"className":3393,"style":903},[612],[573,3395,3247],{"className":3396},[617],[573,3398,3400],{"className":3399},[617],[573,3401,875],{"className":3402},[914,915],[573,3404],{"className":3405,"style":748},[747],[573,3407,878],{"className":3408},[752],[573,3410],{"className":3411,"style":748},[747],[573,3413,3415,3419,3537,3540,3543],{"className":3414},[608],[573,3416],{"className":3417,"style":3418},[612],"height:2.1771em;vertical-align:-0.686em;",[573,3420,3422,3425,3534],{"className":3421},[617],[573,3423],{"className":3424},[996,997],[573,3426,3428],{"className":3427},[880],[573,3429,3431,3526],{"className":3430},[669,1004],[573,3432,3434,3523],{"className":3433},[673],[573,3435,3438,3478,3486],{"className":3436,"style":3437},[677],"height:1.4911em;",[573,3439,3440,3443],{"style":1014},[573,3441],{"className":3442,"style":1018},[684],[573,3444,3446,3449],{"className":3445},[617],[573,3447,884],{"className":3448},[617],[573,3450,3452,3455],{"className":3451},[617],[573,3453,790],{"className":3454},[617],[573,3456,3458],{"className":3457},[665],[573,3459,3461],{"className":3460},[669],[573,3462,3464],{"className":3463},[673],[573,3465,3467],{"className":3466,"style":1040},[677],[573,3468,3469,3472],{"style":1043},[573,3470],{"className":3471,"style":685},[684],[573,3473,3475],{"className":3474},[689,690,691,692],[573,3476,641],{"className":3477},[617,692],[573,3479,3480,3483],{"style":1055},[573,3481],{"className":3482,"style":1018},[684],[573,3484],{"className":3485,"style":1063},[1062],[573,3487,3488,3491],{"style":1066},[573,3489],{"className":3490,"style":1018},[684],[573,3492,3494],{"className":3493},[617],[573,3495,3497,3500],{"className":3496},[617],[573,3498,2454],{"className":3499},[617],[573,3501,3503],{"className":3502},[665],[573,3504,3506],{"className":3505},[669],[573,3507,3509],{"className":3508},[673],[573,3510,3512],{"className":3511,"style":654},[677],[573,3513,3514,3517],{"style":680},[573,3515],{"className":3516,"style":685},[684],[573,3518,3520],{"className":3519},[689,690,691,692],[573,3521,641],{"className":3522},[617,692],[573,3524,1080],{"className":3525},[1079],[573,3527,3529],{"className":3528},[673],[573,3530,3532],{"className":3531,"style":1087},[677],[573,3533],{},[573,3535],{"className":3536},[1093,997],[573,3538],{"className":3539,"style":748},[747],[573,3541,722],{"className":3542},[752],[573,3544],{"className":3545,"style":748},[747],[573,3547,3549,3552,3555,3561],{"className":3548},[608],[573,3550],{"className":3551,"style":3019},[612],[573,3553,790],{"className":3554},[617],[573,3556,3558],{"className":3557},[617],[573,3559,3030],{"className":3560},[3029],[573,3562,3564],{"className":3563},[617],"16",[565,3566,3567,3568,3619,3620,3784,3785,3819,3820,3872,3873,4017,4018,4068,4069,4118],{},"Mit ",[573,3569,3571,3589],{"className":3570},[576],[573,3572,3574],{"className":3573},[580],[582,3575,3576],{"xmlns":584},[586,3577,3578,3586],{},[589,3579,3580,3582,3584],{},[592,3581,725],{},[720,3583,722],{},[639,3585,641],{},[596,3587,3588],{"encoding":598},"k = 2",[573,3590,3592,3610],{"className":3591,"ariaHidden":604},[603],[573,3593,3595,3598,3601,3604,3607],{"className":3594},[608],[573,3596],{"className":3597,"style":762},[612],[573,3599,725],{"className":3600,"style":766},[617,618],[573,3602],{"className":3603,"style":748},[747],[573,3605,722],{"className":3606},[752],[573,3608],{"className":3609,"style":748},[747],[573,3611,3613,3616],{"className":3612},[608],[573,3614],{"className":3615,"style":822},[612],[573,3617,641],{"className":3618},[617]," liegen höchstens ",[573,3621,3623,3654],{"className":3622},[576],[573,3624,3626],{"className":3625},[580],[582,3627,3628],{"xmlns":584},[586,3629,3630,3651],{},[589,3631,3632,3642,3644,3646,3648],{},[880,3633,3634,3636],{},[639,3635,884],{},[633,3637,3638,3640],{},[639,3639,641],{},[639,3641,641],{},[720,3643,722],{},[639,3645,3089],{},[3118,3647,3120],{},[592,3649,3650],{"mathvariant":854},"%",[596,3652,3653],{"encoding":598},"\\frac{1}{2^2} = 25\\,\\%",[573,3655,3657,3768],{"className":3656,"ariaHidden":604},[603],[573,3658,3660,3664,3759,3762,3765],{"className":3659},[608],[573,3661],{"className":3662,"style":3663},[612],"height:1.1901em;vertical-align:-0.345em;",[573,3665,3667,3670,3756],{"className":3666},[617],[573,3668],{"className":3669},[996,997],[573,3671,3673],{"className":3672},[880],[573,3674,3676,3748],{"className":3675},[669,1004],[573,3677,3679,3745],{"className":3678},[673],[573,3680,3683,3723,3731],{"className":3681,"style":3682},[677],"height:0.8451em;",[573,3684,3685,3688],{"style":1354},[573,3686],{"className":3687,"style":1018},[684],[573,3689,3691],{"className":3690},[689,690,691,692],[573,3692,3694],{"className":3693},[617,692],[573,3695,3697,3700],{"className":3696},[617,692],[573,3698,641],{"className":3699},[617,692],[573,3701,3703],{"className":3702},[665],[573,3704,3706],{"className":3705},[669],[573,3707,3709],{"className":3708},[673],[573,3710,3712],{"className":3711,"style":1382},[677],[573,3713,3714,3717],{"style":1385},[573,3715],{"className":3716,"style":1389},[684],[573,3718,3720],{"className":3719},[689,1393,915,692],[573,3721,641],{"className":3722},[617,692],[573,3724,3725,3728],{"style":1055},[573,3726],{"className":3727,"style":1018},[684],[573,3729],{"className":3730,"style":1063},[1062],[573,3732,3733,3736],{"style":1407},[573,3734],{"className":3735,"style":1018},[684],[573,3737,3739],{"className":3738},[689,690,691,692],[573,3740,3742],{"className":3741},[617,692],[573,3743,884],{"className":3744},[617,692],[573,3746,1080],{"className":3747},[1079],[573,3749,3751],{"className":3750},[673],[573,3752,3754],{"className":3753,"style":1457},[677],[573,3755],{},[573,3757],{"className":3758},[1093,997],[573,3760],{"className":3761,"style":748},[747],[573,3763,722],{"className":3764},[752],[573,3766],{"className":3767,"style":748},[747],[573,3769,3771,3775,3778,3781],{"className":3770},[608],[573,3772],{"className":3773,"style":3774},[612],"height:0.8056em;vertical-align:-0.0556em;",[573,3776,3089],{"className":3777},[617],[573,3779],{"className":3780,"style":3160},[747],[573,3782,3650],{"className":3783},[617]," der Werte außerhalb der ",[573,3786,3788,3804],{"className":3787},[576],[573,3789,3791],{"className":3790},[580],[582,3792,3793],{"xmlns":584},[586,3794,3795,3801],{},[589,3796,3797,3799],{},[639,3798,641],{},[592,3800,637],{},[596,3802,3803],{"encoding":598},"2\\sigma",[573,3805,3807],{"className":3806,"ariaHidden":604},[603],[573,3808,3810,3813,3816],{"className":3809},[608],[573,3811],{"className":3812,"style":822},[612],[573,3814,641],{"className":3815},[617],[573,3817,637],{"className":3818,"style":661},[617,618],"-Umgebung, mit ",[573,3821,3823,3842],{"className":3822},[576],[573,3824,3826],{"className":3825},[580],[582,3827,3828],{"xmlns":584},[586,3829,3830,3839],{},[589,3831,3832,3834,3836],{},[592,3833,725],{},[720,3835,722],{},[639,3837,3838],{},"3",[596,3840,3841],{"encoding":598},"k = 3",[573,3843,3845,3863],{"className":3844,"ariaHidden":604},[603],[573,3846,3848,3851,3854,3857,3860],{"className":3847},[608],[573,3849],{"className":3850,"style":762},[612],[573,3852,725],{"className":3853,"style":766},[617,618],[573,3855],{"className":3856,"style":748},[747],[573,3858,722],{"className":3859},[752],[573,3861],{"className":3862,"style":748},[747],[573,3864,3866,3869],{"className":3865},[608],[573,3867],{"className":3868,"style":822},[612],[573,3870,3838],{"className":3871},[617]," höchstens ",[573,3874,3876,3905],{"className":3875},[576],[573,3877,3879],{"className":3878},[580],[582,3880,3881],{"xmlns":584},[586,3882,3883,3902],{},[589,3884,3885,3892,3895,3898,3900],{},[880,3886,3887,3889],{},[639,3888,884],{},[639,3890,3891],{},"9",[720,3893,3894],{},"≈",[639,3896,3897],{},"11,1",[3118,3899,3120],{},[592,3901,3650],{"mathvariant":854},[596,3903,3904],{"encoding":598},"\\frac{1}{9} \\approx 11{,}1\\,\\%",[573,3906,3908,3991],{"className":3907,"ariaHidden":604},[603],[573,3909,3911,3914,3982,3985,3988],{"className":3910},[608],[573,3912],{"className":3913,"style":3663},[612],[573,3915,3917,3920,3979],{"className":3916},[617],[573,3918],{"className":3919},[996,997],[573,3921,3923],{"className":3922},[880],[573,3924,3926,3971],{"className":3925},[669,1004],[573,3927,3929,3968],{"className":3928},[673],[573,3930,3932,3946,3954],{"className":3931,"style":3682},[677],[573,3933,3934,3937],{"style":1354},[573,3935],{"className":3936,"style":1018},[684],[573,3938,3940],{"className":3939},[689,690,691,692],[573,3941,3943],{"className":3942},[617,692],[573,3944,3891],{"className":3945},[617,692],[573,3947,3948,3951],{"style":1055},[573,3949],{"className":3950,"style":1018},[684],[573,3952],{"className":3953,"style":1063},[1062],[573,3955,3956,3959],{"style":1407},[573,3957],{"className":3958,"style":1018},[684],[573,3960,3962],{"className":3961},[689,690,691,692],[573,3963,3965],{"className":3964},[617,692],[573,3966,884],{"className":3967},[617,692],[573,3969,1080],{"className":3970},[1079],[573,3972,3974],{"className":3973},[673],[573,3975,3977],{"className":3976,"style":1457},[677],[573,3978],{},[573,3980],{"className":3981},[1093,997],[573,3983],{"className":3984,"style":748},[747],[573,3986,3894],{"className":3987},[752],[573,3989],{"className":3990,"style":748},[747],[573,3992,3994,3998,4002,4008,4011,4014],{"className":3993},[608],[573,3995],{"className":3996,"style":3997},[612],"height:0.9444em;vertical-align:-0.1944em;",[573,3999,4001],{"className":4000},[617],"11",[573,4003,4005],{"className":4004},[617],[573,4006,3030],{"className":4007},[3029],[573,4009,884],{"className":4010},[617],[573,4012],{"className":4013,"style":3160},[747],[573,4015,3650],{"className":4016},[617],". Bei einer Normalverteilung wären es nur etwa ",[573,4019,4021,4040],{"className":4020},[576],[573,4022,4024],{"className":4023},[580],[582,4025,4026],{"xmlns":584},[586,4027,4028,4037],{},[589,4029,4030,4033,4035],{},[639,4031,4032],{},"4,6",[3118,4034,3120],{},[592,4036,3650],{"mathvariant":854},[596,4038,4039],{"encoding":598},"4{,}6\\,\\%",[573,4041,4043],{"className":4042,"ariaHidden":604},[603],[573,4044,4046,4049,4052,4058,4062,4065],{"className":4045},[608],[573,4047],{"className":4048,"style":3997},[612],[573,4050,2454],{"className":4051},[617],[573,4053,4055],{"className":4054},[617],[573,4056,3030],{"className":4057},[3029],[573,4059,4061],{"className":4060},[617],"6",[573,4063],{"className":4064,"style":3160},[747],[573,4066,3650],{"className":4067},[617]," bzw. ",[573,4070,4072,4091],{"className":4071},[576],[573,4073,4075],{"className":4074},[580],[582,4076,4077],{"xmlns":584},[586,4078,4079,4088],{},[589,4080,4081,4084,4086],{},[639,4082,4083],{},"0,3",[3118,4085,3120],{},[592,4087,3650],{"mathvariant":854},[596,4089,4090],{"encoding":598},"0{,}3\\,\\%",[573,4092,4094],{"className":4093,"ariaHidden":604},[603],[573,4095,4097,4100,4103,4109,4112,4115],{"className":4096},[608],[573,4098],{"className":4099,"style":3997},[612],[573,4101,790],{"className":4102},[617],[573,4104,4106],{"className":4105},[617],[573,4107,3030],{"className":4108},[3029],[573,4110,3838],{"className":4111},[617],[573,4113],{"className":4114,"style":3160},[747],[573,4116,3650],{"className":4117},[617],"; die Schranke ist grob, dafür allgemein.",[565,4120,4121,4122,4174,4175,4372,4373,4412,4413,4441],{},"Münzwurf mit ",[573,4123,4125,4144],{"className":4124},[576],[573,4126,4128],{"className":4127},[580],[582,4129,4130],{"xmlns":584},[586,4131,4132,4141],{},[589,4133,4134,4136,4138],{},[592,4135,2045],{},[720,4137,722],{},[639,4139,4140],{},"1000",[596,4142,4143],{"encoding":598},"n = 1000",[573,4145,4147,4165],{"className":4146,"ariaHidden":604},[603],[573,4148,4150,4153,4156,4159,4162],{"className":4149},[608],[573,4151],{"className":4152,"style":740},[612],[573,4154,2045],{"className":4155},[617,618],[573,4157],{"className":4158,"style":748},[747],[573,4160,722],{"className":4161},[752],[573,4163],{"className":4164,"style":748},[747],[573,4166,4168,4171],{"className":4167},[608],[573,4169],{"className":4170,"style":822},[612],[573,4172,4140],{"className":4173},[617],": Die relative Häufigkeit weicht nur mit einer Wahrscheinlichkeit von höchstens ",[573,4176,4178,4216],{"className":4177},[576],[573,4179,4181],{"className":4180},[580],[582,4182,4183],{"xmlns":584},[586,4184,4185,4213],{},[589,4186,4187,4208,4210],{},[880,4188,4189,4191],{},[639,4190,884],{},[589,4192,4193,4195,4197,4199,4201],{},[639,4194,2454],{},[720,4196,1574],{},[639,4198,4140],{},[720,4200,1574],{},[633,4202,4203,4206],{},[639,4204,4205],{},"0,05",[639,4207,641],{},[720,4209,722],{},[639,4211,4212],{},"0,1",[596,4214,4215],{"encoding":598},"\\frac{1}{4 \\cdot 1000 \\cdot 0{,}05^2} = 0{,}1",[573,4217,4219,4354],{"className":4218,"ariaHidden":604},[603],[573,4220,4222,4226,4345,4348,4351],{"className":4221},[608],[573,4223],{"className":4224,"style":4225},[612],"height:1.3262em;vertical-align:-0.4811em;",[573,4227,4229,4232,4342],{"className":4228},[617],[573,4230],{"className":4231},[996,997],[573,4233,4235],{"className":4234},[880],[573,4236,4238,4333],{"className":4237},[669,1004],[573,4239,4241,4330],{"className":4240},[673],[573,4242,4244,4308,4316],{"className":4243,"style":3682},[677],[573,4245,4246,4249],{"style":1354},[573,4247],{"className":4248,"style":1018},[684],[573,4250,4252],{"className":4251},[689,690,691,692],[573,4253,4255,4258,4261,4264,4267,4270,4276,4279],{"className":4254},[617,692],[573,4256,2454],{"className":4257},[617,692],[573,4259,1574],{"className":4260},[930,692],[573,4262,4140],{"className":4263},[617,692],[573,4265,1574],{"className":4266},[930,692],[573,4268,790],{"className":4269},[617,692],[573,4271,4273],{"className":4272},[617,692],[573,4274,3030],{"className":4275},[3029,692],[573,4277,790],{"className":4278},[617,692],[573,4280,4282,4285],{"className":4281},[617,692],[573,4283,3034],{"className":4284},[617,692],[573,4286,4288],{"className":4287},[665],[573,4289,4291],{"className":4290},[669],[573,4292,4294],{"className":4293},[673],[573,4295,4297],{"className":4296,"style":1382},[677],[573,4298,4299,4302],{"style":1385},[573,4300],{"className":4301,"style":1389},[684],[573,4303,4305],{"className":4304},[689,1393,915,692],[573,4306,641],{"className":4307},[617,692],[573,4309,4310,4313],{"style":1055},[573,4311],{"className":4312,"style":1018},[684],[573,4314],{"className":4315,"style":1063},[1062],[573,4317,4318,4321],{"style":1407},[573,4319],{"className":4320,"style":1018},[684],[573,4322,4324],{"className":4323},[689,690,691,692],[573,4325,4327],{"className":4326},[617,692],[573,4328,884],{"className":4329},[617,692],[573,4331,1080],{"className":4332},[1079],[573,4334,4336],{"className":4335},[673],[573,4337,4340],{"className":4338,"style":4339},[677],"height:0.4811em;",[573,4341],{},[573,4343],{"className":4344},[1093,997],[573,4346],{"className":4347,"style":748},[747],[573,4349,722],{"className":4350},[752],[573,4352],{"className":4353,"style":748},[747],[573,4355,4357,4360,4363,4369],{"className":4356},[608],[573,4358],{"className":4359,"style":3019},[612],[573,4361,790],{"className":4362},[617],[573,4364,4366],{"className":4365},[617],[573,4367,3030],{"className":4368},[3029],[573,4370,884],{"className":4371},[617]," um ",[573,4374,4376,4390],{"className":4375},[576],[573,4377,4379],{"className":4378},[580],[582,4380,4381],{"xmlns":584},[586,4382,4383,4387],{},[589,4384,4385],{},[639,4386,4205],{},[596,4388,4389],{"encoding":598},"0{,}05",[573,4391,4393],{"className":4392,"ariaHidden":604},[603],[573,4394,4396,4399,4402,4408],{"className":4395},[608],[573,4397],{"className":4398,"style":3019},[612],[573,4400,790],{"className":4401},[617],[573,4403,4405],{"className":4404},[617],[573,4406,3030],{"className":4407},[3029],[573,4409,4411],{"className":4410},[617],"05"," oder mehr von ",[573,4414,4416,4429],{"className":4415},[576],[573,4417,4419],{"className":4418},[580],[582,4420,4421],{"xmlns":584},[586,4422,4423,4427],{},[589,4424,4425],{},[592,4426,565],{},[596,4428,565],{"encoding":598},[573,4430,4432],{"className":4431,"ariaHidden":604},[603],[573,4433,4435,4438],{"className":4434},[608],[573,4436],{"className":4437,"style":613},[612],[573,4439,565],{"className":4440},[617,618]," ab.",[560,4443,4445],{"id":4444},"typische-fehler","Typische Fehler",[4447,4448,4449,4496,4719,4818],"ul",{},[4450,4451,4452,4453,4491,4492,4495],"li",{},"Die Schranke als Näherungswert lesen. ",[573,4454,4456,4470],{"className":4455},[576],[573,4457,4459],{"className":4458},[580],[582,4460,4461],{"xmlns":584},[586,4462,4463,4467],{},[589,4464,4465],{},[639,4466,3332],{},[596,4468,4469],{"encoding":598},"0{,}16",[573,4471,4473],{"className":4472,"ariaHidden":604},[603],[573,4474,4476,4479,4482,4488],{"className":4475},[608],[573,4477],{"className":4478,"style":3019},[612],[573,4480,790],{"className":4481},[617],[573,4483,4485],{"className":4484},[617],[573,4486,3030],{"className":4487},[3029],[573,4489,3564],{"className":4490},[617]," ist nur eine ",[569,4493,4494],{},"obere Grenze","; die tatsächliche Wahrscheinlichkeit kann viel kleiner sein.",[4450,4497,4498,4527,4528,4586,4587,4718],{},[573,4499,4501,4515],{"className":4500},[576],[573,4502,4504],{"className":4503},[580],[582,4505,4506],{"xmlns":584},[586,4507,4508,4512],{},[589,4509,4510],{},[592,4511,637],{},[596,4513,4514],{"encoding":598},"\\sigma",[573,4516,4518],{"className":4517,"ariaHidden":604},[603],[573,4519,4521,4524],{"className":4520},[608],[573,4522],{"className":4523,"style":740},[612],[573,4525,637],{"className":4526,"style":661},[617,618]," statt ",[573,4529,4531,4548],{"className":4530},[576],[573,4532,4534],{"className":4533},[580],[582,4535,4536],{"xmlns":584},[586,4537,4538,4546],{},[589,4539,4540],{},[633,4541,4542,4544],{},[592,4543,637],{},[639,4545,641],{},[596,4547,644],{"encoding":598},[573,4549,4551],{"className":4550,"ariaHidden":604},[603],[573,4552,4554,4557],{"className":4553},[608],[573,4555],{"className":4556,"style":654},[612],[573,4558,4560,4563],{"className":4559},[617],[573,4561,637],{"className":4562,"style":661},[617,618],[573,4564,4566],{"className":4565},[665],[573,4567,4569],{"className":4568},[669],[573,4570,4572],{"className":4571},[673],[573,4573,4575],{"className":4574,"style":654},[677],[573,4576,4577,4580],{"style":680},[573,4578],{"className":4579,"style":685},[684],[573,4581,4583],{"className":4582},[689,690,691,692],[573,4584,641],{"className":4585},[617,692]," im Zähler einsetzen. Mit ",[573,4588,4590,4612],{"className":4589},[576],[573,4591,4593],{"className":4592},[580],[582,4594,4595],{"xmlns":584},[586,4596,4597,4609],{},[589,4598,4599],{},[880,4600,4601,4603],{},[639,4602,2454],{},[633,4604,4605,4607],{},[639,4606,3247],{},[639,4608,641],{},[596,4610,4611],{"encoding":598},"\\frac{4}{10^2}",[573,4613,4615],{"className":4614,"ariaHidden":604},[603],[573,4616,4618,4621],{"className":4617},[608],[573,4619],{"className":4620,"style":3663},[612],[573,4622,4624,4627,4715],{"className":4623},[617],[573,4625],{"className":4626},[996,997],[573,4628,4630],{"className":4629},[880],[573,4631,4633,4707],{"className":4632},[669,1004],[573,4634,4636,4704],{"className":4635},[673],[573,4637,4639,4682,4690],{"className":4638,"style":3682},[677],[573,4640,4641,4644],{"style":1354},[573,4642],{"className":4643,"style":1018},[684],[573,4645,4647],{"className":4646},[689,690,691,692],[573,4648,4650,4653],{"className":4649},[617,692],[573,4651,884],{"className":4652},[617,692],[573,4654,4656,4659],{"className":4655},[617,692],[573,4657,790],{"className":4658},[617,692],[573,4660,4662],{"className":4661},[665],[573,4663,4665],{"className":4664},[669],[573,4666,4668],{"className":4667},[673],[573,4669,4671],{"className":4670,"style":1382},[677],[573,4672,4673,4676],{"style":1385},[573,4674],{"className":4675,"style":1389},[684],[573,4677,4679],{"className":4678},[689,1393,915,692],[573,4680,641],{"className":4681},[617,692],[573,4683,4684,4687],{"style":1055},[573,4685],{"className":4686,"style":1018},[684],[573,4688],{"className":4689,"style":1063},[1062],[573,4691,4692,4695],{"style":1407},[573,4693],{"className":4694,"style":1018},[684],[573,4696,4698],{"className":4697},[689,690,691,692],[573,4699,4701],{"className":4700},[617,692],[573,4702,2454],{"className":4703},[617,692],[573,4705,1080],{"className":4706},[1079],[573,4708,4710],{"className":4709},[673],[573,4711,4713],{"className":4712,"style":1457},[677],[573,4714],{},[573,4716],{"className":4717},[1093,997]," wäre die Schranke falsch.",[4450,4720,4721,4722,4772,4773,4817],{},"Die Ungleichung für ",[573,4723,4725,4742],{"className":4724},[576],[573,4726,4728],{"className":4727},[580],[582,4729,4730],{"xmlns":584},[586,4731,4732,4740],{},[589,4733,4734,4736,4738],{},[592,4735,725],{},[720,4737,878],{},[639,4739,884],{},[596,4741,1117],{"encoding":598},[573,4743,4745,4763],{"className":4744,"ariaHidden":604},[603],[573,4746,4748,4751,4754,4757,4760],{"className":4747},[608],[573,4749],{"className":4750,"style":1127},[612],[573,4752,725],{"className":4753,"style":766},[617,618],[573,4755],{"className":4756,"style":748},[747],[573,4758,878],{"className":4759},[752],[573,4761],{"className":4762,"style":748},[747],[573,4764,4766,4769],{"className":4765},[608],[573,4767],{"className":4768,"style":822},[612],[573,4770,884],{"className":4771},[617]," anwenden und sich über eine nutzlose Schranke ",[573,4774,4776,4792],{"className":4775},[576],[573,4777,4779],{"className":4778},[580],[582,4780,4781],{"xmlns":584},[586,4782,4783,4789],{},[589,4784,4785,4787],{},[720,4786,868],{},[639,4788,884],{},[596,4790,4791],{"encoding":598},"\\geq 1",[573,4793,4795,4808],{"className":4794,"ariaHidden":604},[603],[573,4796,4798,4802,4805],{"className":4797},[608],[573,4799],{"className":4800,"style":4801},[612],"height:0.7719em;vertical-align:-0.136em;",[573,4803,868],{"className":4804},[752],[573,4806],{"className":4807,"style":748},[747],[573,4809,4811,4814],{"className":4810},[608],[573,4812],{"className":4813,"style":822},[612],[573,4815,884],{"className":4816},[617]," wundern.",[4450,4819,4820],{},"Die Sigma-Regeln der Normalverteilung auf beliebige Verteilungen übertragen. Ohne Verteilungsannahme gilt nur Tschebyscheff.",{"title":4822,"searchDepth":4823,"depth":4823,"links":4824},"",2,[4825,4826,4827],{"id":562,"depth":4823,"text":563},{"id":3093,"depth":4823,"text":3094},{"id":4444,"depth":4823,"text":4445},[4829,4832,4835,4838,4841,4844,4847,4850,4853],{"lhs":4830,"rhs":4831},"s^2 \u002F (k*s)^2","1 \u002F k^2",{"lhs":4833,"rhs":4834},"4^2 \u002F 10^2","0.16",{"lhs":4836,"rhs":4837},"1 \u002F 2^2","0.25",{"lhs":4839,"rhs":4840},"round(1 - erf(2\u002Fsqrt(2)), 3)","0.046",{"lhs":4842,"rhs":4843},"round((1 - erf(3\u002Fsqrt(2))) * 100, 1)","0.3",{"lhs":4845,"rhs":4846},"1 \u002F 3^2","1\u002F9",{"lhs":4848,"rhs":4849},"round(1\u002F9, 3)","0.111",{"lhs":4851,"rhs":4852},"1 \u002F (4 * 1000 * 0.05^2)","0.1",{"lhs":4854,"rhs":4837},"0.5 * 0.5","c > 0,\\ \\mu = E(X),\\ \\sigma^2 = \\operatorname{Var}(X) \u003C \\infty","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c > 0,\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\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\">0\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>μ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu = E(X),\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\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>\u003Cmsup>\u003Cmi>σ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Var\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sigma^2 = \\operatorname{Var}(X) < \\infty\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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=\"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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","chebyshev-inequality","P\\big(|X - \\mu| \\geq c\\big) \\leq \\frac{\\sigma^2}{c^2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>P\u003C\u002Fmi>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">(\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>μ\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo fence=\"false\" stretchy=\"true\" minsize=\"1.2em\" maxsize=\"1.2em\">)\u003C\u002Fmo>\u003Cmo>≤\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>σ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmsup>\u003Cmi>c\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">P\\big(|X - \\mu| \\geq c\\big) \\leq \\frac{\\sigma^2}{c^2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"delimsizing size1\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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\">μ\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"delimsizing size1\">)\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:2.1771em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7401em;\">\u003Cspan style=\"top:-2.989em;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>\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\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Ftschebyscheff-ungleichung",[],[4868,4869,4870,4871],"variance-random-variable","sigma-rules","expected-value","relative-frequency",{"title":548,"description":4822},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ftschebyscheff-ungleichung","Die Wahrscheinlichkeit, dass X mindestens um c von μ abweicht, ist höchstens σ²\u002Fc², für jede Verteilung.",[4876,4877,4878,4879],"abschätzung","varianz","erwartungswert","gesetz der großen zahlen",[4881,4884,4887,4890],{"symbol":858,"meaning":4882,"symbolHtml":4883},"Zufallsgröße mit beliebiger Verteilung","\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":599,"meaning":4885,"symbolHtml":4886},"Erwartungswert von X","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mu\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":644,"meaning":4888,"symbolHtml":4889},"Varianz von X","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>σ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sigma^2\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:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":718,"meaning":4891,"symbolHtml":4892},"Mindestabstand vom Erwartungswert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c\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\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","UX5xvXMQ6DX8_KPKNEJZuQ1Dh8gv536WjJXR9ZXUGqg",[4895,4898,4901,4904],{"stem":4896,"title":4897,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert","Erwartungswert",{"stem":4899,"title":4900,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Frelative-haeufigkeit","Relative Häufigkeit",{"stem":4902,"title":4903,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fsigma-regeln","Sigma-Regeln",{"stem":4905,"title":4906,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Varianz einer Zufallsgröße",1793824288189]