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Dichten aufstellen.",[914,961,962,963,1258,1259,1290,1291,1320],{},"Logarithmieren: ",[569,964,966,1046],{"className":965},[572],[569,967,969],{"className":968},[576],[578,970,971],{"xmlns":580},[582,972,973,1043],{},[585,974,975,979,981,983,985,988,991,994,996,998,1000,1002,1004,1021,1023,1025,1028,1030,1036,1039,1041],{},[591,976,978],{"mathvariant":977},"normal","ℓ",[599,980,811],{"stretchy":810},[591,982,769],{},[599,984,816],{"stretchy":810},[599,986,987],{},"=",[591,989,990],{},"ln",[599,992,993],{},"⁡",[591,995,807],{},[599,997,811],{"stretchy":810},[591,999,769],{},[599,1001,816],{"stretchy":810},[599,1003,987],{},[1005,1006,1007,1010,1019],"msubsup",{},[599,1008,1009],{},"∑",[585,1011,1012,1015,1017],{},[591,1013,1014],{},"i",[599,1016,987],{},[595,1018,597],{},[591,1020,614],{},[591,1022,990],{},[599,1024,993],{},[591,1026,1027],{},"f",[599,1029,811],{"stretchy":810},[588,1031,1032,1034],{},[591,1033,593],{},[591,1035,1014],{},[599,1037,1038],{"separator":601},";",[591,1040,769],{},[599,1042,816],{"stretchy":810},[616,1044,1045],{"encoding":618},"\\ell(\\theta) = \\ln L(\\theta) = \\sum_{i=1}^{n} \\ln f(x_i; \\theta)",[569,1047,1049,1078,1112],{"className":1048,"ariaHidden":601},[623],[569,1050,1052,1055,1058,1061,1064,1067,1071,1075],{"className":1051},[627],[569,1053],{"className":1054,"style":829},[631],[569,1056,978],{"className":1057},[636],[569,1059,811],{"className":1060},[836],[569,1062,769],{"className":1063,"style":786},[636,640],[569,1065,816],{"className":1066},[843],[569,1068],{"className":1069,"style":1070},[698],"margin-right:0.2778em;",[569,1072,987],{"className":1073},[1074],"mrel",[569,1076],{"className":1077,"style":1070},[698],[569,1079,1081,1084,1088,1091,1094,1097,1100,1103,1106,1109],{"className":1080},[627],[569,1082],{"className":1083,"style":829},[631],[569,1085,990],{"className":1086},[1087],"mop",[569,1089],{"className":1090,"style":699},[698],[569,1092,807],{"className":1093},[636,640],[569,1095,811],{"className":1096},[836],[569,1098,769],{"className":1099,"style":786},[636,640],[569,1101,816],{"className":1102},[843],[569,1104],{"className":1105,"style":1070},[698],[569,1107,987],{"className":1108},[1074],[569,1110],{"className":1111,"style":1070},[698],[569,1113,1115,1119,1189,1192,1195,1198,1202,1205,1246,1249,1252,1255],{"className":1114},[627],[569,1116],{"className":1117,"style":1118},[631],"height:1.104em;vertical-align:-0.2997em;",[569,1120,1122,1128],{"className":1121},[1087],[569,1123,1009],{"className":1124,"style":1127},[1087,1125,1126],"op-symbol","small-op","position:relative;top:0em;",[569,1129,1131],{"className":1130},[644],[569,1132,1134,1180],{"className":1133},[648,649],[569,1135,1137,1177],{"className":1136},[653],[569,1138,1141,1162],{"className":1139,"style":1140},[657],"height:0.8043em;",[569,1142,1144,1147],{"style":1143},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[569,1145],{"className":1146,"style":666},[665],[569,1148,1150],{"className":1149},[670,671,672,673],[569,1151,1153,1156,1159],{"className":1152},[636,673],[569,1154,1014],{"className":1155},[636,640,673],[569,1157,987],{"className":1158},[1074,673],[569,1160,597],{"className":1161},[636,673],[569,1163,1165,1168],{"style":1164},"top:-3.2029em;margin-right:0.05em;",[569,1166],{"className":1167,"style":666},[665],[569,1169,1171],{"className":1170},[670,671,672,673],[569,1172,1174],{"className":1173},[636,673],[569,1175,614],{"className":1176},[636,640,673],[569,1178,681],{"className":1179},[680],[569,1181,1183],{"className":1182},[653],[569,1184,1187],{"className":1185,"style":1186},[657],"height:0.2997em;",[569,1188],{},[569,1190],{"className":1191,"style":699},[698],[569,1193,990],{"className":1194},[1087],[569,1196],{"className":1197,"style":699},[698],[569,1199,1027],{"className":1200,"style":1201},[636,640],"margin-right:0.1076em;",[569,1203,811],{"className":1204},[836],[569,1206,1208,1211],{"className":1207},[636],[569,1209,593],{"className":1210},[636,640],[569,1212,1214],{"className":1213},[644],[569,1215,1217,1238],{"className":1216},[648,649],[569,1218,1220,1235],{"className":1219},[653],[569,1221,1224],{"className":1222,"style":1223},[657],"height:0.3117em;",[569,1225,1226,1229],{"style":661},[569,1227],{"className":1228,"style":666},[665],[569,1230,1232],{"className":1231},[670,671,672,673],[569,1233,1014],{"className":1234},[636,640,673],[569,1236,681],{"className":1237},[680],[569,1239,1241],{"className":1240},[653],[569,1242,1244],{"className":1243,"style":688},[657],[569,1245],{},[569,1247,1038],{"className":1248},[694],[569,1250],{"className":1251,"style":699},[698],[569,1253,769],{"className":1254,"style":786},[636,640],[569,1256,816],{"className":1257},[843],". Da ",[569,1260,1262,1278],{"className":1261},[572],[569,1263,1265],{"className":1264},[576],[578,1266,1267],{"xmlns":580},[582,1268,1269,1275],{},[585,1270,1271,1273],{},[591,1272,990],{},[599,1274,993],{},[616,1276,1277],{"encoding":618},"\\ln",[569,1279,1281],{"className":1280,"ariaHidden":601},[623],[569,1282,1284,1287],{"className":1283},[627],[569,1285],{"className":1286,"style":782},[631],[569,1288,990],{"className":1289},[1087]," streng monoton wächst, hat ",[569,1292,1294,1308],{"className":1293},[572],[569,1295,1297],{"className":1296},[576],[578,1298,1299],{"xmlns":580},[582,1300,1301,1305],{},[585,1302,1303],{},[591,1304,978],{"mathvariant":977},[616,1306,1307],{"encoding":618},"\\ell",[569,1309,1311],{"className":1310,"ariaHidden":601},[623],[569,1312,1314,1317],{"className":1313},[627],[569,1315],{"className":1316,"style":782},[631],[569,1318,978],{"className":1319},[636]," dasselbe Maximum, und aus dem Produkt wird eine Summe.",[914,1322,1323,1324,1431,1432,1435],{},"Ableiten und null setzen: ",[569,1325,1327,1359],{"className":1326},[572],[569,1328,1330],{"className":1329},[576],[578,1331,1332],{"xmlns":580},[582,1333,1334,1356],{},[585,1335,1336,1345,1347,1349,1351,1353],{},[1337,1338,1339,1341],"msup",{},[591,1340,978],{"mathvariant":977},[599,1342,1344],{"mathvariant":977,"lspace":1343,"rspace":1343},"0em","′",[599,1346,811],{"stretchy":810},[591,1348,769],{},[599,1350,816],{"stretchy":810},[599,1352,987],{},[595,1354,1355],{},"0",[616,1357,1358],{"encoding":618},"\\ell'(\\theta) = 0",[569,1360,1362,1421],{"className":1361,"ariaHidden":601},[623],[569,1363,1365,1369,1403,1406,1409,1412,1415,1418],{"className":1364},[627],[569,1366],{"className":1367,"style":1368},[631],"height:1.0019em;vertical-align:-0.25em;",[569,1370,1372,1375],{"className":1371},[636],[569,1373,978],{"className":1374},[636],[569,1376,1378],{"className":1377},[644],[569,1379,1381],{"className":1380},[648],[569,1382,1384],{"className":1383},[653],[569,1385,1388],{"className":1386,"style":1387},[657],"height:0.7519em;",[569,1389,1391,1394],{"style":1390},"top:-3.063em;margin-right:0.05em;",[569,1392],{"className":1393,"style":666},[665],[569,1395,1397],{"className":1396},[670,671,672,673],[569,1398,1400],{"className":1399},[636,673],[569,1401,1344],{"className":1402},[636,673],[569,1404,811],{"className":1405},[836],[569,1407,769],{"className":1408,"style":786},[636,640],[569,1410,816],{"className":1411},[843],[569,1413],{"className":1414,"style":1070},[698],[569,1416,987],{"className":1417},[1074],[569,1419],{"className":1420,"style":1070},[698],[569,1422,1424,1428],{"className":1423},[627],[569,1425],{"className":1426,"style":1427},[631],"height:0.6444em;",[569,1429,1355],{"className":1430},[636]," (",[789,1433,1434],{},"Likelihood-Gleichung",").",[914,1437,1438],{},"Prüfen, dass wirklich ein Maximum vorliegt (zweite Ableitung oder Randverhalten).",[565,1440,1441],{},"Wichtige Ergebnisse:",[1443,1444,1445,1633,1758,1948],"ul",{},[914,1446,1447,1448,1632],{},"Bernoulli bzw. Binomial: ",[569,1449,1451,1481],{"className":1450},[572],[569,1452,1454],{"className":1453},[576],[578,1455,1456],{"xmlns":580},[582,1457,1458,1478],{},[585,1459,1460,1468,1470],{},[1461,1462,1463,1465],"mover",{"accent":601},[591,1464,565],{},[599,1466,1467],{},"^",[599,1469,987],{},[1471,1472,1473,1476],"mfrac",{},[591,1474,1475],{},"k",[591,1477,614],{},[616,1479,1480],{"encoding":618},"\\hat{p} = \\frac{k}{n}",[569,1482,1484,1548],{"className":1483,"ariaHidden":601},[623],[569,1485,1487,1491,1539,1542,1545],{"className":1486},[627],[569,1488],{"className":1489,"style":1490},[631],"height:0.8889em;vertical-align:-0.1944em;",[569,1492,1495],{"className":1493},[636,1494],"accent",[569,1496,1498,1530],{"className":1497},[648,649],[569,1499,1501,1527],{"className":1500},[653],[569,1502,1504,1514],{"className":1503,"style":782},[657],[569,1505,1507,1511],{"style":1506},"top:-3em;",[569,1508],{"className":1509,"style":1510},[665],"height:3em;",[569,1512,565],{"className":1513},[636,640],[569,1515,1516,1519],{"style":1506},[569,1517],{"className":1518,"style":1510},[665],[569,1520,1524],{"className":1521,"style":1523},[1522],"accent-body","left:-0.1667em;",[569,1525,1467],{"className":1526},[636],[569,1528,681],{"className":1529},[680],[569,1531,1533],{"className":1532},[653],[569,1534,1537],{"className":1535,"style":1536},[657],"height:0.1944em;",[569,1538],{},[569,1540],{"className":1541,"style":1070},[698],[569,1543,987],{"className":1544},[1074],[569,1546],{"className":1547,"style":1070},[698],[569,1549,1551,1555],{"className":1550},[627],[569,1552],{"className":1553,"style":1554},[631],"height:1.2251em;vertical-align:-0.345em;",[569,1556,1558,1562,1629],{"className":1557},[636],[569,1559],{"className":1560},[836,1561],"nulldelimiter",[569,1563,1565],{"className":1564},[1471],[569,1566,1568,1620],{"className":1567},[648,649],[569,1569,1571,1617],{"className":1570},[653],[569,1572,1575,1590,1601],{"className":1573,"style":1574},[657],"height:0.8801em;",[569,1576,1578,1581],{"style":1577},"top:-2.655em;",[569,1579],{"className":1580,"style":1510},[665],[569,1582,1584],{"className":1583},[670,671,672,673],[569,1585,1587],{"className":1586},[636,673],[569,1588,614],{"className":1589},[636,640,673],[569,1591,1593,1596],{"style":1592},"top:-3.23em;",[569,1594],{"className":1595,"style":1510},[665],[569,1597],{"className":1598,"style":1600},[1599],"frac-line","border-bottom-width:0.04em;",[569,1602,1604,1607],{"style":1603},"top:-3.394em;",[569,1605],{"className":1606,"style":1510},[665],[569,1608,1610],{"className":1609},[670,671,672,673],[569,1611,1613],{"className":1612},[636,673],[569,1614,1475],{"className":1615,"style":1616},[636,640,673],"margin-right:0.0315em;",[569,1618,681],{"className":1619},[680],[569,1621,1623],{"className":1622},[653],[569,1624,1627],{"className":1625,"style":1626},[657],"height:0.345em;",[569,1628],{},[569,1630],{"className":1631},[843,1561]," (relative Trefferhäufigkeit)",[914,1634,1635,1636],{},"Poisson: ",[569,1637,1639,1667],{"className":1638},[572],[569,1640,1642],{"className":1641},[576],[578,1643,1644],{"xmlns":580},[582,1645,1646,1664],{},[585,1647,1648,1655,1657],{},[1461,1649,1650,1653],{"accent":601},[591,1651,1652],{},"λ",[599,1654,1467],{},[599,1656,987],{},[1461,1658,1659,1661],{"accent":601},[591,1660,593],{},[599,1662,1663],{},"ˉ",[616,1665,1666],{"encoding":618},"\\hat{\\lambda} = \\bar{x}",[569,1668,1670,1719],{"className":1669,"ariaHidden":601},[623],[569,1671,1673,1677,1710,1713,1716],{"className":1672},[627],[569,1674],{"className":1675,"style":1676},[631],"height:0.9579em;",[569,1678,1680],{"className":1679},[636,1494],[569,1681,1683],{"className":1682},[648],[569,1684,1686],{"className":1685},[653],[569,1687,1689,1697],{"className":1688,"style":1676},[657],[569,1690,1691,1694],{"style":1506},[569,1692],{"className":1693,"style":1510},[665],[569,1695,1652],{"className":1696},[636,640],[569,1698,1700,1703],{"style":1699},"top:-3.2634em;",[569,1701],{"className":1702,"style":1510},[665],[569,1704,1707],{"className":1705,"style":1706},[1522],"left:-0.25em;",[569,1708,1467],{"className":1709},[636],[569,1711],{"className":1712,"style":1070},[698],[569,1714,987],{"className":1715},[1074],[569,1717],{"className":1718,"style":1070},[698],[569,1720,1722,1726],{"className":1721},[627],[569,1723],{"className":1724,"style":1725},[631],"height:0.5678em;",[569,1727,1729],{"className":1728},[636,1494],[569,1730,1732],{"className":1731},[648],[569,1733,1735],{"className":1734},[653],[569,1736,1738,1746],{"className":1737,"style":1725},[657],[569,1739,1740,1743],{"style":1506},[569,1741],{"className":1742,"style":1510},[665],[569,1744,593],{"className":1745},[636,640],[569,1747,1748,1751],{"style":1506},[569,1749],{"className":1750,"style":1510},[665],[569,1752,1755],{"className":1753,"style":1754},[1522],"left:-0.2222em;",[569,1756,1663],{"className":1757},[636],[914,1759,1760,1761],{},"Exponentialverteilung: ",[569,1762,1764,1794],{"className":1763},[572],[569,1765,1767],{"className":1766},[576],[578,1768,1769],{"xmlns":580},[582,1770,1771,1791],{},[585,1772,1773,1779,1781],{},[1461,1774,1775,1777],{"accent":601},[591,1776,1652],{},[599,1778,1467],{},[599,1780,987],{},[1471,1782,1783,1785],{},[595,1784,597],{},[1461,1786,1787,1789],{"accent":601},[591,1788,593],{},[599,1790,1663],{},[616,1792,1793],{"encoding":618},"\\hat{\\lambda} = \\frac{1}{\\bar{x}}",[569,1795,1797,1843],{"className":1796,"ariaHidden":601},[623],[569,1798,1800,1803,1834,1837,1840],{"className":1799},[627],[569,1801],{"className":1802,"style":1676},[631],[569,1804,1806],{"className":1805},[636,1494],[569,1807,1809],{"className":1808},[648],[569,1810,1812],{"className":1811},[653],[569,1813,1815,1823],{"className":1814,"style":1676},[657],[569,1816,1817,1820],{"style":1506},[569,1818],{"className":1819,"style":1510},[665],[569,1821,1652],{"className":1822},[636,640],[569,1824,1825,1828],{"style":1699},[569,1826],{"className":1827,"style":1510},[665],[569,1829,1831],{"className":1830,"style":1706},[1522],[569,1832,1467],{"className":1833},[636],[569,1835],{"className":1836,"style":1070},[698],[569,1838,987],{"className":1839},[1074],[569,1841],{"className":1842,"style":1070},[698],[569,1844,1846,1850],{"className":1845},[627],[569,1847],{"className":1848,"style":1849},[631],"height:1.1901em;vertical-align:-0.345em;",[569,1851,1853,1856,1945],{"className":1852},[636],[569,1854],{"className":1855},[836,1561],[569,1857,1859],{"className":1858},[1471],[569,1860,1862,1937],{"className":1861},[648,649],[569,1863,1865,1934],{"className":1864},[653],[569,1866,1869,1912,1920],{"className":1867,"style":1868},[657],"height:0.8451em;",[569,1870,1871,1874],{"style":1577},[569,1872],{"className":1873,"style":1510},[665],[569,1875,1877],{"className":1876},[670,671,672,673],[569,1878,1880],{"className":1879},[636,673],[569,1881,1883],{"className":1882},[636,1494,673],[569,1884,1886],{"className":1885},[648],[569,1887,1889],{"className":1888},[653],[569,1890,1892,1901],{"className":1891,"style":1725},[657],[569,1893,1895,1898],{"style":1894},"top:-2.7em;",[569,1896],{"className":1897,"style":666},[665],[569,1899,593],{"className":1900},[636,640,673],[569,1902,1903,1906],{"style":1894},[569,1904],{"className":1905,"style":666},[665],[569,1907,1909],{"className":1908,"style":1754},[1522],[569,1910,1663],{"className":1911},[636,673],[569,1913,1914,1917],{"style":1592},[569,1915],{"className":1916,"style":1510},[665],[569,1918],{"className":1919,"style":1600},[1599],[569,1921,1922,1925],{"style":1603},[569,1923],{"className":1924,"style":1510},[665],[569,1926,1928],{"className":1927},[670,671,672,673],[569,1929,1931],{"className":1930},[636,673],[569,1932,597],{"className":1933},[636,673],[569,1935,681],{"className":1936},[680],[569,1938,1940],{"className":1939},[653],[569,1941,1943],{"className":1942,"style":1626},[657],[569,1944],{},[569,1946],{"className":1947},[843,1561],[914,1949,1950,1951,2078,2079],{},"Normalverteilung: ",[569,1952,1954,1981],{"className":1953},[572],[569,1955,1957],{"className":1956},[576],[578,1958,1959],{"xmlns":580},[582,1960,1961,1978],{},[585,1962,1963,1970,1972],{},[1461,1964,1965,1968],{"accent":601},[591,1966,1967],{},"μ",[599,1969,1467],{},[599,1971,987],{},[1461,1973,1974,1976],{"accent":601},[591,1975,593],{},[599,1977,1663],{},[616,1979,1980],{"encoding":618},"\\hat{\\mu} = \\bar{x}",[569,1982,1984,2041],{"className":1983,"ariaHidden":601},[623],[569,1985,1987,1990,2032,2035,2038],{"className":1986},[627],[569,1988],{"className":1989,"style":1490},[631],[569,1991,1993],{"className":1992},[636,1494],[569,1994,1996,2024],{"className":1995},[648,649],[569,1997,1999,2021],{"className":1998},[653],[569,2000,2002,2010],{"className":2001,"style":782},[657],[569,2003,2004,2007],{"style":1506},[569,2005],{"className":2006,"style":1510},[665],[569,2008,1967],{"className":2009},[636,640],[569,2011,2012,2015],{"style":1506},[569,2013],{"className":2014,"style":1510},[665],[569,2016,2018],{"className":2017,"style":1754},[1522],[569,2019,1467],{"className":2020},[636],[569,2022,681],{"className":2023},[680],[569,2025,2027],{"className":2026},[653],[569,2028,2030],{"className":2029,"style":1536},[657],[569,2031],{},[569,2033],{"className":2034,"style":1070},[698],[569,2036,987],{"className":2037},[1074],[569,2039],{"className":2040,"style":1070},[698],[569,2042,2044,2047],{"className":2043},[627],[569,2045],{"className":2046,"style":1725},[631],[569,2048,2050],{"className":2049},[636,1494],[569,2051,2053],{"className":2052},[648],[569,2054,2056],{"className":2055},[653],[569,2057,2059,2067],{"className":2058,"style":1725},[657],[569,2060,2061,2064],{"style":1506},[569,2062],{"className":2063,"style":1510},[665],[569,2065,593],{"className":2066},[636,640],[569,2068,2069,2072],{"style":1506},[569,2070],{"className":2071,"style":1510},[665],[569,2073,2075],{"className":2074,"style":1754},[1522],[569,2076,1663],{"className":2077},[636],", ",[569,2080,2082,2151],{"className":2081},[572],[569,2083,2085],{"className":2084},[576],[578,2086,2087],{"xmlns":580},[582,2088,2089,2148],{},[585,2090,2091,2103,2105,2111,2125,2127,2133,2136,2142],{},[1337,2092,2093,2100],{},[1461,2094,2095,2098],{"accent":601},[591,2096,2097],{},"σ",[599,2099,1467],{},[595,2101,2102],{},"2",[599,2104,987],{},[1471,2106,2107,2109],{},[595,2108,597],{},[591,2110,614],{},[1005,2112,2113,2115,2123],{},[599,2114,1009],{},[585,2116,2117,2119,2121],{},[591,2118,1014],{},[599,2120,987],{},[595,2122,597],{},[591,2124,614],{},[599,2126,811],{"stretchy":810},[588,2128,2129,2131],{},[591,2130,593],{},[591,2132,1014],{},[599,2134,2135],{},"−",[1461,2137,2138,2140],{"accent":601},[591,2139,593],{},[599,2141,1663],{},[1337,2143,2144,2146],{},[599,2145,816],{"stretchy":810},[595,2147,2102],{},[616,2149,2150],{"encoding":618},"\\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\bar{x})^2",[569,2152,2154,2228,2422],{"className":2153,"ariaHidden":601},[623],[569,2155,2157,2161,2219,2222,2225],{"className":2156},[627],[569,2158],{"className":2159,"style":2160},[631],"height:0.8141em;",[569,2162,2164,2196],{"className":2163},[636],[569,2165,2167],{"className":2166},[636,1494],[569,2168,2170],{"className":2169},[648],[569,2171,2173],{"className":2172},[653],[569,2174,2176,2185],{"className":2175,"style":782},[657],[569,2177,2178,2181],{"style":1506},[569,2179],{"className":2180,"style":1510},[665],[569,2182,2097],{"className":2183,"style":2184},[636,640],"margin-right:0.0359em;",[569,2186,2187,2190],{"style":1506},[569,2188],{"className":2189,"style":1510},[665],[569,2191,2193],{"className":2192,"style":1706},[1522],[569,2194,1467],{"className":2195},[636],[569,2197,2199],{"className":2198},[644],[569,2200,2202],{"className":2201},[648],[569,2203,2205],{"className":2204},[653],[569,2206,2208],{"className":2207,"style":2160},[657],[569,2209,2210,2213],{"style":1390},[569,2211],{"className":2212,"style":666},[665],[569,2214,2216],{"className":2215},[670,671,672,673],[569,2217,2102],{"className":2218},[636,673],[569,2220],{"className":2221,"style":1070},[698],[569,2223,987],{"className":2224},[1074],[569,2226],{"className":2227,"style":1070},[698],[569,2229,2231,2234,2302,2305,2368,2371,2411,2415,2419],{"className":2230},[627],[569,2232],{"className":2233,"style":1849},[631],[569,2235,2237,2240,2299],{"className":2236},[636],[569,2238],{"className":2239},[836,1561],[569,2241,2243],{"className":2242},[1471],[569,2244,2246,2291],{"className":2245},[648,649],[569,2247,2249,2288],{"className":2248},[653],[569,2250,2252,2266,2274],{"className":2251,"style":1868},[657],[569,2253,2254,2257],{"style":1577},[569,2255],{"className":2256,"style":1510},[665],[569,2258,2260],{"className":2259},[670,671,672,673],[569,2261,2263],{"className":2262},[636,673],[569,2264,614],{"className":2265},[636,640,673],[569,2267,2268,2271],{"style":1592},[569,2269],{"className":2270,"style":1510},[665],[569,2272],{"className":2273,"style":1600},[1599],[569,2275,2276,2279],{"style":1603},[569,2277],{"className":2278,"style":1510},[665],[569,2280,2282],{"className":2281},[670,671,672,673],[569,2283,2285],{"className":2284},[636,673],[569,2286,597],{"className":2287},[636,673],[569,2289,681],{"className":2290},[680],[569,2292,2294],{"className":2293},[653],[569,2295,2297],{"className":2296,"style":1626},[657],[569,2298],{},[569,2300],{"className":2301},[843,1561],[569,2303],{"className":2304,"style":699},[698],[569,2306,2308,2311],{"className":2307},[1087],[569,2309,1009],{"className":2310,"style":1127},[1087,1125,1126],[569,2312,2314],{"className":2313},[644],[569,2315,2317,2360],{"className":2316},[648,649],[569,2318,2320,2357],{"className":2319},[653],[569,2321,2323,2343],{"className":2322,"style":1140},[657],[569,2324,2325,2328],{"style":1143},[569,2326],{"className":2327,"style":666},[665],[569,2329,2331],{"className":2330},[670,671,672,673],[569,2332,2334,2337,2340],{"className":2333},[636,673],[569,2335,1014],{"className":2336},[636,640,673],[569,2338,987],{"className":2339},[1074,673],[569,2341,597],{"className":2342},[636,673],[569,2344,2345,2348],{"style":1164},[569,2346],{"className":2347,"style":666},[665],[569,2349,2351],{"className":2350},[670,671,672,673],[569,2352,2354],{"className":2353},[636,673],[569,2355,614],{"className":2356},[636,640,673],[569,2358,681],{"className":2359},[680],[569,2361,2363],{"className":2362},[653],[569,2364,2366],{"className":2365,"style":1186},[657],[569,2367],{},[569,2369,811],{"className":2370},[836],[569,2372,2374,2377],{"className":2373},[636],[569,2375,593],{"className":2376},[636,640],[569,2378,2380],{"className":2379},[644],[569,2381,2383,2403],{"className":2382},[648,649],[569,2384,2386,2400],{"className":2385},[653],[569,2387,2389],{"className":2388,"style":1223},[657],[569,2390,2391,2394],{"style":661},[569,2392],{"className":2393,"style":666},[665],[569,2395,2397],{"className":2396},[670,671,672,673],[569,2398,1014],{"className":2399},[636,640,673],[569,2401,681],{"className":2402},[680],[569,2404,2406],{"className":2405},[653],[569,2407,2409],{"className":2408,"style":688},[657],[569,2410],{},[569,2412],{"className":2413,"style":2414},[698],"margin-right:0.2222em;",[569,2416,2135],{"className":2417},[2418],"mbin",[569,2420],{"className":2421,"style":2414},[698],[569,2423,2425,2429,2460],{"className":2424},[627],[569,2426],{"className":2427,"style":2428},[631],"height:1.0641em;vertical-align:-0.25em;",[569,2430,2432],{"className":2431},[636,1494],[569,2433,2435],{"className":2434},[648],[569,2436,2438],{"className":2437},[653],[569,2439,2441,2449],{"className":2440,"style":1725},[657],[569,2442,2443,2446],{"style":1506},[569,2444],{"className":2445,"style":1510},[665],[569,2447,593],{"className":2448},[636,640],[569,2450,2451,2454],{"style":1506},[569,2452],{"className":2453,"style":1510},[665],[569,2455,2457],{"className":2456,"style":1754},[1522],[569,2458,1663],{"className":2459},[636],[569,2461,2463,2466],{"className":2462},[843],[569,2464,816],{"className":2465},[843],[569,2467,2469],{"className":2468},[644],[569,2470,2472],{"className":2471},[648],[569,2473,2475],{"className":2474},[653],[569,2476,2478],{"className":2477,"style":2160},[657],[569,2479,2480,2483],{"style":1390},[569,2481],{"className":2482,"style":666},[665],[569,2484,2486],{"className":2485},[670,671,672,673],[569,2487,2102],{"className":2488},[636,673],[565,2490,2491,2492,2495],{},"ML-Schätzer sind unter milden Voraussetzungen ",[789,2493,2494],{},"konsistent"," und asymptotisch normalverteilt, aber nicht immer erwartungstreu.",[560,2497,2499],{"id":2498},"beispiele","Beispiele",[565,2501,2502,2503,2556,2557,2609,2610,2765],{},"In ",[569,2504,2506,2525],{"className":2505},[572],[569,2507,2509],{"className":2508},[576],[578,2510,2511],{"xmlns":580},[582,2512,2513,2522],{},[585,2514,2515,2517,2519],{},[591,2516,614],{},[599,2518,987],{},[595,2520,2521],{},"20",[616,2523,2524],{"encoding":618},"n = 20",[569,2526,2528,2547],{"className":2527,"ariaHidden":601},[623],[569,2529,2531,2535,2538,2541,2544],{"className":2530},[627],[569,2532],{"className":2533,"style":2534},[631],"height:0.4306em;",[569,2536,614],{"className":2537},[636,640],[569,2539],{"className":2540,"style":1070},[698],[569,2542,987],{"className":2543},[1074],[569,2545],{"className":2546,"style":1070},[698],[569,2548,2550,2553],{"className":2549},[627],[569,2551],{"className":2552,"style":1427},[631],[569,2554,2521],{"className":2555},[636]," Versuchen gibt es ",[569,2558,2560,2579],{"className":2559},[572],[569,2561,2563],{"className":2562},[576],[578,2564,2565],{"xmlns":580},[582,2566,2567,2576],{},[585,2568,2569,2571,2573],{},[591,2570,1475],{},[599,2572,987],{},[595,2574,2575],{},"7",[616,2577,2578],{"encoding":618},"k = 7",[569,2580,2582,2600],{"className":2581,"ariaHidden":601},[623],[569,2583,2585,2588,2591,2594,2597],{"className":2584},[627],[569,2586],{"className":2587,"style":782},[631],[569,2589,1475],{"className":2590,"style":1616},[636,640],[569,2592],{"className":2593,"style":1070},[698],[569,2595,987],{"className":2596},[1074],[569,2598],{"className":2599,"style":1070},[698],[569,2601,2603,2606],{"className":2602},[627],[569,2604],{"className":2605,"style":1427},[631],[569,2607,2575],{"className":2608},[636]," Treffer. Die Log-Likelihood ist ",[569,2611,2613,2663],{"className":2612},[572],[569,2614,2616],{"className":2615},[576],[578,2617,2618],{"xmlns":580},[582,2619,2620,2660],{},[585,2621,2622,2624,2626,2628,2630,2632,2634,2636,2638,2640,2643,2646,2648,2650,2652,2654,2656,2658],{},[591,2623,978],{"mathvariant":977},[599,2625,811],{"stretchy":810},[591,2627,565],{},[599,2629,816],{"stretchy":810},[599,2631,987],{},[595,2633,2575],{},[591,2635,990],{},[599,2637,993],{},[591,2639,565],{},[599,2641,2642],{},"+",[595,2644,2645],{},"13",[591,2647,990],{},[599,2649,993],{},[599,2651,811],{"stretchy":810},[595,2653,597],{},[599,2655,2135],{},[591,2657,565],{},[599,2659,816],{"stretchy":810},[616,2661,2662],{"encoding":618},"\\ell(p) = 7 \\ln p + 13 \\ln(1 - p)",[569,2664,2666,2693,2723,2753],{"className":2665,"ariaHidden":601},[623],[569,2667,2669,2672,2675,2678,2681,2684,2687,2690],{"className":2668},[627],[569,2670],{"className":2671,"style":829},[631],[569,2673,978],{"className":2674},[636],[569,2676,811],{"className":2677},[836],[569,2679,565],{"className":2680},[636,640],[569,2682,816],{"className":2683},[843],[569,2685],{"className":2686,"style":1070},[698],[569,2688,987],{"className":2689},[1074],[569,2691],{"className":2692,"style":1070},[698],[569,2694,2696,2699,2702,2705,2708,2711,2714,2717,2720],{"className":2695},[627],[569,2697],{"className":2698,"style":1490},[631],[569,2700,2575],{"className":2701},[636],[569,2703],{"className":2704,"style":699},[698],[569,2706,990],{"className":2707},[1087],[569,2709],{"className":2710,"style":699},[698],[569,2712,565],{"className":2713},[636,640],[569,2715],{"className":2716,"style":2414},[698],[569,2718,2642],{"className":2719},[2418],[569,2721],{"className":2722,"style":2414},[698],[569,2724,2726,2729,2732,2735,2738,2741,2744,2747,2750],{"className":2725},[627],[569,2727],{"className":2728,"style":829},[631],[569,2730,2645],{"className":2731},[636],[569,2733],{"className":2734,"style":699},[698],[569,2736,990],{"className":2737},[1087],[569,2739,811],{"className":2740},[836],[569,2742,597],{"className":2743},[636],[569,2745],{"className":2746,"style":2414},[698],[569,2748,2135],{"className":2749},[2418],[569,2751],{"className":2752,"style":2414},[698],[569,2754,2756,2759,2762],{"className":2755},[627],[569,2757],{"className":2758,"style":829},[631],[569,2760,565],{"className":2761},[636,640],[569,2763,816],{"className":2764},[843],", also",[569,2767,2770],{"className":2768},[2769],"katex-display",[569,2771,2773,2851],{"className":2772},[572],[569,2774,2776],{"className":2775},[576],[578,2777,2779],{"xmlns":580,"display":2778},"block",[582,2780,2781,2848],{},[585,2782,2783,2789,2791,2793,2795,2797,2803,2805,2817,2819,2821,2824,2827,2829,2835,2837,2843,2845],{},[1337,2784,2785,2787],{},[591,2786,978],{"mathvariant":977},[599,2788,1344],{"mathvariant":977,"lspace":1343,"rspace":1343},[599,2790,811],{"stretchy":810},[591,2792,565],{},[599,2794,816],{"stretchy":810},[599,2796,987],{},[1471,2798,2799,2801],{},[595,2800,2575],{},[591,2802,565],{},[599,2804,2135],{},[1471,2806,2807,2809],{},[595,2808,2645],{},[585,2810,2811,2813,2815],{},[595,2812,597],{},[599,2814,2135],{},[591,2816,565],{},[599,2818,987],{},[595,2820,1355],{},[698,2822],{"width":2823},"1em",[599,2825,2826],{},"⇒",[698,2828],{"width":2823},[1461,2830,2831,2833],{"accent":601},[591,2832,565],{},[599,2834,1467],{},[599,2836,987],{},[1471,2838,2839,2841],{},[595,2840,2575],{},[595,2842,2521],{},[599,2844,987],{},[595,2846,2847],{},"0,35",[616,2849,2850],{"encoding":618},"\\ell'(p) = \\frac{7}{p} - \\frac{13}{1 - p} = 0 \\quad \\Rightarrow \\quad \\hat{p} = \\frac{7}{20} = 0{,}35",[569,2852,2854,2913,2995,3084,3109,3166,3245],{"className":2853,"ariaHidden":601},[623],[569,2855,2857,2861,2895,2898,2901,2904,2907,2910],{"className":2856},[627],[569,2858],{"className":2859,"style":2860},[631],"height:1.0519em;vertical-align:-0.25em;",[569,2862,2864,2867],{"className":2863},[636],[569,2865,978],{"className":2866},[636],[569,2868,2870],{"className":2869},[644],[569,2871,2873],{"className":2872},[648],[569,2874,2876],{"className":2875},[653],[569,2877,2880],{"className":2878,"style":2879},[657],"height:0.8019em;",[569,2881,2883,2886],{"style":2882},"top:-3.113em;margin-right:0.05em;",[569,2884],{"className":2885,"style":666},[665],[569,2887,2889],{"className":2888},[670,671,672,673],[569,2890,2892],{"className":2891},[636,673],[569,2893,1344],{"className":2894},[636,673],[569,2896,811],{"className":2897},[836],[569,2899,565],{"className":2900},[636,640],[569,2902,816],{"className":2903},[843],[569,2905],{"className":2906,"style":1070},[698],[569,2908,987],{"className":2909},[1074],[569,2911],{"className":2912,"style":1070},[698],[569,2914,2916,2920,2986,2989,2992],{"className":2915},[627],[569,2917],{"className":2918,"style":2919},[631],"height:2.2019em;vertical-align:-0.8804em;",[569,2921,2923,2926,2983],{"className":2922},[636],[569,2924],{"className":2925},[836,1561],[569,2927,2929],{"className":2928},[1471],[569,2930,2932,2974],{"className":2931},[648,649],[569,2933,2935,2971],{"className":2934},[653],[569,2936,2939,2951,2959],{"className":2937,"style":2938},[657],"height:1.3214em;",[569,2940,2942,2945],{"style":2941},"top:-2.314em;",[569,2943],{"className":2944,"style":1510},[665],[569,2946,2948],{"className":2947},[636],[569,2949,565],{"className":2950},[636,640],[569,2952,2953,2956],{"style":1592},[569,2954],{"className":2955,"style":1510},[665],[569,2957],{"className":2958,"style":1600},[1599],[569,2960,2962,2965],{"style":2961},"top:-3.677em;",[569,2963],{"className":2964,"style":1510},[665],[569,2966,2968],{"className":2967},[636],[569,2969,2575],{"className":2970},[636],[569,2972,681],{"className":2973},[680],[569,2975,2977],{"className":2976},[653],[569,2978,2981],{"className":2979,"style":2980},[657],"height:0.8804em;",[569,2982],{},[569,2984],{"className":2985},[843,1561],[569,2987],{"className":2988,"style":2414},[698],[569,2990,2135],{"className":2991},[2418],[569,2993],{"className":2994,"style":2414},[698],[569,2996,2998,3001,3075,3078,3081],{"className":2997},[627],[569,2999],{"className":3000,"style":2919},[631],[569,3002,3004,3007,3072],{"className":3003},[636],[569,3005],{"className":3006},[836,1561],[569,3008,3010],{"className":3009},[1471],[569,3011,3013,3064],{"className":3012},[648,649],[569,3014,3016,3061],{"className":3015},[653],[569,3017,3019,3042,3050],{"className":3018,"style":2938},[657],[569,3020,3021,3024],{"style":2941},[569,3022],{"className":3023,"style":1510},[665],[569,3025,3027,3030,3033,3036,3039],{"className":3026},[636],[569,3028,597],{"className":3029},[636],[569,3031],{"className":3032,"style":2414},[698],[569,3034,2135],{"className":3035},[2418],[569,3037],{"className":3038,"style":2414},[698],[569,3040,565],{"className":3041},[636,640],[569,3043,3044,3047],{"style":1592},[569,3045],{"className":3046,"style":1510},[665],[569,3048],{"className":3049,"style":1600},[1599],[569,3051,3052,3055],{"style":2961},[569,3053],{"className":3054,"style":1510},[665],[569,3056,3058],{"className":3057},[636],[569,3059,2645],{"className":3060},[636],[569,3062,681],{"className":3063},[680],[569,3065,3067],{"className":3066},[653],[569,3068,3070],{"className":3069,"style":2980},[657],[569,3071],{},[569,3073],{"className":3074},[843,1561],[569,3076],{"className":3077,"style":1070},[698],[569,3079,987],{"className":3080},[1074],[569,3082],{"className":3083,"style":1070},[698],[569,3085,3087,3090,3093,3097,3100,3103,3106],{"className":3086},[627],[569,3088],{"className":3089,"style":1427},[631],[569,3091,1355],{"className":3092},[636],[569,3094],{"className":3095,"style":3096},[698],"margin-right:1em;",[569,3098],{"className":3099,"style":1070},[698],[569,3101,2826],{"className":3102},[1074],[569,3104],{"className":3105,"style":3096},[698],[569,3107],{"className":3108,"style":1070},[698],[569,3110,3112,3115,3157,3160,3163],{"className":3111},[627],[569,3113],{"className":3114,"style":1490},[631],[569,3116,3118],{"className":3117},[636,1494],[569,3119,3121,3149],{"className":3120},[648,649],[569,3122,3124,3146],{"className":3123},[653],[569,3125,3127,3135],{"className":3126,"style":782},[657],[569,3128,3129,3132],{"style":1506},[569,3130],{"className":3131,"style":1510},[665],[569,3133,565],{"className":3134},[636,640],[569,3136,3137,3140],{"style":1506},[569,3138],{"className":3139,"style":1510},[665],[569,3141,3143],{"className":3142,"style":1523},[1522],[569,3144,1467],{"className":3145},[636],[569,3147,681],{"className":3148},[680],[569,3150,3152],{"className":3151},[653],[569,3153,3155],{"className":3154,"style":1536},[657],[569,3156],{},[569,3158],{"className":3159,"style":1070},[698],[569,3161,987],{"className":3162},[1074],[569,3164],{"className":3165,"style":1070},[698],[569,3167,3169,3173,3236,3239,3242],{"className":3168},[627],[569,3170],{"className":3171,"style":3172},[631],"height:2.0074em;vertical-align:-0.686em;",[569,3174,3176,3179,3233],{"className":3175},[636],[569,3177],{"className":3178},[836,1561],[569,3180,3182],{"className":3181},[1471],[569,3183,3185,3224],{"className":3184},[648,649],[569,3186,3188,3221],{"className":3187},[653],[569,3189,3191,3202,3210],{"className":3190,"style":2938},[657],[569,3192,3193,3196],{"style":2941},[569,3194],{"className":3195,"style":1510},[665],[569,3197,3199],{"className":3198},[636],[569,3200,2521],{"className":3201},[636],[569,3203,3204,3207],{"style":1592},[569,3205],{"className":3206,"style":1510},[665],[569,3208],{"className":3209,"style":1600},[1599],[569,3211,3212,3215],{"style":2961},[569,3213],{"className":3214,"style":1510},[665],[569,3216,3218],{"className":3217},[636],[569,3219,2575],{"className":3220},[636],[569,3222,681],{"className":3223},[680],[569,3225,3227],{"className":3226},[653],[569,3228,3231],{"className":3229,"style":3230},[657],"height:0.686em;",[569,3232],{},[569,3234],{"className":3235},[843,1561],[569,3237],{"className":3238,"style":1070},[698],[569,3240,987],{"className":3241},[1074],[569,3243],{"className":3244,"style":1070},[698],[569,3246,3248,3252,3255,3261],{"className":3247},[627],[569,3249],{"className":3250,"style":3251},[631],"height:0.8389em;vertical-align:-0.1944em;",[569,3253,1355],{"className":3254},[636],[569,3256,3258],{"className":3257},[636],[569,3259,602],{"className":3260},[694],[569,3262,3264],{"className":3263},[636],"35",[565,3266,3267,3268,3546],{},"Probe: ",[569,3269,3271,3310],{"className":3270},[572],[569,3272,3274],{"className":3273},[576],[578,3275,3276],{"xmlns":580},[582,3277,3278,3307],{},[585,3279,3280,3286,3288,3295,3297,3299,3301,3303,3305],{},[1471,3281,3282,3284],{},[595,3283,2575],{},[595,3285,2847],{},[599,3287,2135],{},[1471,3289,3290,3292],{},[595,3291,2645],{},[595,3293,3294],{},"0,65",[599,3296,987],{},[595,3298,2521],{},[599,3300,2135],{},[595,3302,2521],{},[599,3304,987],{},[595,3306,1355],{},[616,3308,3309],{"encoding":618},"\\frac{7}{0{,}35} - \\frac{13}{0{,}65} = 20 - 20 = 0",[569,3311,3313,3407,3500,3519,3537],{"className":3312,"ariaHidden":601},[623],[569,3314,3316,3320,3398,3401,3404],{"className":3315},[627],[569,3317],{"className":3318,"style":3319},[631],"height:1.3262em;vertical-align:-0.4811em;",[569,3321,3323,3326,3395],{"className":3322},[636],[569,3324],{"className":3325},[836,1561],[569,3327,3329],{"className":3328},[1471],[569,3330,3332,3386],{"className":3331},[648,649],[569,3333,3335,3383],{"className":3334},[653],[569,3336,3338,3361,3369],{"className":3337,"style":1868},[657],[569,3339,3340,3343],{"style":1577},[569,3341],{"className":3342,"style":1510},[665],[569,3344,3346],{"className":3345},[670,671,672,673],[569,3347,3349,3352,3358],{"className":3348},[636,673],[569,3350,1355],{"className":3351},[636,673],[569,3353,3355],{"className":3354},[636,673],[569,3356,602],{"className":3357},[694,673],[569,3359,3264],{"className":3360},[636,673],[569,3362,3363,3366],{"style":1592},[569,3364],{"className":3365,"style":1510},[665],[569,3367],{"className":3368,"style":1600},[1599],[569,3370,3371,3374],{"style":1603},[569,3372],{"className":3373,"style":1510},[665],[569,3375,3377],{"className":3376},[670,671,672,673],[569,3378,3380],{"className":3379},[636,673],[569,3381,2575],{"className":3382},[636,673],[569,3384,681],{"className":3385},[680],[569,3387,3389],{"className":3388},[653],[569,3390,3393],{"className":3391,"style":3392},[657],"height:0.4811em;",[569,3394],{},[569,3396],{"className":3397},[843,1561],[569,3399],{"className":3400,"style":2414},[698],[569,3402,2135],{"className":3403},[2418],[569,3405],{"className":3406,"style":2414},[698],[569,3408,3410,3413,3491,3494,3497],{"className":3409},[627],[569,3411],{"className":3412,"style":3319},[631],[569,3414,3416,3419,3488],{"className":3415},[636],[569,3417],{"className":3418},[836,1561],[569,3420,3422],{"className":3421},[1471],[569,3423,3425,3480],{"className":3424},[648,649],[569,3426,3428,3477],{"className":3427},[653],[569,3429,3431,3455,3463],{"className":3430,"style":1868},[657],[569,3432,3433,3436],{"style":1577},[569,3434],{"className":3435,"style":1510},[665],[569,3437,3439],{"className":3438},[670,671,672,673],[569,3440,3442,3445,3451],{"className":3441},[636,673],[569,3443,1355],{"className":3444},[636,673],[569,3446,3448],{"className":3447},[636,673],[569,3449,602],{"className":3450},[694,673],[569,3452,3454],{"className":3453},[636,673],"65",[569,3456,3457,3460],{"style":1592},[569,3458],{"className":3459,"style":1510},[665],[569,3461],{"className":3462,"style":1600},[1599],[569,3464,3465,3468],{"style":1603},[569,3466],{"className":3467,"style":1510},[665],[569,3469,3471],{"className":3470},[670,671,672,673],[569,3472,3474],{"className":3473},[636,673],[569,3475,2645],{"className":3476},[636,673],[569,3478,681],{"className":3479},[680],[569,3481,3483],{"className":3482},[653],[569,3484,3486],{"className":3485,"style":3392},[657],[569,3487],{},[569,3489],{"className":3490},[843,1561],[569,3492],{"className":3493,"style":1070},[698],[569,3495,987],{"className":3496},[1074],[569,3498],{"className":3499,"style":1070},[698],[569,3501,3503,3507,3510,3513,3516],{"className":3502},[627],[569,3504],{"className":3505,"style":3506},[631],"height:0.7278em;vertical-align:-0.0833em;",[569,3508,2521],{"className":3509},[636],[569,3511],{"className":3512,"style":2414},[698],[569,3514,2135],{"className":3515},[2418],[569,3517],{"className":3518,"style":2414},[698],[569,3520,3522,3525,3528,3531,3534],{"className":3521},[627],[569,3523],{"className":3524,"style":1427},[631],[569,3526,2521],{"className":3527},[636],[569,3529],{"className":3530,"style":1070},[698],[569,3532,987],{"className":3533},[1074],[569,3535],{"className":3536,"style":1070},[698],[569,3538,3540,3543],{"className":3539},[627],[569,3541],{"className":3542,"style":1427},[631],[569,3544,1355],{"className":3545},[636],".",[565,3548,3549,3550,2078,3578,3607,3608,3637,3638,3823],{},"Drei Bauteile halten ",[569,3551,3553,3566],{"className":3552},[572],[569,3554,3556],{"className":3555},[576],[578,3557,3558],{"xmlns":580},[582,3559,3560,3564],{},[585,3561,3562],{},[595,3563,2102],{},[616,3565,2102],{"encoding":618},[569,3567,3569],{"className":3568,"ariaHidden":601},[623],[569,3570,3572,3575],{"className":3571},[627],[569,3573],{"className":3574,"style":1427},[631],[569,3576,2102],{"className":3577},[636],[569,3579,3581,3595],{"className":3580},[572],[569,3582,3584],{"className":3583},[576],[578,3585,3586],{"xmlns":580},[582,3587,3588,3593],{},[585,3589,3590],{},[595,3591,3592],{},"5",[616,3594,3592],{"encoding":618},[569,3596,3598],{"className":3597,"ariaHidden":601},[623],[569,3599,3601,3604],{"className":3600},[627],[569,3602],{"className":3603,"style":1427},[631],[569,3605,3592],{"className":3606},[636]," und ",[569,3609,3611,3625],{"className":3610},[572],[569,3612,3614],{"className":3613},[576],[578,3615,3616],{"xmlns":580},[582,3617,3618,3623],{},[585,3619,3620],{},[595,3621,3622],{},"8",[616,3624,3622],{"encoding":618},[569,3626,3628],{"className":3627,"ariaHidden":601},[623],[569,3629,3631,3634],{"className":3630},[627],[569,3632],{"className":3633,"style":1427},[631],[569,3635,3622],{"className":3636},[636]," Jahre, angenommen wird eine Exponentialverteilung. Dann ist ",[569,3639,3641,3693],{"className":3640},[572],[569,3642,3644],{"className":3643},[576],[578,3645,3646],{"xmlns":580},[582,3647,3648,3690],{},[585,3649,3650,3652,3654,3656,3658,3660,3663,3665,3667,3669,3671,3673,3676,3678,3680,3682,3684,3686,3688],{},[591,3651,978],{"mathvariant":977},[599,3653,811],{"stretchy":810},[591,3655,1652],{},[599,3657,816],{"stretchy":810},[599,3659,987],{},[595,3661,3662],{},"3",[591,3664,990],{},[599,3666,993],{},[591,3668,1652],{},[599,3670,2135],{},[591,3672,1652],{},[599,3674,3675],{},"⋅",[599,3677,811],{"stretchy":810},[595,3679,2102],{},[599,3681,2642],{},[595,3683,3592],{},[599,3685,2642],{},[595,3687,3622],{},[599,3689,816],{"stretchy":810},[616,3691,3692],{"encoding":618},"\\ell(\\lambda) = 3 \\ln \\lambda - \\lambda \\cdot (2 + 5 + 8)",[569,3694,3696,3723,3754,3772,3793,3811],{"className":3695,"ariaHidden":601},[623],[569,3697,3699,3702,3705,3708,3711,3714,3717,3720],{"className":3698},[627],[569,3700],{"className":3701,"style":829},[631],[569,3703,978],{"className":3704},[636],[569,3706,811],{"className":3707},[836],[569,3709,1652],{"className":3710},[636,640],[569,3712,816],{"className":3713},[843],[569,3715],{"className":3716,"style":1070},[698],[569,3718,987],{"className":3719},[1074],[569,3721],{"className":3722,"style":1070},[698],[569,3724,3726,3730,3733,3736,3739,3742,3745,3748,3751],{"className":3725},[627],[569,3727],{"className":3728,"style":3729},[631],"height:0.7778em;vertical-align:-0.0833em;",[569,3731,3662],{"className":3732},[636],[569,3734],{"className":3735,"style":699},[698],[569,3737,990],{"className":3738},[1087],[569,3740],{"className":3741,"style":699},[698],[569,3743,1652],{"className":3744},[636,640],[569,3746],{"className":3747,"style":2414},[698],[569,3749,2135],{"className":3750},[2418],[569,3752],{"className":3753,"style":2414},[698],[569,3755,3757,3760,3763,3766,3769],{"className":3756},[627],[569,3758],{"className":3759,"style":782},[631],[569,3761,1652],{"className":3762},[636,640],[569,3764],{"className":3765,"style":2414},[698],[569,3767,3675],{"className":3768},[2418],[569,3770],{"className":3771,"style":2414},[698],[569,3773,3775,3778,3781,3784,3787,3790],{"className":3774},[627],[569,3776],{"className":3777,"style":829},[631],[569,3779,811],{"className":3780},[836],[569,3782,2102],{"className":3783},[636],[569,3785],{"className":3786,"style":2414},[698],[569,3788,2642],{"className":3789},[2418],[569,3791],{"className":3792,"style":2414},[698],[569,3794,3796,3799,3802,3805,3808],{"className":3795},[627],[569,3797],{"className":3798,"style":3506},[631],[569,3800,3592],{"className":3801},[636],[569,3803],{"className":3804,"style":2414},[698],[569,3806,2642],{"className":3807},[2418],[569,3809],{"className":3810,"style":2414},[698],[569,3812,3814,3817,3820],{"className":3813},[627],[569,3815],{"className":3816,"style":829},[631],[569,3818,3622],{"className":3819},[636],[569,3821,816],{"className":3822},[843]," und",[569,3825,3827],{"className":3826},[2769],[569,3828,3830,3896],{"className":3829},[572],[569,3831,3833],{"className":3832},[576],[578,3834,3835],{"xmlns":580,"display":2778},[582,3836,3837,3893],{},[585,3838,3839,3845,3847,3849,3851,3853,3859,3861,3864,3866,3868,3870,3872,3874,3880,3882,3888,3890],{},[1337,3840,3841,3843],{},[591,3842,978],{"mathvariant":977},[599,3844,1344],{"mathvariant":977,"lspace":1343,"rspace":1343},[599,3846,811],{"stretchy":810},[591,3848,1652],{},[599,3850,816],{"stretchy":810},[599,3852,987],{},[1471,3854,3855,3857],{},[595,3856,3662],{},[591,3858,1652],{},[599,3860,2135],{},[595,3862,3863],{},"15",[599,3865,987],{},[595,3867,1355],{},[698,3869],{"width":2823},[599,3871,2826],{},[698,3873],{"width":2823},[1461,3875,3876,3878],{"accent":601},[591,3877,1652],{},[599,3879,1467],{},[599,3881,987],{},[1471,3883,3884,3886],{},[595,3885,597],{},[595,3887,3592],{},[599,3889,987],{},[595,3891,3892],{},"0,2",[616,3894,3895],{"encoding":618},"\\ell'(\\lambda) = \\frac{3}{\\lambda} - 15 = 0 \\quad \\Rightarrow \\quad \\hat{\\lambda} = \\frac{1}{5} = 0{,}2",[569,3897,3899,3955,4032,4050,4074,4120,4197],{"className":3898,"ariaHidden":601},[623],[569,3900,3902,3905,3937,3940,3943,3946,3949,3952],{"className":3901},[627],[569,3903],{"className":3904,"style":2860},[631],[569,3906,3908,3911],{"className":3907},[636],[569,3909,978],{"className":3910},[636],[569,3912,3914],{"className":3913},[644],[569,3915,3917],{"className":3916},[648],[569,3918,3920],{"className":3919},[653],[569,3921,3923],{"className":3922,"style":2879},[657],[569,3924,3925,3928],{"style":2882},[569,3926],{"className":3927,"style":666},[665],[569,3929,3931],{"className":3930},[670,671,672,673],[569,3932,3934],{"className":3933},[636,673],[569,3935,1344],{"className":3936},[636,673],[569,3938,811],{"className":3939},[836],[569,3941,1652],{"className":3942},[636,640],[569,3944,816],{"className":3945},[843],[569,3947],{"className":3948,"style":1070},[698],[569,3950,987],{"className":3951},[1074],[569,3953],{"className":3954,"style":1070},[698],[569,3956,3958,3961,4023,4026,4029],{"className":3957},[627],[569,3959],{"className":3960,"style":3172},[631],[569,3962,3964,3967,4020],{"className":3963},[636],[569,3965],{"className":3966},[836,1561],[569,3968,3970],{"className":3969},[1471],[569,3971,3973,4012],{"className":3972},[648,649],[569,3974,3976,4009],{"className":3975},[653],[569,3977,3979,3990,3998],{"className":3978,"style":2938},[657],[569,3980,3981,3984],{"style":2941},[569,3982],{"className":3983,"style":1510},[665],[569,3985,3987],{"className":3986},[636],[569,3988,1652],{"className":3989},[636,640],[569,3991,3992,3995],{"style":1592},[569,3993],{"className":3994,"style":1510},[665],[569,3996],{"className":3997,"style":1600},[1599],[569,3999,4000,4003],{"style":2961},[569,4001],{"className":4002,"style":1510},[665],[569,4004,4006],{"className":4005},[636],[569,4007,3662],{"className":4008},[636],[569,4010,681],{"className":4011},[680],[569,4013,4015],{"className":4014},[653],[569,4016,4018],{"className":4017,"style":3230},[657],[569,4019],{},[569,4021],{"className":4022},[843,1561],[569,4024],{"className":4025,"style":2414},[698],[569,4027,2135],{"className":4028},[2418],[569,4030],{"className":4031,"style":2414},[698],[569,4033,4035,4038,4041,4044,4047],{"className":4034},[627],[569,4036],{"className":4037,"style":1427},[631],[569,4039,3863],{"className":4040},[636],[569,4042],{"className":4043,"style":1070},[698],[569,4045,987],{"className":4046},[1074],[569,4048],{"className":4049,"style":1070},[698],[569,4051,4053,4056,4059,4062,4065,4068,4071],{"className":4052},[627],[569,4054],{"className":4055,"style":1427},[631],[569,4057,1355],{"className":4058},[636],[569,4060],{"className":4061,"style":3096},[698],[569,4063],{"className":4064,"style":1070},[698],[569,4066,2826],{"className":4067},[1074],[569,4069],{"className":4070,"style":3096},[698],[569,4072],{"className":4073,"style":1070},[698],[569,4075,4077,4080,4111,4114,4117],{"className":4076},[627],[569,4078],{"className":4079,"style":1676},[631],[569,4081,4083],{"className":4082},[636,1494],[569,4084,4086],{"className":4085},[648],[569,4087,4089],{"className":4088},[653],[569,4090,4092,4100],{"className":4091,"style":1676},[657],[569,4093,4094,4097],{"style":1506},[569,4095],{"className":4096,"style":1510},[665],[569,4098,1652],{"className":4099},[636,640],[569,4101,4102,4105],{"style":1699},[569,4103],{"className":4104,"style":1510},[665],[569,4106,4108],{"className":4107,"style":1706},[1522],[569,4109,1467],{"className":4110},[636],[569,4112],{"className":4113,"style":1070},[698],[569,4115,987],{"className":4116},[1074],[569,4118],{"className":4119,"style":1070},[698],[569,4121,4123,4126,4188,4191,4194],{"className":4122},[627],[569,4124],{"className":4125,"style":3172},[631],[569,4127,4129,4132,4185],{"className":4128},[636],[569,4130],{"className":4131},[836,1561],[569,4133,4135],{"className":4134},[1471],[569,4136,4138,4177],{"className":4137},[648,649],[569,4139,4141,4174],{"className":4140},[653],[569,4142,4144,4155,4163],{"className":4143,"style":2938},[657],[569,4145,4146,4149],{"style":2941},[569,4147],{"className":4148,"style":1510},[665],[569,4150,4152],{"className":4151},[636],[569,4153,3592],{"className":4154},[636],[569,4156,4157,4160],{"style":1592},[569,4158],{"className":4159,"style":1510},[665],[569,4161],{"className":4162,"style":1600},[1599],[569,4164,4165,4168],{"style":2961},[569,4166],{"className":4167,"style":1510},[665],[569,4169,4171],{"className":4170},[636],[569,4172,597],{"className":4173},[636],[569,4175,681],{"className":4176},[680],[569,4178,4180],{"className":4179},[653],[569,4181,4183],{"className":4182,"style":3230},[657],[569,4184],{},[569,4186],{"className":4187},[843,1561],[569,4189],{"className":4190,"style":1070},[698],[569,4192,987],{"className":4193},[1074],[569,4195],{"className":4196,"style":1070},[698],[569,4198,4200,4203,4206,4212],{"className":4199},[627],[569,4201],{"className":4202,"style":3251},[631],[569,4204,1355],{"className":4205},[636],[569,4207,4209],{"className":4208},[636],[569,4210,602],{"className":4211},[694],[569,4213,2102],{"className":4214},[636],[565,4216,4217,4218,3607,4312,4540,4541,4662],{},"Unter Normalverteilungsannahme ergäben dieselben Daten ",[569,4219,4221,4243],{"className":4220},[572],[569,4222,4224],{"className":4223},[576],[578,4225,4226],{"xmlns":580},[582,4227,4228,4240],{},[585,4229,4230,4236,4238],{},[1461,4231,4232,4234],{"accent":601},[591,4233,1967],{},[599,4235,1467],{},[599,4237,987],{},[595,4239,3592],{},[616,4241,4242],{"encoding":618},"\\hat{\\mu} = 5",[569,4244,4246,4303],{"className":4245,"ariaHidden":601},[623],[569,4247,4249,4252,4294,4297,4300],{"className":4248},[627],[569,4250],{"className":4251,"style":1490},[631],[569,4253,4255],{"className":4254},[636,1494],[569,4256,4258,4286],{"className":4257},[648,649],[569,4259,4261,4283],{"className":4260},[653],[569,4262,4264,4272],{"className":4263,"style":782},[657],[569,4265,4266,4269],{"style":1506},[569,4267],{"className":4268,"style":1510},[665],[569,4270,1967],{"className":4271},[636,640],[569,4273,4274,4277],{"style":1506},[569,4275],{"className":4276,"style":1510},[665],[569,4278,4280],{"className":4279,"style":1754},[1522],[569,4281,1467],{"className":4282},[636],[569,4284,681],{"className":4285},[680],[569,4287,4289],{"className":4288},[653],[569,4290,4292],{"className":4291,"style":1536},[657],[569,4293],{},[569,4295],{"className":4296,"style":1070},[698],[569,4298,987],{"className":4299},[1074],[569,4301],{"className":4302,"style":1070},[698],[569,4304,4306,4309],{"className":4305},[627],[569,4307],{"className":4308,"style":1427},[631],[569,4310,3592],{"className":4311},[636],[569,4313,4315,4361],{"className":4314},[572],[569,4316,4318],{"className":4317},[576],[578,4319,4320],{"xmlns":580},[582,4321,4322,4358],{},[585,4323,4324,4334,4336,4353,4355],{},[1337,4325,4326,4332],{},[1461,4327,4328,4330],{"accent":601},[591,4329,2097],{},[599,4331,1467],{},[595,4333,2102],{},[599,4335,987],{},[1471,4337,4338,4351],{},[585,4339,4340,4343,4345,4347,4349],{},[595,4341,4342],{},"9",[599,4344,2642],{},[595,4346,1355],{},[599,4348,2642],{},[595,4350,4342],{},[595,4352,3662],{},[599,4354,987],{},[595,4356,4357],{},"6",[616,4359,4360],{"encoding":618},"\\hat{\\sigma}^2 = \\frac{9 + 0 + 9}{3} = 6",[569,4362,4364,4436,4531],{"className":4363,"ariaHidden":601},[623],[569,4365,4367,4370,4427,4430,4433],{"className":4366},[627],[569,4368],{"className":4369,"style":2160},[631],[569,4371,4373,4404],{"className":4372},[636],[569,4374,4376],{"className":4375},[636,1494],[569,4377,4379],{"className":4378},[648],[569,4380,4382],{"className":4381},[653],[569,4383,4385,4393],{"className":4384,"style":782},[657],[569,4386,4387,4390],{"style":1506},[569,4388],{"className":4389,"style":1510},[665],[569,4391,2097],{"className":4392,"style":2184},[636,640],[569,4394,4395,4398],{"style":1506},[569,4396],{"className":4397,"style":1510},[665],[569,4399,4401],{"className":4400,"style":1706},[1522],[569,4402,1467],{"className":4403},[636],[569,4405,4407],{"className":4406},[644],[569,4408,4410],{"className":4409},[648],[569,4411,4413],{"className":4412},[653],[569,4414,4416],{"className":4415,"style":2160},[657],[569,4417,4418,4421],{"style":1390},[569,4419],{"className":4420,"style":666},[665],[569,4422,4424],{"className":4423},[670,671,672,673],[569,4425,2102],{"className":4426},[636,673],[569,4428],{"className":4429,"style":1070},[698],[569,4431,987],{"className":4432},[1074],[569,4434],{"className":4435,"style":1070},[698],[569,4437,4439,4442,4522,4525,4528],{"className":4438},[627],[569,4440],{"className":4441,"style":1849},[631],[569,4443,4445,4448,4519],{"className":4444},[636],[569,4446],{"className":4447},[836,1561],[569,4449,4451],{"className":4450},[1471],[569,4452,4454,4511],{"className":4453},[648,649],[569,4455,4457,4508],{"className":4456},[653],[569,4458,4460,4474,4482],{"className":4459,"style":1868},[657],[569,4461,4462,4465],{"style":1577},[569,4463],{"className":4464,"style":1510},[665],[569,4466,4468],{"className":4467},[670,671,672,673],[569,4469,4471],{"className":4470},[636,673],[569,4472,3662],{"className":4473},[636,673],[569,4475,4476,4479],{"style":1592},[569,4477],{"className":4478,"style":1510},[665],[569,4480],{"className":4481,"style":1600},[1599],[569,4483,4484,4487],{"style":1603},[569,4485],{"className":4486,"style":1510},[665],[569,4488,4490],{"className":4489},[670,671,672,673],[569,4491,4493,4496,4499,4502,4505],{"className":4492},[636,673],[569,4494,4342],{"className":4495},[636,673],[569,4497,2642],{"className":4498},[2418,673],[569,4500,1355],{"className":4501},[636,673],[569,4503,2642],{"className":4504},[2418,673],[569,4506,4342],{"className":4507},[636,673],[569,4509,681],{"className":4510},[680],[569,4512,4514],{"className":4513},[653],[569,4515,4517],{"className":4516,"style":1626},[657],[569,4518],{},[569,4520],{"className":4521},[843,1561],[569,4523],{"className":4524,"style":1070},[698],[569,4526,987],{"className":4527},[1074],[569,4529],{"className":4530,"style":1070},[698],[569,4532,4534,4537],{"className":4533},[627],[569,4535],{"className":4536,"style":1427},[631],[569,4538,4357],{"className":4539},[636],", während die korrigierte Stichprobenvarianz ",[569,4542,4544,4567],{"className":4543},[572],[569,4545,4547],{"className":4546},[576],[578,4548,4549],{"xmlns":580},[582,4550,4551,4564],{},[585,4552,4553,4560,4562],{},[1471,4554,4555,4558],{},[595,4556,4557],{},"18",[595,4559,2102],{},[599,4561,987],{},[595,4563,4342],{},[616,4565,4566],{"encoding":618},"\\frac{18}{2} = 9",[569,4568,4570,4653],{"className":4569,"ariaHidden":601},[623],[569,4571,4573,4576,4644,4647,4650],{"className":4572},[627],[569,4574],{"className":4575,"style":1849},[631],[569,4577,4579,4582,4641],{"className":4578},[636],[569,4580],{"className":4581},[836,1561],[569,4583,4585],{"className":4584},[1471],[569,4586,4588,4633],{"className":4587},[648,649],[569,4589,4591,4630],{"className":4590},[653],[569,4592,4594,4608,4616],{"className":4593,"style":1868},[657],[569,4595,4596,4599],{"style":1577},[569,4597],{"className":4598,"style":1510},[665],[569,4600,4602],{"className":4601},[670,671,672,673],[569,4603,4605],{"className":4604},[636,673],[569,4606,2102],{"className":4607},[636,673],[569,4609,4610,4613],{"style":1592},[569,4611],{"className":4612,"style":1510},[665],[569,4614],{"className":4615,"style":1600},[1599],[569,4617,4618,4621],{"style":1603},[569,4619],{"className":4620,"style":1510},[665],[569,4622,4624],{"className":4623},[670,671,672,673],[569,4625,4627],{"className":4626},[636,673],[569,4628,4557],{"className":4629},[636,673],[569,4631,681],{"className":4632},[680],[569,4634,4636],{"className":4635},[653],[569,4637,4639],{"className":4638,"style":1626},[657],[569,4640],{},[569,4642],{"className":4643},[843,1561],[569,4645],{"className":4646,"style":1070},[698],[569,4648,987],{"className":4649},[1074],[569,4651],{"className":4652,"style":1070},[698],[569,4654,4656,4659],{"className":4655},[627],[569,4657],{"className":4658,"style":1427},[631],[569,4660,4342],{"className":4661},[636]," ist.",[560,4664,4666],{"id":4665},"typische-fehler","Typische Fehler",[1443,4668,4669,4773,5016,5200],{},[914,4670,4671,4672,4700,4701,4744,4745,3546],{},"Die Likelihood als Wahrscheinlichkeit für ",[569,4673,4675,4688],{"className":4674},[572],[569,4676,4678],{"className":4677},[576],[578,4679,4680],{"xmlns":580},[582,4681,4682,4686],{},[585,4683,4684],{},[591,4685,769],{},[616,4687,772],{"encoding":618},[569,4689,4691],{"className":4690,"ariaHidden":601},[623],[569,4692,4694,4697],{"className":4693},[627],[569,4695],{"className":4696,"style":782},[631],[569,4698,769],{"className":4699,"style":786},[636,640]," lesen. ",[569,4702,4704,4723],{"className":4703},[572],[569,4705,4707],{"className":4706},[576],[578,4708,4709],{"xmlns":580},[582,4710,4711,4721],{},[585,4712,4713,4715,4717,4719],{},[591,4714,807],{},[599,4716,811],{"stretchy":810},[591,4718,769],{},[599,4720,816],{"stretchy":810},[616,4722,819],{"encoding":618},[569,4724,4726],{"className":4725,"ariaHidden":601},[623],[569,4727,4729,4732,4735,4738,4741],{"className":4728},[627],[569,4730],{"className":4731,"style":829},[631],[569,4733,807],{"className":4734},[636,640],[569,4736,811],{"className":4737},[836],[569,4739,769],{"className":4740,"style":786},[636,640],[569,4742,816],{"className":4743},[843]," ist eine Funktion des Parameters, aber keine Verteilung über ",[569,4746,4748,4761],{"className":4747},[572],[569,4749,4751],{"className":4750},[576],[578,4752,4753],{"xmlns":580},[582,4754,4755,4759],{},[585,4756,4757],{},[591,4758,769],{},[616,4760,772],{"encoding":618},[569,4762,4764],{"className":4763,"ariaHidden":601},[623],[569,4765,4767,4770],{"className":4766},[627],[569,4768],{"className":4769,"style":782},[631],[569,4771,769],{"className":4772,"style":786},[636,640],[914,4774,4775,4776,4934,4935,3546],{},"Nach dem Logarithmieren Produkte falsch in Summen umwandeln, z.B. ",[569,4777,4779,4828],{"className":4778},[572],[569,4780,4782],{"className":4781},[576],[578,4783,4784],{"xmlns":580},[582,4785,4786,4825],{},[585,4787,4788,4790,4792,4794,4796,4809,4811,4813,4815,4817,4819,4821,4823],{},[591,4789,990],{},[599,4791,993],{},[599,4793,811],{"stretchy":810},[591,4795,1652],{},[1337,4797,4798,4801],{},[591,4799,4800],{},"e",[585,4802,4803,4805,4807],{},[599,4804,2135],{},[591,4806,1652],{},[591,4808,593],{},[599,4810,816],{"stretchy":810},[599,4812,987],{},[591,4814,990],{},[599,4816,993],{},[591,4818,1652],{},[599,4820,2135],{},[591,4822,1652],{},[591,4824,593],{},[616,4826,4827],{"encoding":618},"\\ln(\\lambda e^{-\\lambda x}) = \\ln \\lambda - \\lambda x",[569,4829,4831,4898,4922],{"className":4830,"ariaHidden":601},[623],[569,4832,4834,4838,4841,4844,4847,4886,4889,4892,4895],{"className":4833},[627],[569,4835],{"className":4836,"style":4837},[631],"height:1.0991em;vertical-align:-0.25em;",[569,4839,990],{"className":4840},[1087],[569,4842,811],{"className":4843},[836],[569,4845,1652],{"className":4846},[636,640],[569,4848,4850,4853],{"className":4849},[636],[569,4851,4800],{"className":4852},[636,640],[569,4854,4856],{"className":4855},[644],[569,4857,4859],{"className":4858},[648],[569,4860,4862],{"className":4861},[653],[569,4863,4866],{"className":4864,"style":4865},[657],"height:0.8491em;",[569,4867,4868,4871],{"style":1390},[569,4869],{"className":4870,"style":666},[665],[569,4872,4874],{"className":4873},[670,671,672,673],[569,4875,4877,4880,4883],{"className":4876},[636,673],[569,4878,2135],{"className":4879},[636,673],[569,4881,1652],{"className":4882},[636,640,673],[569,4884,593],{"className":4885},[636,640,673],[569,4887,816],{"className":4888},[843],[569,4890],{"className":4891,"style":1070},[698],[569,4893,987],{"className":4894},[1074],[569,4896],{"className":4897,"style":1070},[698],[569,4899,4901,4904,4907,4910,4913,4916,4919],{"className":4900},[627],[569,4902],{"className":4903,"style":3729},[631],[569,4905,990],{"className":4906},[1087],[569,4908],{"className":4909,"style":699},[698],[569,4911,1652],{"className":4912},[636,640],[569,4914],{"className":4915,"style":2414},[698],[569,4917,2135],{"className":4918},[2418],[569,4920],{"className":4921,"style":2414},[698],[569,4923,4925,4928,4931],{"className":4924},[627],[569,4926],{"className":4927,"style":782},[631],[569,4929,1652],{"className":4930},[636,640],[569,4932,593],{"className":4933},[636,640],", nicht ",[569,4936,4938,4968],{"className":4937},[572],[569,4939,4941],{"className":4940},[576],[578,4942,4943],{"xmlns":580},[582,4944,4945,4965],{},[585,4946,4947,4949,4951,4953,4955,4957,4959,4961,4963],{},[591,4948,990],{},[599,4950,993],{},[591,4952,1652],{},[599,4954,3675],{},[599,4956,811],{"stretchy":810},[599,4958,2135],{},[591,4960,1652],{},[591,4962,593],{},[599,4964,816],{"stretchy":810},[616,4966,4967],{"encoding":618},"\\ln \\lambda \\cdot (-\\lambda x)",[569,4969,4971,4995],{"className":4970,"ariaHidden":601},[623],[569,4972,4974,4977,4980,4983,4986,4989,4992],{"className":4973},[627],[569,4975],{"className":4976,"style":782},[631],[569,4978,990],{"className":4979},[1087],[569,4981],{"className":4982,"style":699},[698],[569,4984,1652],{"className":4985},[636,640],[569,4987],{"className":4988,"style":2414},[698],[569,4990,3675],{"className":4991},[2418],[569,4993],{"className":4994,"style":2414},[698],[569,4996,4998,5001,5004,5007,5010,5013],{"className":4997},[627],[569,4999],{"className":5000,"style":829},[631],[569,5002,811],{"className":5003},[836],[569,5005,2135],{"className":5006},[636],[569,5008,1652],{"className":5009},[636,640],[569,5011,593],{"className":5012},[636,640],[569,5014,816],{"className":5015},[843],[914,5017,5018,5019,5110,5111,5139,5140,5199],{},"Annehmen, der ML-Schätzer sei immer erwartungstreu. ",[569,5020,5022,5044],{"className":5021},[572],[569,5023,5025],{"className":5024},[576],[578,5026,5027],{"xmlns":580},[582,5028,5029,5041],{},[585,5030,5031],{},[1337,5032,5033,5039],{},[1461,5034,5035,5037],{"accent":601},[591,5036,2097],{},[599,5038,1467],{},[595,5040,2102],{},[616,5042,5043],{"encoding":618},"\\hat{\\sigma}^2",[569,5045,5047],{"className":5046,"ariaHidden":601},[623],[569,5048,5050,5053],{"className":5049},[627],[569,5051],{"className":5052,"style":2160},[631],[569,5054,5056,5087],{"className":5055},[636],[569,5057,5059],{"className":5058},[636,1494],[569,5060,5062],{"className":5061},[648],[569,5063,5065],{"className":5064},[653],[569,5066,5068,5076],{"className":5067,"style":782},[657],[569,5069,5070,5073],{"style":1506},[569,5071],{"className":5072,"style":1510},[665],[569,5074,2097],{"className":5075,"style":2184},[636,640],[569,5077,5078,5081],{"style":1506},[569,5079],{"className":5080,"style":1510},[665],[569,5082,5084],{"className":5083,"style":1706},[1522],[569,5085,1467],{"className":5086},[636],[569,5088,5090],{"className":5089},[644],[569,5091,5093],{"className":5092},[648],[569,5094,5096],{"className":5095},[653],[569,5097,5099],{"className":5098,"style":2160},[657],[569,5100,5101,5104],{"style":1390},[569,5102],{"className":5103,"style":666},[665],[569,5105,5107],{"className":5106},[670,671,672,673],[569,5108,2102],{"className":5109},[636,673]," mit Nenner ",[569,5112,5114,5127],{"className":5113},[572],[569,5115,5117],{"className":5116},[576],[578,5118,5119],{"xmlns":580},[582,5120,5121,5125],{},[585,5122,5123],{},[591,5124,614],{},[616,5126,614],{"encoding":618},[569,5128,5130],{"className":5129,"ariaHidden":601},[623],[569,5131,5133,5136],{"className":5132},[627],[569,5134],{"className":5135,"style":2534},[631],[569,5137,614],{"className":5138},[636,640]," unterschätzt ",[569,5141,5143,5161],{"className":5142},[572],[569,5144,5146],{"className":5145},[576],[578,5147,5148],{"xmlns":580},[582,5149,5150,5158],{},[585,5151,5152],{},[1337,5153,5154,5156],{},[591,5155,2097],{},[595,5157,2102],{},[616,5159,5160],{"encoding":618},"\\sigma^2",[569,5162,5164],{"className":5163,"ariaHidden":601},[623],[569,5165,5167,5170],{"className":5166},[627],[569,5168],{"className":5169,"style":2160},[631],[569,5171,5173,5176],{"className":5172},[636],[569,5174,2097],{"className":5175,"style":2184},[636,640],[569,5177,5179],{"className":5178},[644],[569,5180,5182],{"className":5181},[648],[569,5183,5185],{"className":5184},[653],[569,5186,5188],{"className":5187,"style":2160},[657],[569,5189,5190,5193],{"style":1390},[569,5191],{"className":5192,"style":666},[665],[569,5194,5196],{"className":5195},[670,671,672,673],[569,5197,2102],{"className":5198},[636,673]," im Mittel.",[914,5201,5202,5203,5254,5255,5317],{},"Die Nullstelle der Ableitung ungeprüft übernehmen. Liegt das Maximum am Rand (z.B. ",[569,5204,5206,5224],{"className":5205},[572],[569,5207,5209],{"className":5208},[576],[578,5210,5211],{"xmlns":580},[582,5212,5213,5221],{},[585,5214,5215,5217,5219],{},[591,5216,1475],{},[599,5218,987],{},[595,5220,1355],{},[616,5222,5223],{"encoding":618},"k = 0",[569,5225,5227,5245],{"className":5226,"ariaHidden":601},[623],[569,5228,5230,5233,5236,5239,5242],{"className":5229},[627],[569,5231],{"className":5232,"style":782},[631],[569,5234,1475],{"className":5235,"style":1616},[636,640],[569,5237],{"className":5238,"style":1070},[698],[569,5240,987],{"className":5241},[1074],[569,5243],{"className":5244,"style":1070},[698],[569,5246,5248,5251],{"className":5247},[627],[569,5249],{"className":5250,"style":1427},[631],[569,5252,1355],{"className":5253},[636],"), hat ",[569,5256,5258,5276],{"className":5257},[572],[569,5259,5261],{"className":5260},[576],[578,5262,5263],{"xmlns":580},[582,5264,5265,5273],{},[585,5266,5267],{},[1337,5268,5269,5271],{},[591,5270,978],{"mathvariant":977},[599,5272,1344],{"mathvariant":977,"lspace":1343,"rspace":1343},[616,5274,5275],{"encoding":618},"\\ell'",[569,5277,5279],{"className":5278,"ariaHidden":601},[623],[569,5280,5282,5285],{"className":5281},[627],[569,5283],{"className":5284,"style":1387},[631],[569,5286,5288,5291],{"className":5287},[636],[569,5289,978],{"className":5290},[636],[569,5292,5294],{"className":5293},[644],[569,5295,5297],{"className":5296},[648],[569,5298,5300],{"className":5299},[653],[569,5301,5303],{"className":5302,"style":1387},[657],[569,5304,5305,5308],{"style":1390},[569,5306],{"className":5307,"style":666},[665],[569,5309,5311],{"className":5310},[670,671,672,673],[569,5312,5314],{"className":5313},[636,673],[569,5315,1344],{"className":5316},[636,673]," keine Nullstelle im Inneren.",{"title":5319,"searchDepth":5320,"depth":5320,"links":5321},"",2,[5322,5323,5324],{"id":562,"depth":5320,"text":563},{"id":2498,"depth":5320,"text":2499},{"id":4665,"depth":5320,"text":4666},[5326,5331,5334,5336,5338,5340,5342,5344],{"lhs":5327,"rhs":1355,"where":5328},"k\u002F(k\u002Fn) - (n - k)\u002F(1 - k\u002Fn)",{"k":5329,"n":5330},7,20,{"lhs":5332,"rhs":5333},"7 \u002F 20","0.35",{"lhs":5335,"rhs":1355},"7\u002F0.35 - 13\u002F0.65",{"lhs":5337,"rhs":597},"sign(min(0.35^7 * 0.65^13 - 0.3^7 * 0.7^13, 0.35^7 * 0.65^13 - 0.4^7 * 0.6^13))",{"lhs":5339,"rhs":3592},"(2 + 5 + 8) \u002F 3",{"lhs":5341,"rhs":1355},"3\u002F0.2 - (2 + 5 + 8)",{"lhs":5343,"rhs":4357},"((2-5)^2 + (5-5)^2 + (8-5)^2) \u002F 3",{"lhs":5345,"rhs":4342},"((2-5)^2 + (5-5)^2 + (8-5)^2) \u002F 2","x_1, \\ldots, x_n \\text{ Realisierungen unabhängiger, identisch verteilter } X_i,\\ \\text{Maximum existiert}","\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>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">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:0em;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=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">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:0em;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> \u003Cspan class=\"katex\">Realisierungen unabhängiger, identisch verteilter\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>X\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X_i,\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:0.3117em;\">\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=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">Maximum existiert\u003C\u002Fspan>",null,"md","maximum-likelihood","\\hat{\\theta} = \\arg\\max_{\\theta} L(\\theta), \\quad L(\\theta) = \\prod_{i=1}^{n} f(x_i; \\theta)","\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>\u003Cmover accent=\"true\">\u003Cmi>θ\u003C\u002Fmi>\u003Cmo>^\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>arg\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmunder>\u003Cmrow>\u003Cmi>max\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>θ\u003C\u002Fmi>\u003C\u002Fmunder>\u003Cmi>L\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>θ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi>L\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>θ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∏\u003C\u002Fmo>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">;\u003C\u002Fmo>\u003Cmi>θ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\hat{\\theta} = \\arg\\max_{\\theta} L(\\theta), \\quad L(\\theta) = \\prod_{i=1}^{n} f(x_i; \\theta)\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:0.9579em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9579em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1667em;\">\u003Cspan class=\"mord\">^\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:1.5021em;vertical-align:-0.7521em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">ar\u003Cspan style=\"margin-right:0.0139em;\">g\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.4306em;\">\u003Cspan style=\"top:-2.3479em;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\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">max\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:0.7521em;\">\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\">L\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">L\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9291em;vertical-align:-1.2777em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">i\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∏\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\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:1.2777em;\">\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:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">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:0em;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=\"mpunct\">;\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmaximum-likelihood-schaetzer",[],[5359,5360,5361,5362],"binomial-distribution","exponential-distribution","derivative-ln","arithmetic-mean",{"title":548,"description":5319},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fmaximum-likelihood-schaetzer","Der Maximum-Likelihood-Schätzer wählt den Parameterwert, unter dem die beobachteten Daten am wahrscheinlichsten sind.",[5367,5368,5369,5370,5371],"parameterschätzung","likelihood-funktion","schätzer","log-likelihood","statistik",[5373,5377,5380,5383,5387,5391],{"symbol":5374,"meaning":5375,"symbolHtml":5376},"\\hat{\\theta}","Maximum-Likelihood-Schätzwert für den Parameter","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover 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class=\"mord\">^\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":772,"meaning":5378,"symbolHtml":5379},"unbekannter Parameter der Verteilung (auch mehrere Parameter)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>θ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\theta\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":819,"meaning":5381,"symbolHtml":5382},"Likelihood-Funktion, Plausibilität des Parameters bei gegebenen Daten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>L\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>θ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">L(\\theta)\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\">L\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord 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class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">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:0em;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=\"mpunct\">;\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">θ\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5388,"meaning":5389,"symbolHtml":5390},"x_i","beobachtete Werte der Stichprobe","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_i\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">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:0em;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\" 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mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","C6Atcpgo9yFArSdRZ1_tjllVTX95A1N1hiGAYC3mNg4",[5396,5399,5402,5405],{"stem":5397,"title":5398,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Fableitung-ln","Ableitung des natürlichen Logarithmus",{"stem":5400,"title":5401,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Farithmetisches-mittel","Arithmetisches Mittel",{"stem":5403,"title":5404,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fbinomialverteilung","Binomialverteilung",{"stem":5406,"title":5407,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fexponentialverteilung","Exponentialverteilung",1793824286454]