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\\approx N\\!\\left(n\\mu,\\ n\\sigma^2\\right), \\qquad \\bar{X}_n = \\frac{S_n}{n} \\approx N\\!\\left(\\mu,\\ \\frac{\\sigma^2}{n}\\right)",[578,921,923,986,1176,1299],{"className":922,"ariaHidden":609},[608],[578,924,926,930,977,980,983],{"className":925},[613],[578,927],{"className":928,"style":929},[617],"height:0.8333em;vertical-align:-0.15em;",[578,931,933,937],{"className":932},[622],[578,934,818],{"className":935,"style":936},[622,623],"margin-right:0.0576em;",[578,938,940],{"className":939},[670],[578,941,944,968],{"className":942},[674,943],"vlist-t2",[578,945,947,963],{"className":946},[678],[578,948,951],{"className":949,"style":950},[682],"height:0.1514em;",[578,952,954,957],{"style":953},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[578,955],{"className":956,"style":690},[689],[578,958,960],{"className":959},[694,695,696,697],[578,961,779],{"className":962},[622,623,697],[578,964,967],{"className":965},[966],"vlist-s","​",[578,969,971],{"className":970},[678],[578,972,975],{"className":973,"style":974},[682],"height:0.15em;",[578,976],{},[578,978],{"className":979,"style":743},[742],[578,981,823],{"className":982},[747],[578,984],{"className":985,"style":743},[742],[578,987,989,993,997,1001,1005,1077,1080,1083,1087,1090,1167,1170,1173],{"className":988},[613],[578,990],{"className":991,"style":992},[617],"height:1.2141em;vertical-align:-0.35em;",[578,994,826],{"className":995,"style":996},[622,623],"margin-right:0.109em;",[578,998],{"className":999,"style":1000},[742],"margin-right:-0.1667em;",[578,1002],{"className":1003,"style":1004},[742],"margin-right:0.1667em;",[578,1006,1009,1020,1023,1026,1030,1033,1036,1039,1070],{"className":1007},[1008],"minner",[578,1010,1015],{"className":1011,"style":1014},[1012,1013],"mopen","delimcenter","top:0em;",[578,1016,835],{"className":1017},[1018,1019],"delimsizing","size1",[578,1021,779],{"className":1022},[622,623],[578,1024,599],{"className":1025},[622,623],[578,1027,842],{"className":1028},[1029],"mpunct",[578,1031,845],{"className":1032},[742],[578,1034],{"className":1035,"style":1004},[742],[578,1037,779],{"className":1038},[622,623],[578,1040,1042,1045],{"className":1041},[622],[578,1043,642],{"className":1044,"style":666},[622,623],[578,1046,1048],{"className":1047},[670],[578,1049,1051],{"className":1050},[674],[578,1052,1054],{"className":1053},[678],[578,1055,1058],{"className":1056,"style":1057},[682],"height:0.8641em;",[578,1059,1061,1064],{"style":1060},"top:-3.113em;margin-right:0.05em;",[578,1062],{"className":1063,"style":690},[689],[578,1065,1067],{"className":1066},[694,695,696,697],[578,1068,646],{"className":1069},[622,697],[578,1071,1074],{"className":1072,"style":1014},[1073,1013],"mclose",[578,1075,856],{"className":1076},[1018,1019],[578,1078],{"className":1079,"style":1004},[742],[578,1081,842],{"className":1082},[1029],[578,1084],{"className":1085,"style":1086},[742],"margin-right:2em;",[578,1088],{"className":1089,"style":1004},[742],[578,1091,1093,1132],{"className":1092},[622],[578,1094,1097],{"className":1095},[622,1096],"accent",[578,1098,1100],{"className":1099},[674],[578,1101,1103],{"className":1102},[678],[578,1104,1107,1118],{"className":1105,"style":1106},[682],"height:0.8201em;",[578,1108,1110,1114],{"style":1109},"top:-3em;",[578,1111],{"className":1112,"style":1113},[689],"height:3em;",[578,1115,869],{"className":1116,"style":1117},[622,623],"margin-right:0.0785em;",[578,1119,1121,1124],{"style":1120},"top:-3.2523em;",[578,1122],{"className":1123,"style":1113},[689],[578,1125,1129],{"className":1126,"style":1128},[1127],"accent-body","left:-0.1667em;",[578,1130,872],{"className":1131},[622],[578,1133,1135],{"className":1134},[670],[578,1136,1138,1159],{"className":1137},[674,943],[578,1139,1141,1156],{"className":1140},[678],[578,1142,1144],{"className":1143,"style":950},[682],[578,1145,1147,1150],{"style":1146},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[578,1148],{"className":1149,"style":690},[689],[578,1151,1153],{"className":1152},[694,695,696,697],[578,1154,779],{"className":1155},[622,623,697],[578,1157,967],{"className":1158},[966],[578,1160,1162],{"className":1161},[678],[578,1163,1165],{"className":1164,"style":974},[682],[578,1166],{},[578,1168],{"className":1169,"style":743},[742],[578,1171,877],{"className":1172},[747],[578,1174],{"className":1175,"style":743},[742],[578,1177,1179,1183,1290,1293,1296],{"className":1178},[613],[578,1180],{"className":1181,"style":1182},[617],"height:2.0463em;vertical-align:-0.686em;",[578,1184,1186,1190,1287],{"className":1185},[622],[578,1187],{"className":1188},[1012,1189],"nulldelimiter",[578,1191,1193],{"className":1192},[879],[578,1194,1196,1278],{"className":1195},[674,943],[578,1197,1199,1275],{"className":1198},[678],[578,1200,1203,1215,1226],{"className":1201,"style":1202},[682],"height:1.3603em;",[578,1204,1206,1209],{"style":1205},"top:-2.314em;",[578,1207],{"className":1208,"style":1113},[689],[578,1210,1212],{"className":1211},[622],[578,1213,779],{"className":1214},[622,623],[578,1216,1218,1221],{"style":1217},"top:-3.23em;",[578,1219],{"className":1220,"style":1113},[689],[578,1222],{"className":1223,"style":1225},[1224],"frac-line","border-bottom-width:0.04em;",[578,1227,1229,1232],{"style":1228},"top:-3.677em;",[578,1230],{"className":1231,"style":1113},[689],[578,1233,1235],{"className":1234},[622],[578,1236,1238,1241],{"className":1237},[622],[578,1239,818],{"className":1240,"style":936},[622,623],[578,1242,1244],{"className":1243},[670],[578,1245,1247,1267],{"className":1246},[674,943],[578,1248,1250,1264],{"className":1249},[678],[578,1251,1253],{"className":1252,"style":950},[682],[578,1254,1255,1258],{"style":953},[578,1256],{"className":1257,"style":690},[689],[578,1259,1261],{"className":1260},[694,695,696,697],[578,1262,779],{"className":1263},[622,623,697],[578,1265,967],{"className":1266},[966],[578,1268,1270],{"className":1269},[678],[578,1271,1273],{"className":1272,"style":974},[682],[578,1274],{},[578,1276,967],{"className":1277},[966],[578,1279,1281],{"className":1280},[678],[578,1282,1285],{"className":1283,"style":1284},[682],"height:0.686em;",[578,1286],{},[578,1288],{"className":1289},[1073,1189],[578,1291],{"className":1292,"style":743},[742],[578,1294,823],{"className":1295},[747],[578,1297],{"className":1298,"style":743},[742],[578,1300,1302,1306,1309,1312,1315],{"className":1301},[613],[578,1303],{"className":1304,"style":1305},[617],"height:2.4411em;vertical-align:-0.95em;",[578,1307,826],{"className":1308,"style":996},[622,623],[578,1310],{"className":1311,"style":1000},[742],[578,1313],{"className":1314,"style":1004},[742],[578,1316,1318,1324,1327,1330,1333,1336,1425],{"className":1317},[1008],[578,1319,1321],{"className":1320,"style":1014},[1012,1013],[578,1322,835],{"className":1323},[1018,696],[578,1325,599],{"className":1326},[622,623],[578,1328,842],{"className":1329},[1029],[578,1331,845],{"className":1332},[742],[578,1334],{"className":1335,"style":1004},[742],[578,1337,1339,1342,1422],{"className":1338},[622],[578,1340],{"className":1341},[1012,1189],[578,1343,1345],{"className":1344},[879],[578,1346,1348,1414],{"className":1347},[674,943],[578,1349,1351,1411],{"className":1350},[678],[578,1352,1355,1366,1374],{"className":1353,"style":1354},[682],"height:1.4911em;",[578,1356,1357,1360],{"style":1205},[578,1358],{"className":1359,"style":1113},[689],[578,1361,1363],{"className":1362},[622],[578,1364,779],{"className":1365},[622,623],[578,1367,1368,1371],{"style":1217},[578,1369],{"className":1370,"style":1113},[689],[578,1372],{"className":1373,"style":1225},[1224],[578,1375,1376,1379],{"style":1228},[578,1377],{"className":1378,"style":1113},[689],[578,1380,1382],{"className":1381},[622],[578,1383,1385,1388],{"className":1384},[622],[578,1386,642],{"className":1387,"style":666},[622,623],[578,1389,1391],{"className":1390},[670],[578,1392,1394],{"className":1393},[674],[578,1395,1397],{"className":1396},[678],[578,1398,1400],{"className":1399,"style":659},[682],[578,1401,1402,1405],{"style":685},[578,1403],{"className":1404,"style":690},[689],[578,1406,1408],{"className":1407},[694,695,696,697],[578,1409,646],{"className":1410},[622,697],[578,1412,967],{"className":1413},[966],[578,1415,1417],{"className":1416},[678],[578,1418,1420],{"className":1419,"style":1284},[682],[578,1421],{},[578,1423],{"className":1424},[1073,1189],[578,1426,1428],{"className":1427,"style":1014},[1073,1013],[578,1429,856],{"className":1430},[1018,696],[565,1432,1433,1434,1600,1601,1604,1605,1608,1609,1639,1640,1688],{},"Die Standardabweichung des Mittelwerts ist also ",[578,1435,1437,1458],{"className":1436},[581],[578,1438,1440],{"className":1439},[585],[587,1441,1442],{"xmlns":589},[591,1443,1444,1455],{},[594,1445,1446],{},[879,1447,1448,1450],{},[597,1449,642],{},[1451,1452,1453],"msqrt",{},[597,1454,779],{},[601,1456,1457],{"encoding":603},"\\frac{\\sigma}{\\sqrt{n}}",[578,1459,1461],{"className":1460,"ariaHidden":609},[608],[578,1462,1464,1468],{"className":1463},[613],[578,1465],{"className":1466,"style":1467},[617],"height:1.2334em;vertical-align:-0.538em;",[578,1469,1471,1474,1597],{"className":1470},[622],[578,1472],{"className":1473},[1012,1189],[578,1475,1477],{"className":1476},[879],[578,1478,1480,1588],{"className":1479},[674,943],[578,1481,1483,1585],{"className":1482},[678],[578,1484,1487,1562,1570],{"className":1485,"style":1486},[682],"height:0.6954em;",[578,1488,1490,1493],{"style":1489},"top:-2.6259em;",[578,1491],{"className":1492,"style":1113},[689],[578,1494,1496],{"className":1495},[694,695,696,697],[578,1497,1499],{"className":1498},[622,697],[578,1500,1503],{"className":1501},[622,1502,697],"sqrt",[578,1504,1506,1553],{"className":1505},[674,943],[578,1507,1509,1550],{"className":1508},[678],[578,1510,1513,1527],{"className":1511,"style":1512},[682],"height:0.8059em;",[578,1514,1517,1520],{"className":1515,"style":1109},[1516],"svg-align",[578,1518],{"className":1519,"style":1113},[689],[578,1521,1524],{"className":1522,"style":1523},[622,697],"padding-left:0.833em;",[578,1525,779],{"className":1526},[622,623,697],[578,1528,1530,1533],{"style":1529},"top:-2.7659em;",[578,1531],{"className":1532,"style":1113},[689],[578,1534,1538],{"className":1535,"style":1537},[1536,697],"hide-tail","min-width:0.853em;height:1.08em;",[1539,1540,1546],"svg",{"xmlns":1541,"width":1542,"height":1543,"viewBox":1544,"preserveAspectRatio":1545},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[1547,1548],"path",{"d":1549},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[578,1551,967],{"className":1552},[966],[578,1554,1556],{"className":1555},[678],[578,1557,1560],{"className":1558,"style":1559},[682],"height:0.2341em;",[578,1561],{},[578,1563,1564,1567],{"style":1217},[578,1565],{"className":1566,"style":1113},[689],[578,1568],{"className":1569,"style":1225},[1224],[578,1571,1573,1576],{"style":1572},"top:-3.394em;",[578,1574],{"className":1575,"style":1113},[689],[578,1577,1579],{"className":1578},[694,695,696,697],[578,1580,1582],{"className":1581},[622,697],[578,1583,642],{"className":1584,"style":666},[622,623,697],[578,1586,967],{"className":1587},[966],[578,1589,1591],{"className":1590},[678],[578,1592,1595],{"className":1593,"style":1594},[682],"height:0.538em;",[578,1596],{},[578,1598],{"className":1599},[1073,1189]," (",[569,1602,1603],{},"Standardfehler","). Der Satz ist eine Aussage über ",[569,1606,1607],{},"Konvergenz in Verteilung",": Die Verteilungsfunktionen konvergieren an jeder Stelle ",[578,1610,1612,1626],{"className":1611},[581],[578,1613,1615],{"className":1614},[585],[587,1616,1617],{"xmlns":589},[591,1618,1619,1624],{},[594,1620,1621],{},[597,1622,1623],{},"z",[601,1625,1623],{"encoding":603},[578,1627,1629],{"className":1628,"ariaHidden":609},[608],[578,1630,1632,1635],{"className":1631},[613],[578,1633],{"className":1634,"style":791},[617],[578,1636,1623],{"className":1637,"style":1638},[622,623],"margin-right:0.044em;"," gegen ",[578,1641,1643,1666],{"className":1642},[581],[578,1644,1646],{"className":1645},[585],[587,1647,1648],{"xmlns":589},[591,1649,1650,1663],{},[594,1651,1652,1656,1659,1661],{},[597,1653,1655],{"mathvariant":1654},"normal","Φ",[717,1657,835],{"stretchy":1658},"false",[597,1660,1623],{},[717,1662,856],{"stretchy":1658},[601,1664,1665],{"encoding":603},"\\Phi(z)",[578,1667,1669],{"className":1668,"ariaHidden":609},[608],[578,1670,1672,1676,1679,1682,1685],{"className":1671},[613],[578,1673],{"className":1674,"style":1675},[617],"height:1em;vertical-align:-0.25em;",[578,1677,1655],{"className":1678},[622],[578,1680,835],{"className":1681},[1012],[578,1683,1623],{"className":1684,"style":1638},[622,623],[578,1686,856],{"className":1687},[1073],".",[565,1690,1691,1692,1720,1721,1774],{},"Wie groß ",[578,1693,1695,1708],{"className":1694},[581],[578,1696,1698],{"className":1697},[585],[587,1699,1700],{"xmlns":589},[591,1701,1702,1706],{},[594,1703,1704],{},[597,1705,779],{},[601,1707,779],{"encoding":603},[578,1709,1711],{"className":1710,"ariaHidden":609},[608],[578,1712,1714,1717],{"className":1713},[613],[578,1715],{"className":1716,"style":791},[617],[578,1718,779],{"className":1719},[622,623]," sein muss, hängt von der Schiefe der Ausgangsverteilung ab. Für symmetrische Verteilungen reicht oft ",[578,1722,1724,1743],{"className":1723},[581],[578,1725,1727],{"className":1726},[585],[587,1728,1729],{"xmlns":589},[591,1730,1731,1740],{},[594,1732,1733,1735,1737],{},[597,1734,779],{},[717,1736,823],{},[644,1738,1739],{},"30",[601,1741,1742],{"encoding":603},"n \\approx 30",[578,1744,1746,1765],{"className":1745,"ariaHidden":609},[608],[578,1747,1749,1753,1756,1759,1762],{"className":1748},[613],[578,1750],{"className":1751,"style":1752},[617],"height:0.4831em;",[578,1754,779],{"className":1755},[622,623],[578,1757],{"className":1758,"style":743},[742],[578,1760,823],{"className":1761},[747],[578,1763],{"className":1764,"style":743},[742],[578,1766,1768,1771],{"className":1767},[613],[578,1769],{"className":1770,"style":757},[617],[578,1772,1739],{"className":1773},[622],", für stark schiefe Verteilungen braucht man deutlich mehr. Der Satz von Moivre-Laplace ist der Spezialfall für Bernoulli-verteilte Summanden.",[560,1776,1778],{"id":1777},"beispiele","Beispiele",[565,1780,1781,1782,1811,1812,1876,1877,2033,2034,2108,2109,2277],{},"Ein fairer Würfel wird ",[578,1783,1785,1799],{"className":1784},[581],[578,1786,1788],{"className":1787},[585],[587,1789,1790],{"xmlns":589},[591,1791,1792,1797],{},[594,1793,1794],{},[644,1795,1796],{},"100",[601,1798,1796],{"encoding":603},[578,1800,1802],{"className":1801,"ariaHidden":609},[608],[578,1803,1805,1808],{"className":1804},[613],[578,1806],{"className":1807,"style":757},[617],[578,1809,1796],{"className":1810},[622],"-mal geworfen. Für einen Wurf gilt ",[578,1813,1815,1834],{"className":1814},[581],[578,1816,1818],{"className":1817},[585],[587,1819,1820],{"xmlns":589},[591,1821,1822,1831],{},[594,1823,1824,1826,1828],{},[597,1825,599],{},[717,1827,877],{},[644,1829,1830],{},"3,5",[601,1832,1833],{"encoding":603},"\\mu = 3{,}5",[578,1835,1837,1855],{"className":1836,"ariaHidden":609},[608],[578,1838,1840,1843,1846,1849,1852],{"className":1839},[613],[578,1841],{"className":1842,"style":618},[617],[578,1844,599],{"className":1845},[622,623],[578,1847],{"className":1848,"style":743},[742],[578,1850,877],{"className":1851},[747],[578,1853],{"className":1854,"style":743},[742],[578,1856,1858,1862,1866,1872],{"className":1857},[613],[578,1859],{"className":1860,"style":1861},[617],"height:0.8389em;vertical-align:-0.1944em;",[578,1863,1865],{"className":1864},[622],"3",[578,1867,1869],{"className":1868},[622],[578,1870,842],{"className":1871},[1029],[578,1873,1875],{"className":1874},[622],"5"," und ",[578,1878,1880,1908],{"className":1879},[581],[578,1881,1883],{"className":1882},[585],[587,1884,1885],{"xmlns":589},[591,1886,1887,1905],{},[594,1888,1889,1895,1897],{},[638,1890,1891,1893],{},[597,1892,642],{},[644,1894,646],{},[717,1896,877],{},[879,1898,1899,1902],{},[644,1900,1901],{},"35",[644,1903,1904],{},"12",[601,1906,1907],{"encoding":603},"\\sigma^2 = \\frac{35}{12}",[578,1909,1911,1955],{"className":1910,"ariaHidden":609},[608],[578,1912,1914,1917,1946,1949,1952],{"className":1913},[613],[578,1915],{"className":1916,"style":659},[617],[578,1918,1920,1923],{"className":1919},[622],[578,1921,642],{"className":1922,"style":666},[622,623],[578,1924,1926],{"className":1925},[670],[578,1927,1929],{"className":1928},[674],[578,1930,1932],{"className":1931},[678],[578,1933,1935],{"className":1934,"style":659},[682],[578,1936,1937,1940],{"style":685},[578,1938],{"className":1939,"style":690},[689],[578,1941,1943],{"className":1942},[694,695,696,697],[578,1944,646],{"className":1945},[622,697],[578,1947],{"className":1948,"style":743},[742],[578,1950,877],{"className":1951},[747],[578,1953],{"className":1954,"style":743},[742],[578,1956,1958,1962],{"className":1957},[613],[578,1959],{"className":1960,"style":1961},[617],"height:1.1901em;vertical-align:-0.345em;",[578,1963,1965,1968,2030],{"className":1964},[622],[578,1966],{"className":1967},[1012,1189],[578,1969,1971],{"className":1970},[879],[578,1972,1974,2021],{"className":1973},[674,943],[578,1975,1977,2018],{"className":1976},[678],[578,1978,1981,1996,2004],{"className":1979,"style":1980},[682],"height:0.8451em;",[578,1982,1984,1987],{"style":1983},"top:-2.655em;",[578,1985],{"className":1986,"style":1113},[689],[578,1988,1990],{"className":1989},[694,695,696,697],[578,1991,1993],{"className":1992},[622,697],[578,1994,1904],{"className":1995},[622,697],[578,1997,1998,2001],{"style":1217},[578,1999],{"className":2000,"style":1113},[689],[578,2002],{"className":2003,"style":1225},[1224],[578,2005,2006,2009],{"style":1572},[578,2007],{"className":2008,"style":1113},[689],[578,2010,2012],{"className":2011},[694,695,696,697],[578,2013,2015],{"className":2014},[622,697],[578,2016,1901],{"className":2017},[622,697],[578,2019,967],{"className":2020},[966],[578,2022,2024],{"className":2023},[678],[578,2025,2028],{"className":2026,"style":2027},[682],"height:0.345em;",[578,2029],{},[578,2031],{"className":2032},[1073,1189],". Für die Augensumme ",[578,2035,2037,2055],{"className":2036},[581],[578,2038,2040],{"className":2039},[585],[587,2041,2042],{"xmlns":589},[591,2043,2044,2052],{},[594,2045,2046],{},[814,2047,2048,2050],{},[597,2049,818],{},[644,2051,1796],{},[601,2053,2054],{"encoding":603},"S_{100}",[578,2056,2058],{"className":2057,"ariaHidden":609},[608],[578,2059,2061,2064],{"className":2060},[613],[578,2062],{"className":2063,"style":929},[617],[578,2065,2067,2070],{"className":2066},[622],[578,2068,818],{"className":2069,"style":936},[622,623],[578,2071,2073],{"className":2072},[670],[578,2074,2076,2100],{"className":2075},[674,943],[578,2077,2079,2097],{"className":2078},[678],[578,2080,2083],{"className":2081,"style":2082},[682],"height:0.3011em;",[578,2084,2085,2088],{"style":953},[578,2086],{"className":2087,"style":690},[689],[578,2089,2091],{"className":2090},[694,695,696,697],[578,2092,2094],{"className":2093},[622,697],[578,2095,1796],{"className":2096},[622,697],[578,2098,967],{"className":2099},[966],[578,2101,2103],{"className":2102},[678],[578,2104,2106],{"className":2105,"style":974},[682],[578,2107],{}," ist ",[578,2110,2112,2151],{"className":2111},[581],[578,2113,2115],{"className":2114},[585],[587,2116,2117],{"xmlns":589},[591,2118,2119,2148],{},[594,2120,2121,2124,2126,2132,2134,2136,2138,2141,2143,2145],{},[597,2122,2123],{},"E",[717,2125,835],{"stretchy":1658},[814,2127,2128,2130],{},[597,2129,818],{},[644,2131,1796],{},[717,2133,856],{"stretchy":1658},[717,2135,877],{},[644,2137,1796],{},[717,2139,2140],{},"⋅",[644,2142,1830],{},[717,2144,877],{},[644,2146,2147],{},"350",[601,2149,2150],{"encoding":603},"E(S_{100}) = 100 \\cdot 3{,}5 = 350",[578,2152,2154,2221,2241,2268],{"className":2153,"ariaHidden":609},[608],[578,2155,2157,2160,2163,2166,2209,2212,2215,2218],{"className":2156},[613],[578,2158],{"className":2159,"style":1675},[617],[578,2161,2123],{"className":2162,"style":936},[622,623],[578,2164,835],{"className":2165},[1012],[578,2167,2169,2172],{"className":2168},[622],[578,2170,818],{"className":2171,"style":936},[622,623],[578,2173,2175],{"className":2174},[670],[578,2176,2178,2201],{"className":2177},[674,943],[578,2179,2181,2198],{"className":2180},[678],[578,2182,2184],{"className":2183,"style":2082},[682],[578,2185,2186,2189],{"style":953},[578,2187],{"className":2188,"style":690},[689],[578,2190,2192],{"className":2191},[694,695,696,697],[578,2193,2195],{"className":2194},[622,697],[578,2196,1796],{"className":2197},[622,697],[578,2199,967],{"className":2200},[966],[578,2202,2204],{"className":2203},[678],[578,2205,2207],{"className":2206,"style":974},[682],[578,2208],{},[578,2210,856],{"className":2211},[1073],[578,2213],{"className":2214,"style":743},[742],[578,2216,877],{"className":2217},[747],[578,2219],{"className":2220,"style":743},[742],[578,2222,2224,2227,2230,2234,2238],{"className":2223},[613],[578,2225],{"className":2226,"style":757},[617],[578,2228,1796],{"className":2229},[622],[578,2231],{"className":2232,"style":2233},[742],"margin-right:0.2222em;",[578,2235,2140],{"className":2236},[2237],"mbin",[578,2239],{"className":2240,"style":2233},[742],[578,2242,2244,2247,2250,2256,2259,2262,2265],{"className":2243},[613],[578,2245],{"className":2246,"style":1861},[617],[578,2248,1865],{"className":2249},[622],[578,2251,2253],{"className":2252},[622],[578,2254,842],{"className":2255},[1029],[578,2257,1875],{"className":2258},[622],[578,2260],{"className":2261,"style":743},[742],[578,2263,877],{"className":2264},[747],[578,2266],{"className":2267,"style":743},[742],[578,2269,2271,2274],{"className":2270},[613],[578,2272],{"className":2273,"style":757},[617],[578,2275,2147],{"className":2276},[622]," und",[578,2279,2281],{"className":2280},[799],[578,2282,2284,2326],{"className":2283},[581],[578,2285,2287],{"className":2286},[585],[587,2288,2289],{"xmlns":589,"display":808},[591,2290,2291,2323],{},[594,2292,2293,2299,2301,2318,2320],{},[814,2294,2295,2297],{},[597,2296,642],{},[597,2298,818],{},[717,2300,877],{},[1451,2302,2303],{},[594,2304,2305,2307,2309],{},[644,2306,1796],{},[717,2308,2140],{},[2310,2311,2312],"mstyle",{"scriptlevel":722,"displaystyle":1658},[879,2313,2314,2316],{},[644,2315,1901],{},[644,2317,1904],{},[717,2319,823],{},[644,2321,2322],{},"17,08",[601,2324,2325],{"encoding":603},"\\sigma_{S} = \\sqrt{100 \\cdot \\tfrac{35}{12}} \\approx 17{,}08",[578,2327,2329,2390,2540],{"className":2328,"ariaHidden":609},[608],[578,2330,2332,2336,2381,2384,2387],{"className":2331},[613],[578,2333],{"className":2334,"style":2335},[617],"height:0.5806em;vertical-align:-0.15em;",[578,2337,2339,2342],{"className":2338},[622],[578,2340,642],{"className":2341,"style":666},[622,623],[578,2343,2345],{"className":2344},[670],[578,2346,2348,2373],{"className":2347},[674,943],[578,2349,2351,2370],{"className":2350},[678],[578,2352,2355],{"className":2353,"style":2354},[682],"height:0.3283em;",[578,2356,2358,2361],{"style":2357},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[578,2359],{"className":2360,"style":690},[689],[578,2362,2364],{"className":2363},[694,695,696,697],[578,2365,2367],{"className":2366},[622,697],[578,2368,818],{"className":2369,"style":936},[622,623,697],[578,2371,967],{"className":2372},[966],[578,2374,2376],{"className":2375},[678],[578,2377,2379],{"className":2378,"style":974},[682],[578,2380],{},[578,2382],{"className":2383,"style":743},[742],[578,2385,877],{"className":2386},[747],[578,2388],{"className":2389,"style":743},[742],[578,2391,2393,2397,2531,2534,2537],{"className":2392},[613],[578,2394],{"className":2395,"style":2396},[617],"height:1.84em;vertical-align:-0.5561em;",[578,2398,2400],{"className":2399},[622,1502],[578,2401,2403,2522],{"className":2402},[674,943],[578,2404,2406,2519],{"className":2405},[678],[578,2407,2410,2502],{"className":2408,"style":2409},[682],"height:1.2839em;",[578,2411,2414,2418],{"className":2412,"style":2413},[1516],"top:-3.8em;",[578,2415],{"className":2416,"style":2417},[689],"height:3.8em;",[578,2419,2422,2425,2428,2431,2434],{"className":2420,"style":2421},[622],"padding-left:1em;",[578,2423,1796],{"className":2424},[622],[578,2426],{"className":2427,"style":2233},[742],[578,2429,2140],{"className":2430},[2237],[578,2432],{"className":2433,"style":2233},[742],[578,2435,2437,2440,2499],{"className":2436},[622],[578,2438],{"className":2439},[1012,1189],[578,2441,2443],{"className":2442},[879],[578,2444,2446,2491],{"className":2445},[674,943],[578,2447,2449,2488],{"className":2448},[678],[578,2450,2452,2466,2474],{"className":2451,"style":1980},[682],[578,2453,2454,2457],{"style":1983},[578,2455],{"className":2456,"style":1113},[689],[578,2458,2460],{"className":2459},[694,695,696,697],[578,2461,2463],{"className":2462},[622,697],[578,2464,1904],{"className":2465},[622,697],[578,2467,2468,2471],{"style":1217},[578,2469],{"className":2470,"style":1113},[689],[578,2472],{"className":2473,"style":1225},[1224],[578,2475,2476,2479],{"style":1572},[578,2477],{"className":2478,"style":1113},[689],[578,2480,2482],{"className":2481},[694,695,696,697],[578,2483,2485],{"className":2484},[622,697],[578,2486,1901],{"className":2487},[622,697],[578,2489,967],{"className":2490},[966],[578,2492,2494],{"className":2493},[678],[578,2495,2497],{"className":2496,"style":2027},[682],[578,2498],{},[578,2500],{"className":2501},[1073,1189],[578,2503,2505,2508],{"style":2504},"top:-3.2439em;",[578,2506],{"className":2507,"style":2417},[689],[578,2509,2512],{"className":2510,"style":2511},[1536],"min-width:1.02em;height:1.88em;",[1539,2513,2516],{"xmlns":1541,"width":1542,"height":2514,"viewBox":2515,"preserveAspectRatio":1545},"1.88em","0 0 400000 1944",[1547,2517],{"d":2518},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[578,2520,967],{"className":2521},[966],[578,2523,2525],{"className":2524},[678],[578,2526,2529],{"className":2527,"style":2528},[682],"height:0.5561em;",[578,2530],{},[578,2532],{"className":2533,"style":743},[742],[578,2535,823],{"className":2536},[747],[578,2538],{"className":2539,"style":743},[742],[578,2541,2543,2546,2550,2556],{"className":2542},[613],[578,2544],{"className":2545,"style":1861},[617],[578,2547,2549],{"className":2548},[622],"17",[578,2551,2553],{"className":2552},[622],[578,2554,842],{"className":2555},[1029],[578,2557,2559],{"className":2558},[622],"08",[565,2561,2562,2563,2635],{},"Da ",[578,2564,2566,2583],{"className":2565},[581],[578,2567,2569],{"className":2568},[585],[587,2570,2571],{"xmlns":589},[591,2572,2573,2581],{},[594,2574,2575],{},[814,2576,2577,2579],{},[597,2578,818],{},[644,2580,1796],{},[601,2582,2054],{"encoding":603},[578,2584,2586],{"className":2585,"ariaHidden":609},[608],[578,2587,2589,2592],{"className":2588},[613],[578,2590],{"className":2591,"style":929},[617],[578,2593,2595,2598],{"className":2594},[622],[578,2596,818],{"className":2597,"style":936},[622,623],[578,2599,2601],{"className":2600},[670],[578,2602,2604,2627],{"className":2603},[674,943],[578,2605,2607,2624],{"className":2606},[678],[578,2608,2610],{"className":2609,"style":2082},[682],[578,2611,2612,2615],{"style":953},[578,2613],{"className":2614,"style":690},[689],[578,2616,2618],{"className":2617},[694,695,696,697],[578,2619,2621],{"className":2620},[622,697],[578,2622,1796],{"className":2623},[622,697],[578,2625,967],{"className":2626},[966],[578,2628,2630],{"className":2629},[678],[578,2631,2633],{"className":2632,"style":974},[682],[578,2634],{}," nur ganze Zahlen annimmt, rechnet man mit Stetigkeitskorrektur:",[578,2637,2639],{"className":2638},[799],[578,2640,2642,2715],{"className":2641},[581],[578,2643,2645],{"className":2644},[585],[587,2646,2647],{"xmlns":589,"display":808},[591,2648,2649,2712],{},[594,2650,2651,2654,2656,2662,2665,2668,2670,2672,2674,2676,2696,2698,2700,2702,2705,2707,2709],{},[597,2652,2653],{},"P",[717,2655,835],{"stretchy":1658},[814,2657,2658,2660],{},[597,2659,818],{},[644,2661,1796],{},[717,2663,2664],{},"≤",[644,2666,2667],{},"370",[717,2669,856],{"stretchy":1658},[717,2671,823],{},[597,2673,1655],{"mathvariant":1654},[828,2675,830],{},[594,2677,2678,2680,2694],{},[717,2679,835],{"fence":609},[879,2681,2682,2692],{},[594,2683,2684,2687,2690],{},[644,2685,2686],{},"370,5",[717,2688,2689],{},"−",[644,2691,2147],{},[644,2693,2322],{},[717,2695,856],{"fence":609},[717,2697,823],{},[597,2699,1655],{"mathvariant":1654},[717,2701,835],{"stretchy":1658},[644,2703,2704],{},"1,20",[717,2706,856],{"stretchy":1658},[717,2708,823],{},[644,2710,2711],{},"0,885",[601,2713,2714],{"encoding":603},"P(S_{100} \\leq 370) \\approx \\Phi\\!\\left(\\frac{370{,}5 - 350}{17{,}08}\\right) \\approx \\Phi(1{,}20) \\approx 0{,}885",[578,2716,2718,2783,2804,2938,2976],{"className":2717,"ariaHidden":609},[608],[578,2719,2721,2724,2728,2731,2774,2777,2780],{"className":2720},[613],[578,2722],{"className":2723,"style":1675},[617],[578,2725,2653],{"className":2726,"style":2727},[622,623],"margin-right:0.1389em;",[578,2729,835],{"className":2730},[1012],[578,2732,2734,2737],{"className":2733},[622],[578,2735,818],{"className":2736,"style":936},[622,623],[578,2738,2740],{"className":2739},[670],[578,2741,2743,2766],{"className":2742},[674,943],[578,2744,2746,2763],{"className":2745},[678],[578,2747,2749],{"className":2748,"style":2082},[682],[578,2750,2751,2754],{"style":953},[578,2752],{"className":2753,"style":690},[689],[578,2755,2757],{"className":2756},[694,695,696,697],[578,2758,2760],{"className":2759},[622,697],[578,2761,1796],{"className":2762},[622,697],[578,2764,967],{"className":2765},[966],[578,2767,2769],{"className":2768},[678],[578,2770,2772],{"className":2771,"style":974},[682],[578,2773],{},[578,2775],{"className":2776,"style":743},[742],[578,2778,2664],{"className":2779},[747],[578,2781],{"className":2782,"style":743},[742],[578,2784,2786,2789,2792,2795,2798,2801],{"className":2785},[613],[578,2787],{"className":2788,"style":1675},[617],[578,2790,2667],{"className":2791},[622],[578,2793,856],{"className":2794},[1073],[578,2796],{"className":2797,"style":743},[742],[578,2799,823],{"className":2800},[747],[578,2802],{"className":2803,"style":743},[742],[578,2805,2807,2811,2814,2817,2820,2929,2932,2935],{"className":2806},[613],[578,2808],{"className":2809,"style":2810},[617],"height:2.4em;vertical-align:-0.95em;",[578,2812,1655],{"className":2813},[622],[578,2815],{"className":2816,"style":1000},[742],[578,2818],{"className":2819,"style":1004},[742],[578,2821,2823,2829,2923],{"className":2822},[1008],[578,2824,2826],{"className":2825,"style":1014},[1012,1013],[578,2827,835],{"className":2828},[1018,696],[578,2830,2832,2835,2920],{"className":2831},[622],[578,2833],{"className":2834},[1012,1189],[578,2836,2838],{"className":2837},[879],[578,2839,2841,2911],{"className":2840},[674,943],[578,2842,2844,2908],{"className":2843},[678],[578,2845,2848,2868,2876],{"className":2846,"style":2847},[682],"height:1.3214em;",[578,2849,2850,2853],{"style":1205},[578,2851],{"className":2852,"style":1113},[689],[578,2854,2856,2859,2865],{"className":2855},[622],[578,2857,2549],{"className":2858},[622],[578,2860,2862],{"className":2861},[622],[578,2863,842],{"className":2864},[1029],[578,2866,2559],{"className":2867},[622],[578,2869,2870,2873],{"style":1217},[578,2871],{"className":2872,"style":1113},[689],[578,2874],{"className":2875,"style":1225},[1224],[578,2877,2878,2881],{"style":1228},[578,2879],{"className":2880,"style":1113},[689],[578,2882,2884,2887,2893,2896,2899,2902,2905],{"className":2883},[622],[578,2885,2667],{"className":2886},[622],[578,2888,2890],{"className":2889},[622],[578,2891,842],{"className":2892},[1029],[578,2894,1875],{"className":2895},[622],[578,2897],{"className":2898,"style":2233},[742],[578,2900,2689],{"className":2901},[2237],[578,2903],{"className":2904,"style":2233},[742],[578,2906,2147],{"className":2907},[622],[578,2909,967],{"className":2910},[966],[578,2912,2914],{"className":2913},[678],[578,2915,2918],{"className":2916,"style":2917},[682],"height:0.8804em;",[578,2919],{},[578,2921],{"className":2922},[1073,1189],[578,2924,2926],{"className":2925,"style":1014},[1073,1013],[578,2927,856],{"className":2928},[1018,696],[578,2930],{"className":2931,"style":743},[742],[578,2933,823],{"className":2934},[747],[578,2936],{"className":2937,"style":743},[742],[578,2939,2941,2944,2947,2950,2954,2960,2964,2967,2970,2973],{"className":2940},[613],[578,2942],{"className":2943,"style":1675},[617],[578,2945,1655],{"className":2946},[622],[578,2948,835],{"className":2949},[1012],[578,2951,2953],{"className":2952},[622],"1",[578,2955,2957],{"className":2956},[622],[578,2958,842],{"className":2959},[1029],[578,2961,2963],{"className":2962},[622],"20",[578,2965,856],{"className":2966},[1073],[578,2968],{"className":2969,"style":743},[742],[578,2971,823],{"className":2972},[747],[578,2974],{"className":2975,"style":743},[742],[578,2977,2979,2982,2985,2991],{"className":2978},[613],[578,2980],{"className":2981,"style":1861},[617],[578,2983,722],{"className":2984},[622],[578,2986,2988],{"className":2987},[622],[578,2989,842],{"className":2990},[1029],[578,2992,2994],{"className":2993},[622],"885",[565,2996,2997,2998,3026,3027,3055,3056,3085,3086,3346,3347,3587],{},"Die Lebensdauer eines Bauteils hat Erwartungswert ",[578,2999,3001,3014],{"className":3000},[581],[578,3002,3004],{"className":3003},[585],[587,3005,3006],{"xmlns":589},[591,3007,3008,3012],{},[594,3009,3010],{},[644,3011,1875],{},[601,3013,1875],{"encoding":603},[578,3015,3017],{"className":3016,"ariaHidden":609},[608],[578,3018,3020,3023],{"className":3019},[613],[578,3021],{"className":3022,"style":757},[617],[578,3024,1875],{"className":3025},[622]," Jahre und Standardabweichung ",[578,3028,3030,3043],{"className":3029},[581],[578,3031,3033],{"className":3032},[585],[587,3034,3035],{"xmlns":589},[591,3036,3037,3041],{},[594,3038,3039],{},[644,3040,1875],{},[601,3042,1875],{"encoding":603},[578,3044,3046],{"className":3045,"ariaHidden":609},[608],[578,3047,3049,3052],{"className":3048},[613],[578,3050],{"className":3051,"style":757},[617],[578,3053,1875],{"className":3054},[622]," Jahre (stark schief, z.B. exponentialverteilt). Für den Mittelwert von ",[578,3057,3059,3073],{"className":3058},[581],[578,3060,3062],{"className":3061},[585],[587,3063,3064],{"xmlns":589},[591,3065,3066,3071],{},[594,3067,3068],{},[644,3069,3070],{},"36",[601,3072,3070],{"encoding":603},[578,3074,3076],{"className":3075,"ariaHidden":609},[608],[578,3077,3079,3082],{"className":3078},[613],[578,3080],{"className":3081,"style":757},[617],[578,3083,3070],{"className":3084},[622]," Bauteilen gilt näherungsweise ",[578,3087,3089,3142],{"className":3088},[581],[578,3090,3092],{"className":3091},[585],[587,3093,3094],{"xmlns":589},[591,3095,3096,3139],{},[594,3097,3098,3104,3106,3108,3110],{},[865,3099,3100,3102],{"accent":609},[597,3101,869],{},[717,3103,872],{},[717,3105,823],{},[597,3107,826],{},[828,3109,830],{},[594,3111,3112,3114,3116,3118,3120,3137],{},[717,3113,835],{"fence":609},[644,3115,1875],{},[717,3117,842],{"separator":609},[828,3119,845],{},[638,3121,3122,3135],{},[594,3123,3124,3126,3133],{},[717,3125,835],{"fence":609},[879,3127,3128,3130],{},[644,3129,1875],{},[644,3131,3132],{},"6",[717,3134,856],{"fence":609},[644,3136,646],{},[717,3138,856],{"fence":609},[601,3140,3141],{"encoding":603},"\\bar{X} \\approx N\\!\\left(5,\\ \\left(\\frac{5}{6}\\right)^2\\right)",[578,3143,3145,3191],{"className":3144,"ariaHidden":609},[608],[578,3146,3148,3151,3182,3185,3188],{"className":3147},[613],[578,3149],{"className":3150,"style":1106},[617],[578,3152,3154],{"className":3153},[622,1096],[578,3155,3157],{"className":3156},[674],[578,3158,3160],{"className":3159},[678],[578,3161,3163,3171],{"className":3162,"style":1106},[682],[578,3164,3165,3168],{"style":1109},[578,3166],{"className":3167,"style":1113},[689],[578,3169,869],{"className":3170,"style":1117},[622,623],[578,3172,3173,3176],{"style":1120},[578,3174],{"className":3175,"style":1113},[689],[578,3177,3179],{"className":3178,"style":1128},[1127],[578,3180,872],{"className":3181},[622],[578,3183],{"className":3184,"style":743},[742],[578,3186,823],{"className":3187},[747],[578,3189],{"className":3190,"style":743},[742],[578,3192,3194,3198,3201,3204,3207],{"className":3193},[613],[578,3195],{"className":3196,"style":3197},[617],"height:1.8em;vertical-align:-0.65em;",[578,3199,826],{"className":3200,"style":996},[622,623],[578,3202],{"className":3203,"style":1000},[742],[578,3205],{"className":3206,"style":1004},[742],[578,3208,3210,3217,3220,3223,3226,3229,3340],{"className":3209},[1008],[578,3211,3213],{"className":3212,"style":1014},[1012,1013],[578,3214,835],{"className":3215},[1018,3216],"size2",[578,3218,1875],{"className":3219},[622],[578,3221,842],{"className":3222},[1029],[578,3224,845],{"className":3225},[742],[578,3227],{"className":3228,"style":1004},[742],[578,3230,3232,3315],{"className":3231},[1008],[578,3233,3235,3241,3309],{"className":3234},[1008],[578,3236,3238],{"className":3237,"style":1014},[1012,1013],[578,3239,835],{"className":3240},[1018,1019],[578,3242,3244,3247,3306],{"className":3243},[622],[578,3245],{"className":3246},[1012,1189],[578,3248,3250],{"className":3249},[879],[578,3251,3253,3298],{"className":3252},[674,943],[578,3254,3256,3295],{"className":3255},[678],[578,3257,3259,3273,3281],{"className":3258,"style":1980},[682],[578,3260,3261,3264],{"style":1983},[578,3262],{"className":3263,"style":1113},[689],[578,3265,3267],{"className":3266},[694,695,696,697],[578,3268,3270],{"className":3269},[622,697],[578,3271,3132],{"className":3272},[622,697],[578,3274,3275,3278],{"style":1217},[578,3276],{"className":3277,"style":1113},[689],[578,3279],{"className":3280,"style":1225},[1224],[578,3282,3283,3286],{"style":1572},[578,3284],{"className":3285,"style":1113},[689],[578,3287,3289],{"className":3288},[694,695,696,697],[578,3290,3292],{"className":3291},[622,697],[578,3293,1875],{"className":3294},[622,697],[578,3296,967],{"className":3297},[966],[578,3299,3301],{"className":3300},[678],[578,3302,3304],{"className":3303,"style":2027},[682],[578,3305],{},[578,3307],{"className":3308},[1073,1189],[578,3310,3312],{"className":3311,"style":1014},[1073,1013],[578,3313,856],{"className":3314},[1018,1019],[578,3316,3318],{"className":3317},[670],[578,3319,3321],{"className":3320},[674],[578,3322,3324],{"className":3323},[678],[578,3325,3328],{"className":3326,"style":3327},[682],"height:1.054em;",[578,3329,3331,3334],{"style":3330},"top:-3.3029em;margin-right:0.05em;",[578,3332],{"className":3333,"style":690},[689],[578,3335,3337],{"className":3336},[694,695,696,697],[578,3338,646],{"className":3339},[622,697],[578,3341,3343],{"className":3342,"style":1014},[1073,1013],[578,3344,856],{"className":3345},[1018,3216],", denn ",[578,3348,3350,3378],{"className":3349},[581],[578,3351,3353],{"className":3352},[585],[587,3354,3355],{"xmlns":589},[591,3356,3357,3375],{},[594,3358,3359,3367,3369],{},[879,3360,3361,3363],{},[644,3362,1875],{},[1451,3364,3365],{},[644,3366,3070],{},[717,3368,877],{},[879,3370,3371,3373],{},[644,3372,1875],{},[644,3374,3132],{},[601,3376,3377],{"encoding":603},"\\frac{5}{\\sqrt{36}} = \\frac{5}{6}",[578,3379,3381,3513],{"className":3380,"ariaHidden":609},[608],[578,3382,3384,3388,3504,3507,3510],{"className":3383},[613],[578,3385],{"className":3386,"style":3387},[617],"height:1.3831em;vertical-align:-0.538em;",[578,3389,3391,3394,3501],{"className":3390},[622],[578,3392],{"className":3393},[1012,1189],[578,3395,3397],{"className":3396},[879],[578,3398,3400,3493],{"className":3399},[674,943],[578,3401,3403,3490],{"className":3402},[678],[578,3404,3406,3468,3476],{"className":3405,"style":1980},[682],[578,3407,3409,3412],{"style":3408},"top:-2.551em;",[578,3410],{"className":3411,"style":1113},[689],[578,3413,3415],{"className":3414},[694,695,696,697],[578,3416,3418],{"className":3417},[622,697],[578,3419,3421],{"className":3420},[622,1502,697],[578,3422,3424,3459],{"className":3423},[674,943],[578,3425,3427,3456],{"className":3426},[678],[578,3428,3431,3443],{"className":3429,"style":3430},[682],"height:0.9128em;",[578,3432,3434,3437],{"className":3433,"style":1109},[1516],[578,3435],{"className":3436,"style":1113},[689],[578,3438,3440],{"className":3439,"style":1523},[622,697],[578,3441,3070],{"className":3442},[622,697],[578,3444,3446,3449],{"style":3445},"top:-2.8728em;",[578,3447],{"className":3448,"style":1113},[689],[578,3450,3452],{"className":3451,"style":1537},[1536,697],[1539,3453,3454],{"xmlns":1541,"width":1542,"height":1543,"viewBox":1544,"preserveAspectRatio":1545},[1547,3455],{"d":1549},[578,3457,967],{"className":3458},[966],[578,3460,3462],{"className":3461},[678],[578,3463,3466],{"className":3464,"style":3465},[682],"height:0.1272em;",[578,3467],{},[578,3469,3470,3473],{"style":1217},[578,3471],{"className":3472,"style":1113},[689],[578,3474],{"className":3475,"style":1225},[1224],[578,3477,3478,3481],{"style":1572},[578,3479],{"className":3480,"style":1113},[689],[578,3482,3484],{"className":3483},[694,695,696,697],[578,3485,3487],{"className":3486},[622,697],[578,3488,1875],{"className":3489},[622,697],[578,3491,967],{"className":3492},[966],[578,3494,3496],{"className":3495},[678],[578,3497,3499],{"className":3498,"style":1594},[682],[578,3500],{},[578,3502],{"className":3503},[1073,1189],[578,3505],{"className":3506,"style":743},[742],[578,3508,877],{"className":3509},[747],[578,3511],{"className":3512,"style":743},[742],[578,3514,3516,3519],{"className":3515},[613],[578,3517],{"className":3518,"style":1961},[617],[578,3520,3522,3525,3584],{"className":3521},[622],[578,3523],{"className":3524},[1012,1189],[578,3526,3528],{"className":3527},[879],[578,3529,3531,3576],{"className":3530},[674,943],[578,3532,3534,3573],{"className":3533},[678],[578,3535,3537,3551,3559],{"className":3536,"style":1980},[682],[578,3538,3539,3542],{"style":1983},[578,3540],{"className":3541,"style":1113},[689],[578,3543,3545],{"className":3544},[694,695,696,697],[578,3546,3548],{"className":3547},[622,697],[578,3549,3132],{"className":3550},[622,697],[578,3552,3553,3556],{"style":1217},[578,3554],{"className":3555,"style":1113},[689],[578,3557],{"className":3558,"style":1225},[1224],[578,3560,3561,3564],{"style":1572},[578,3562],{"className":3563,"style":1113},[689],[578,3565,3567],{"className":3566},[694,695,696,697],[578,3568,3570],{"className":3569},[622,697],[578,3571,1875],{"className":3572},[622,697],[578,3574,967],{"className":3575},[966],[578,3577,3579],{"className":3578},[678],[578,3580,3582],{"className":3581,"style":2027},[682],[578,3583],{},[578,3585],{"className":3586},[1073,1189],". Damit",[578,3589,3591],{"className":3590},[799],[578,3592,3594,3677],{"className":3593},[581],[578,3595,3597],{"className":3596},[585],[587,3598,3599],{"xmlns":589,"display":808},[591,3600,3601,3674],{},[594,3602,3603,3605,3607,3613,3615,3617,3619,3621,3623,3625,3627,3629,3654,3656,3658,3660,3662,3664,3667,3669,3671],{},[597,3604,2653],{},[717,3606,835],{"stretchy":1658},[865,3608,3609,3611],{"accent":609},[597,3610,869],{},[717,3612,872],{},[717,3614,719],{},[644,3616,3132],{},[717,3618,856],{"stretchy":1658},[717,3620,823],{},[644,3622,2953],{},[717,3624,2689],{},[597,3626,1655],{"mathvariant":1654},[828,3628,830],{},[594,3630,3631,3633,3652],{},[717,3632,835],{"fence":609},[879,3634,3635,3643],{},[594,3636,3637,3639,3641],{},[644,3638,3132],{},[717,3640,2689],{},[644,3642,1875],{},[594,3644,3645,3647,3650],{},[644,3646,1875],{},[597,3648,3649],{"mathvariant":1654},"\u002F",[644,3651,3132],{},[717,3653,856],{"fence":609},[717,3655,877],{},[644,3657,2953],{},[717,3659,2689],{},[597,3661,1655],{"mathvariant":1654},[717,3663,835],{"stretchy":1658},[644,3665,3666],{},"1,2",[717,3668,856],{"stretchy":1658},[717,3670,823],{},[644,3672,3673],{},"0,1151",[601,3675,3676],{"encoding":603},"P(\\bar{X} > 6) \\approx 1 - \\Phi\\!\\left(\\frac{6 - 5}{5\u002F6}\\right) = 1 - \\Phi(1{,}2) \\approx 0{,}1151",[578,3678,3680,3733,3754,3773,3888,3906,3942],{"className":3679,"ariaHidden":609},[608],[578,3681,3683,3687,3690,3693,3724,3727,3730],{"className":3682},[613],[578,3684],{"className":3685,"style":3686},[617],"height:1.0701em;vertical-align:-0.25em;",[578,3688,2653],{"className":3689,"style":2727},[622,623],[578,3691,835],{"className":3692},[1012],[578,3694,3696],{"className":3695},[622,1096],[578,3697,3699],{"className":3698},[674],[578,3700,3702],{"className":3701},[678],[578,3703,3705,3713],{"className":3704,"style":1106},[682],[578,3706,3707,3710],{"style":1109},[578,3708],{"className":3709,"style":1113},[689],[578,3711,869],{"className":3712,"style":1117},[622,623],[578,3714,3715,3718],{"style":1120},[578,3716],{"className":3717,"style":1113},[689],[578,3719,3721],{"className":3720,"style":1128},[1127],[578,3722,872],{"className":3723},[622],[578,3725],{"className":3726,"style":743},[742],[578,3728,719],{"className":3729},[747],[578,3731],{"className":3732,"style":743},[742],[578,3734,3736,3739,3742,3745,3748,3751],{"className":3735},[613],[578,3737],{"className":3738,"style":1675},[617],[578,3740,3132],{"className":3741},[622],[578,3743,856],{"className":3744},[1073],[578,3746],{"className":3747,"style":743},[742],[578,3749,823],{"className":3750},[747],[578,3752],{"className":3753,"style":743},[742],[578,3755,3757,3761,3764,3767,3770],{"className":3756},[613],[578,3758],{"className":3759,"style":3760},[617],"height:0.7278em;vertical-align:-0.0833em;",[578,3762,2953],{"className":3763},[622],[578,3765],{"className":3766,"style":2233},[742],[578,3768,2689],{"className":3769},[2237],[578,3771],{"className":3772,"style":2233},[742],[578,3774,3776,3779,3782,3785,3788,3879,3882,3885],{"className":3775},[613],[578,3777],{"className":3778,"style":2810},[617],[578,3780,1655],{"className":3781},[622],[578,3783],{"className":3784,"style":1000},[742],[578,3786],{"className":3787,"style":1004},[742],[578,3789,3791,3797,3873],{"className":3790},[1008],[578,3792,3794],{"className":3793,"style":1014},[1012,1013],[578,3795,835],{"className":3796},[1018,696],[578,3798,3800,3803,3870],{"className":3799},[622],[578,3801],{"className":3802},[1012,1189],[578,3804,3806],{"className":3805},[879],[578,3807,3809,3861],{"className":3808},[674,943],[578,3810,3812,3858],{"className":3811},[678],[578,3813,3815,3827,3835],{"className":3814,"style":2847},[682],[578,3816,3817,3820],{"style":1205},[578,3818],{"className":3819,"style":1113},[689],[578,3821,3823],{"className":3822},[622],[578,3824,3826],{"className":3825},[622],"5\u002F6",[578,3828,3829,3832],{"style":1217},[578,3830],{"className":3831,"style":1113},[689],[578,3833],{"className":3834,"style":1225},[1224],[578,3836,3837,3840],{"style":1228},[578,3838],{"className":3839,"style":1113},[689],[578,3841,3843,3846,3849,3852,3855],{"className":3842},[622],[578,3844,3132],{"className":3845},[622],[578,3847],{"className":3848,"style":2233},[742],[578,3850,2689],{"className":3851},[2237],[578,3853],{"className":3854,"style":2233},[742],[578,3856,1875],{"className":3857},[622],[578,3859,967],{"className":3860},[966],[578,3862,3864],{"className":3863},[678],[578,3865,3868],{"className":3866,"style":3867},[682],"height:0.936em;",[578,3869],{},[578,3871],{"className":3872},[1073,1189],[578,3874,3876],{"className":3875,"style":1014},[1073,1013],[578,3877,856],{"className":3878},[1018,696],[578,3880],{"className":3881,"style":743},[742],[578,3883,877],{"className":3884},[747],[578,3886],{"className":3887,"style":743},[742],[578,3889,3891,3894,3897,3900,3903],{"className":3890},[613],[578,3892],{"className":3893,"style":3760},[617],[578,3895,2953],{"className":3896},[622],[578,3898],{"className":3899,"style":2233},[742],[578,3901,2689],{"className":3902},[2237],[578,3904],{"className":3905,"style":2233},[742],[578,3907,3909,3912,3915,3918,3921,3927,3930,3933,3936,3939],{"className":3908},[613],[578,3910],{"className":3911,"style":1675},[617],[578,3913,1655],{"className":3914},[622],[578,3916,835],{"className":3917},[1012],[578,3919,2953],{"className":3920},[622],[578,3922,3924],{"className":3923},[622],[578,3925,842],{"className":3926},[1029],[578,3928,646],{"className":3929},[622],[578,3931,856],{"className":3932},[1073],[578,3934],{"className":3935,"style":743},[742],[578,3937,823],{"className":3938},[747],[578,3940],{"className":3941,"style":743},[742],[578,3943,3945,3948,3951,3957],{"className":3944},[613],[578,3946],{"className":3947,"style":1861},[617],[578,3949,722],{"className":3950},[622],[578,3952,3954],{"className":3953},[622],[578,3955,842],{"className":3956},[1029],[578,3958,3960],{"className":3959},[622],"1151",[560,3962,3964],{"id":3963},"typische-fehler","Typische Fehler",[3966,3967,3968,4049,4255,4258],"ul",{},[3969,3970,3971,3972,4044,4045,4048],"li",{},"Behaupten, die einzelnen ",[578,3973,3975,3994],{"className":3974},[581],[578,3976,3978],{"className":3977},[585],[587,3979,3980],{"xmlns":589},[591,3981,3982,3991],{},[594,3983,3984],{},[814,3985,3986,3988],{},[597,3987,869],{},[597,3989,3990],{},"i",[601,3992,3993],{"encoding":603},"X_i",[578,3995,3997],{"className":3996,"ariaHidden":609},[608],[578,3998,4000,4003],{"className":3999},[613],[578,4001],{"className":4002,"style":929},[617],[578,4004,4006,4009],{"className":4005},[622],[578,4007,869],{"className":4008,"style":1117},[622,623],[578,4010,4012],{"className":4011},[670],[578,4013,4015,4036],{"className":4014},[674,943],[578,4016,4018,4033],{"className":4017},[678],[578,4019,4022],{"className":4020,"style":4021},[682],"height:0.3117em;",[578,4023,4024,4027],{"style":1146},[578,4025],{"className":4026,"style":690},[689],[578,4028,4030],{"className":4029},[694,695,696,697],[578,4031,3990],{"className":4032},[622,623,697],[578,4034,967],{"className":4035},[966],[578,4037,4039],{"className":4038},[678],[578,4040,4042],{"className":4041,"style":974},[682],[578,4043],{}," würden normalverteilt. Nur die Summe bzw. der Mittelwert ist ",[569,4046,4047],{},"näherungsweise"," normalverteilt.",[3969,4050,4051,4052,4081,4082,4225,4226,4254],{},"Beim Mittelwert mit ",[578,4053,4055,4069],{"className":4054},[581],[578,4056,4058],{"className":4057},[585],[587,4059,4060],{"xmlns":589},[591,4061,4062,4066],{},[594,4063,4064],{},[597,4065,642],{},[601,4067,4068],{"encoding":603},"\\sigma",[578,4070,4072],{"className":4071,"ariaHidden":609},[608],[578,4073,4075,4078],{"className":4074},[613],[578,4076],{"className":4077,"style":791},[617],[578,4079,642],{"className":4080,"style":666},[622,623]," statt ",[578,4083,4085,4104],{"className":4084},[581],[578,4086,4088],{"className":4087},[585],[587,4089,4090],{"xmlns":589},[591,4091,4092,4102],{},[594,4093,4094],{},[879,4095,4096,4098],{},[597,4097,642],{},[1451,4099,4100],{},[597,4101,779],{},[601,4103,1457],{"encoding":603},[578,4105,4107],{"className":4106,"ariaHidden":609},[608],[578,4108,4110,4113],{"className":4109},[613],[578,4111],{"className":4112,"style":1467},[617],[578,4114,4116,4119,4222],{"className":4115},[622],[578,4117],{"className":4118},[1012,1189],[578,4120,4122],{"className":4121},[879],[578,4123,4125,4214],{"className":4124},[674,943],[578,4126,4128,4211],{"className":4127},[678],[578,4129,4131,4189,4197],{"className":4130,"style":1486},[682],[578,4132,4133,4136],{"style":1489},[578,4134],{"className":4135,"style":1113},[689],[578,4137,4139],{"className":4138},[694,695,696,697],[578,4140,4142],{"className":4141},[622,697],[578,4143,4145],{"className":4144},[622,1502,697],[578,4146,4148,4181],{"className":4147},[674,943],[578,4149,4151,4178],{"className":4150},[678],[578,4152,4154,4166],{"className":4153,"style":1512},[682],[578,4155,4157,4160],{"className":4156,"style":1109},[1516],[578,4158],{"className":4159,"style":1113},[689],[578,4161,4163],{"className":4162,"style":1523},[622,697],[578,4164,779],{"className":4165},[622,623,697],[578,4167,4168,4171],{"style":1529},[578,4169],{"className":4170,"style":1113},[689],[578,4172,4174],{"className":4173,"style":1537},[1536,697],[1539,4175,4176],{"xmlns":1541,"width":1542,"height":1543,"viewBox":1544,"preserveAspectRatio":1545},[1547,4177],{"d":1549},[578,4179,967],{"className":4180},[966],[578,4182,4184],{"className":4183},[678],[578,4185,4187],{"className":4186,"style":1559},[682],[578,4188],{},[578,4190,4191,4194],{"style":1217},[578,4192],{"className":4193,"style":1113},[689],[578,4195],{"className":4196,"style":1225},[1224],[578,4198,4199,4202],{"style":1572},[578,4200],{"className":4201,"style":1113},[689],[578,4203,4205],{"className":4204},[694,695,696,697],[578,4206,4208],{"className":4207},[622,697],[578,4209,642],{"className":4210,"style":666},[622,623,697],[578,4212,967],{"className":4213},[966],[578,4215,4217],{"className":4216},[678],[578,4218,4220],{"className":4219,"style":1594},[682],[578,4221],{},[578,4223],{"className":4224},[1073,1189]," standardisieren. Das unterschätzt die Konzentration um ",[578,4227,4229,4242],{"className":4228},[581],[578,4230,4232],{"className":4231},[585],[587,4233,4234],{"xmlns":589},[591,4235,4236,4240],{},[594,4237,4238],{},[597,4239,599],{},[601,4241,604],{"encoding":603},[578,4243,4245],{"className":4244,"ariaHidden":609},[608],[578,4246,4248,4251],{"className":4247},[613],[578,4249],{"className":4250,"style":618},[617],[578,4252,599],{"className":4253},[622,623]," stark.",[3969,4256,4257],{},"Den Satz ohne Voraussetzungen anwenden. Bei unendlicher Varianz (z.B. Cauchy-Verteilung) oder stark abhängigen Summanden gilt er nicht.",[3969,4259,4260,4261,4387],{},"Den zentralen Grenzwertsatz mit dem Gesetz der großen Zahlen verwechseln. Dieses sagt nur ",[578,4262,4264,4291],{"className":4263},[581],[578,4265,4267],{"className":4266},[585],[587,4268,4269],{"xmlns":589},[591,4270,4271,4288],{},[594,4272,4273,4283,4286],{},[814,4274,4275,4281],{},[865,4276,4277,4279],{"accent":609},[597,4278,869],{},[717,4280,872],{},[597,4282,779],{},[717,4284,4285],{},"→",[597,4287,599],{},[601,4289,4290],{"encoding":603},"\\bar{X}_n \\to \\mu",[578,4292,4294,4378],{"className":4293,"ariaHidden":609},[608],[578,4295,4297,4301,4369,4372,4375],{"className":4296},[613],[578,4298],{"className":4299,"style":4300},[617],"height:0.9701em;vertical-align:-0.15em;",[578,4302,4304,4335],{"className":4303},[622],[578,4305,4307],{"className":4306},[622,1096],[578,4308,4310],{"className":4309},[674],[578,4311,4313],{"className":4312},[678],[578,4314,4316,4324],{"className":4315,"style":1106},[682],[578,4317,4318,4321],{"style":1109},[578,4319],{"className":4320,"style":1113},[689],[578,4322,869],{"className":4323,"style":1117},[622,623],[578,4325,4326,4329],{"style":1120},[578,4327],{"className":4328,"style":1113},[689],[578,4330,4332],{"className":4331,"style":1128},[1127],[578,4333,872],{"className":4334},[622],[578,4336,4338],{"className":4337},[670],[578,4339,4341,4361],{"className":4340},[674,943],[578,4342,4344,4358],{"className":4343},[678],[578,4345,4347],{"className":4346,"style":950},[682],[578,4348,4349,4352],{"style":1146},[578,4350],{"className":4351,"style":690},[689],[578,4353,4355],{"className":4354},[694,695,696,697],[578,4356,779],{"className":4357},[622,623,697],[578,4359,967],{"className":4360},[966],[578,4362,4364],{"className":4363},[678],[578,4365,4367],{"className":4366,"style":974},[682],[578,4368],{},[578,4370],{"className":4371,"style":743},[742],[578,4373,4285],{"className":4374},[747],[578,4376],{"className":4377,"style":743},[742],[578,4379,4381,4384],{"className":4380},[613],[578,4382],{"className":4383,"style":618},[617],[578,4385,599],{"className":4386},[622,623],", nicht, wie die Abweichung verteilt ist.",{"title":4389,"searchDepth":4390,"depth":4390,"links":4391},"",2,[4392,4393,4394],{"id":562,"depth":4390,"text":563},{"id":1777,"depth":4390,"text":1778},{"id":3963,"depth":4390,"text":3964},[4396,4399,4401,4404,4407,4410,4412,4415],{"lhs":4397,"rhs":4398},"(S - n*u) \u002F (s*sqrt(n))","(S\u002Fn - u) \u002F (s\u002Fsqrt(n))",{"lhs":4400,"rhs":2147},"100 * 3.5",{"lhs":4402,"rhs":4403},"round(sqrt(100 * 35\u002F12), 2)","17.08",{"lhs":4405,"rhs":4406},"round((370.5 - 350) \u002F sqrt(100 * 35\u002F12), 2)","1.20",{"lhs":4408,"rhs":4409},"round(0.5 * (1 + erf((370.5 - 350) \u002F sqrt(100 * 35\u002F12) \u002F sqrt(2))), 3)","0.885",{"lhs":4411,"rhs":3826},"5 \u002F sqrt(36)",{"lhs":4413,"rhs":4414},"(6 - 5) \u002F (5\u002F6)","1.2",{"lhs":4416,"rhs":4417},"round(1 - 0.5 * (1 + erf(1.2 \u002F sqrt(2))), 4)","0.1151","X_1, X_2, \\ldots \\text{ unabhängig und identisch verteilt},\\ E(X_i) = \\mu,\\ 0 \u003C V(X_i) = \\sigma^2 \u003C \\infty,\\ z \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X_1, X_2, \\ldots\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">unabhängig und identisch\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">verteilt\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>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>μ\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(X_i) = \\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: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\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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\">i\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>0\u003C\u002Fmn>\u003Cmo><\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>σ\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">0 < V(X_i) = \\sigma^2 < \\infty,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6835em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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\">i\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8532em;vertical-align:-0.0391em;\">\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>z\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">z \\in \\mathbb{R}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","central-limit-theorem","\\lim_{n \\to \\infty} P\\left(\\frac{S_n - n\\mu}{\\sigma \\sqrt{n}} \\leq z\\right) = \\Phi(z), \\quad S_n = X_1 + \\ldots + X_n","\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>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmi>P\u003C\u002Fmi>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsub>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>μ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>σ\u003C\u002Fmi>\u003Cmsqrt>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>z\u003C\u002Fmi>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Φ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>z\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmsub>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lim_{n \\to \\infty} P\\left(\\frac{S_n - n\\mu}{\\sigma \\sqrt{n}} \\leq z\\right) = \\Phi(z), \\quad S_n = X_1 + \\ldots + X_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:2.4em;vertical-align:-0.95em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\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:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\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:1.3603em;\">\u003Cspan style=\"top:-2.3097em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">σ\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8003em;\">\u003Cspan class=\"svg-align\" style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:0.833em;\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.7603em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:0.853em;height:1.08em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2397em;\">\u003Cspan>\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:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;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\">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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">μ\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:0.93em;\">\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:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.044em;\">z\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan 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style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0785em;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\">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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fzentraler-grenzwertsatz",[],[4431,4432,4433,4434],"normal-distribution","standardization","law-of-large-numbers","moivre-laplace",{"title":548,"description":4389},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fzentraler-grenzwertsatz","Die standardisierte Summe vieler unabhängiger, gleich verteilter Zufallsgrößen ist für große n annähernd standardnormalverteilt.",[4439,4440,4441,4442,4443],"grenzwertsatz","normalverteilung","summe von zufallsgrößen","konvergenz in 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