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= \\int_{-\\infty}^{\\infty} (x - \\mu)^2 f(x)\\,\\mathrm{d}x = E(X^2) - \\mu^2, \\qquad E(X^2) = \\int_{-\\infty}^{\\infty} x^2 f(x)\\,\\mathrm{d}x",[573,1072,1074,1101,1189,1261,1314,1407],{"className":1073,"ariaHidden":639},[638],[573,1075,1077,1080,1083,1086,1089,1092,1095,1098],{"className":1076},[643],[573,1078],{"className":1079,"style":648},[647],[573,1081,933],{"className":1082,"style":722},[664,668],[573,1084,614],{"className":1085},[743],[573,1087,617],{"className":1088,"style":747},[664,668],[573,1090,629],{"className":1091},[808],[573,1093],{"className":1094,"style":751},[659],[573,1096,620],{"className":1097},[755],[573,1099],{"className":1100,"style":751},[659],[573,1102,1104,1108,1174,1177,1180,1183,1186],{"className":1103},[643],[573,1105],{"className":1106,"style":1107},[647],"height:2.3846em;vertical-align:-0.9703em;",[573,1109,1111,1116],{"className":1110},[652],[573,1112,947],{"className":1113,"style":1115},[652,653,1114],"large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[573,1117,1119],{"className":1118},[672],[573,1120,1122,1165],{"className":1121},[676,677],[573,1123,1125,1162],{"className":1124},[681],[573,1126,1129,1147],{"className":1127,"style":1128},[685],"height:1.4143em;",[573,1130,1132,1135],{"style":1131},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[573,1133],{"className":1134,"style":694},[693],[573,1136,1138],{"className":1137},[698,699,700,701],[573,1139,1141,1144],{"className":1140},[664,701],[573,1142,952],{"className":1143},[664,701],[573,1145,956],{"className":1146},[664,701],[573,1148,1150,1153],{"style":1149},"top:-3.8129em;margin-right:0.05em;",[573,1151],{"className":1152,"style":694},[693],[573,1154,1156],{"className":1155},[698,699,700,701],[573,1157,1159],{"className":1158},[664,701],[573,1160,956],{"className":1161},[664,701],[573,1163,709],{"className":1164},[708],[573,1166,1168],{"className":1167},[681],[573,1169,1172],{"className":1170,"style":1171},[685],"height:0.9703em;",[573,1173],{},[573,1175,614],{"className":1176},[743],[573,1178,601],{"className":1179},[664,668],[573,1181],{"className":1182,"style":722},[659],[573,1184,952],{"className":1185},[726],[573,1187],{"className":1188,"style":722},[659],[573,1190,1192,1196,1199,1230,1233,1236,1239,1242,1245,1249,1252,1255,1258],{"className":1191},[643],[573,1193],{"className":1194,"style":1195},[647],"height:1.1141em;vertical-align:-0.25em;",[573,1197,967],{"className":1198},[664,668],[573,1200,1202,1205],{"className":1201},[808],[573,1203,629],{"className":1204},[808],[573,1206,1208],{"className":1207},[672],[573,1209,1211],{"className":1210},[676],[573,1212,1214],{"className":1213},[681],[573,1215,1218],{"className":1216,"style":1217},[685],"height:0.8641em;",[573,1219,1221,1224],{"style":1220},"top:-3.113em;margin-right:0.05em;",[573,1222],{"className":1223,"style":694},[693],[573,1225,1227],{"className":1226},[698,699,700,701],[573,1228,976],{"className":1229},[664,701],[573,1231,824],{"className":1232,"style":846},[664,668],[573,1234,614],{"className":1235},[743],[573,1237,601],{"className":1238},[664,668],[573,1240,629],{"className":1241},[808],[573,1243],{"className":1244,"style":660},[659],[573,1246,991],{"className":1247},[664,1248],"mathrm",[573,1250,601],{"className":1251},[664,668],[573,1253],{"className":1254,"style":751},[659],[573,1256,620],{"className":1257},[755],[573,1259],{"className":1260,"style":751},[659],[573,1262,1264,1267,1270,1273,1302,1305,1308,1311],{"className":1263},[643],[573,1265],{"className":1266,"style":1195},[647],[573,1268,874],{"className":1269,"style":896},[664,668],[573,1271,614],{"className":1272},[743],[573,1274,1276,1279],{"className":1275},[664],[573,1277,617],{"className":1278,"style":747},[664,668],[573,1280,1282],{"className":1281},[672],[573,1283,1285],{"className":1284},[676],[573,1286,1288],{"className":1287},[681],[573,1289,1291],{"className":1290,"style":1217},[685],[573,1292,1293,1296],{"style":1220},[573,1294],{"className":1295,"style":694},[693],[573,1297,1299],{"className":1298},[698,699,700,701],[573,1300,976],{"className":1301},[664,701],[573,1303,629],{"className":1304},[808],[573,1306],{"className":1307,"style":722},[659],[573,1309,952],{"className":1310},[726],[573,1312],{"className":1313,"style":722},[659],[573,1315,1317,1320,1349,1353,1357,1360,1363,1366,1395,1398,1401,1404],{"className":1316},[643],[573,1318],{"className":1319,"style":1195},[647],[573,1321,1323,1326],{"className":1322},[664],[573,1324,967],{"className":1325},[664,668],[573,1327,1329],{"className":1328},[672],[573,1330,1332],{"className":1331},[676],[573,1333,1335],{"className":1334},[681],[573,1336,1338],{"className":1337,"style":1217},[685],[573,1339,1340,1343],{"style":1220},[573,1341],{"className":1342,"style":694},[693],[573,1344,1346],{"className":1345},[698,699,700,701],[573,1347,976],{"className":1348},[664,701],[573,1350,1018],{"className":1351},[1352],"mpunct",[573,1354],{"className":1355,"style":1356},[659],"margin-right:2em;",[573,1358],{"className":1359,"style":660},[659],[573,1361,874],{"className":1362,"style":896},[664,668],[573,1364,614],{"className":1365},[743],[573,1367,1369,1372],{"className":1368},[664],[573,1370,617],{"className":1371,"style":747},[664,668],[573,1373,1375],{"className":1374},[672],[573,1376,1378],{"className":1377},[676],[573,1379,1381],{"className":1380},[681],[573,1382,1384],{"className":1383,"style":1217},[685],[573,1385,1386,1389],{"style":1220},[573,1387],{"className":1388,"style":694},[693],[573,1390,1392],{"className":1391},[698,699,700,701],[573,1393,976],{"className":1394},[664,701],[573,1396,629],{"className":1397},[808],[573,1399],{"className":1400,"style":751},[659],[573,1402,620],{"className":1403},[755],[573,1405],{"className":1406,"style":751},[659],[573,1408,1410,1413,1473,1476,1505,1508,1511,1514,1517,1520,1523],{"className":1409},[643],[573,1411],{"className":1412,"style":1107},[647],[573,1414,1416,1419],{"className":1415},[652],[573,1417,947],{"className":1418,"style":1115},[652,653,1114],[573,1420,1422],{"className":1421},[672],[573,1423,1425,1465],{"className":1424},[676,677],[573,1426,1428,1462],{"className":1427},[681],[573,1429,1431,1448],{"className":1430,"style":1128},[685],[573,1432,1433,1436],{"style":1131},[573,1434],{"className":1435,"style":694},[693],[573,1437,1439],{"className":1438},[698,699,700,701],[573,1440,1442,1445],{"className":1441},[664,701],[573,1443,952],{"className":1444},[664,701],[573,1446,956],{"className":1447},[664,701],[573,1449,1450,1453],{"style":1149},[573,1451],{"className":1452,"style":694},[693],[573,1454,1456],{"className":1455},[698,699,700,701],[573,1457,1459],{"className":1458},[664,701],[573,1460,956],{"className":1461},[664,701],[573,1463,709],{"className":1464},[708],[573,1466,1468],{"className":1467},[681],[573,1469,1471],{"className":1470,"style":1171},[685],[573,1472],{},[573,1474],{"className":1475,"style":660},[659],[573,1477,1479,1482],{"className":1478},[664],[573,1480,601],{"className":1481},[664,668],[573,1483,1485],{"className":1484},[672],[573,1486,1488],{"className":1487},[676],[573,1489,1491],{"className":1490},[681],[573,1492,1494],{"className":1493,"style":1217},[685],[573,1495,1496,1499],{"style":1220},[573,1497],{"className":1498,"style":694},[693],[573,1500,1502],{"className":1501},[698,699,700,701],[573,1503,976],{"className":1504},[664,701],[573,1506,824],{"className":1507,"style":846},[664,668],[573,1509,614],{"className":1510},[743],[573,1512,601],{"className":1513},[664,668],[573,1515,629],{"className":1516},[808],[573,1518],{"className":1519,"style":660},[659],[573,1521,991],{"className":1522},[664,1248],[573,1524,601],{"className":1525},[664,668],[564,1527,1528,1529,1558,1559,1616,1617,1646,1647,1676,1677,1717],{},"Ist ",[573,1530,1532,1545],{"className":1531},[576],[573,1533,1535],{"className":1534},[580],[582,1536,1537],{"xmlns":584},[586,1538,1539,1543],{},[589,1540,1541],{},[599,1542,824],{},[631,1544,824],{"encoding":633},[573,1546,1548],{"className":1547,"ariaHidden":639},[638],[573,1549,1551,1555],{"className":1550},[643],[573,1552],{"className":1553,"style":1554},[647],"height:0.8889em;vertical-align:-0.1944em;",[573,1556,824],{"className":1557,"style":846},[664,668]," außerhalb eines Intervalls ",[573,1560,1562,1589],{"className":1561},[576],[573,1563,1565],{"className":1564},[580],[582,1566,1567],{"xmlns":584},[586,1568,1569,1586],{},[589,1570,1571,1574,1577,1580,1583],{},[592,1572,1573],{"stretchy":613},"[",[599,1575,1576],{},"a",[592,1578,1579],{"separator":639},";",[599,1581,1582],{},"b",[592,1584,1585],{"stretchy":613},"]",[631,1587,1588],{"encoding":633},"[a; b]",[573,1590,1592],{"className":1591,"ariaHidden":639},[638],[573,1593,1595,1598,1601,1604,1607,1610,1613],{"className":1594},[643],[573,1596],{"className":1597,"style":648},[647],[573,1599,1573],{"className":1600},[743],[573,1602,1576],{"className":1603},[664,668],[573,1605,1579],{"className":1606},[1352],[573,1608],{"className":1609,"style":660},[659],[573,1611,1582],{"className":1612},[664,668],[573,1614,1585],{"className":1615},[808]," null, integriert man nur von ",[573,1618,1620,1633],{"className":1619},[576],[573,1621,1623],{"className":1622},[580],[582,1624,1625],{"xmlns":584},[586,1626,1627,1631],{},[589,1628,1629],{},[599,1630,1576],{},[631,1632,1576],{"encoding":633},[573,1634,1636],{"className":1635,"ariaHidden":639},[638],[573,1637,1639,1643],{"className":1638},[643],[573,1640],{"className":1641,"style":1642},[647],"height:0.4306em;",[573,1644,1576],{"className":1645},[664,668]," bis ",[573,1648,1650,1663],{"className":1649},[576],[573,1651,1653],{"className":1652},[580],[582,1654,1655],{"xmlns":584},[586,1656,1657,1661],{},[589,1658,1659],{},[599,1660,1582],{},[631,1662,1582],{"encoding":633},[573,1664,1666],{"className":1665,"ariaHidden":639},[638],[573,1667,1669,1673],{"className":1668},[643],[573,1670],{"className":1671,"style":1672},[647],"height:0.6944em;",[573,1674,1582],{"className":1675},[664,668],". Die Bedingung mit ",[573,1678,1680,1699],{"className":1679},[576],[573,1681,1683],{"className":1682},[580],[582,1684,1685],{"xmlns":584},[586,1686,1687,1696],{},[589,1688,1689,1692,1694],{},[599,1690,1691],{"mathvariant":955},"∣",[599,1693,601],{},[599,1695,1691],{"mathvariant":955},[631,1697,1698],{"encoding":633},"|x|",[573,1700,1702],{"className":1701,"ariaHidden":639},[638],[573,1703,1705,1708,1711,1714],{"className":1704},[643],[573,1706],{"className":1707,"style":648},[647],[573,1709,1691],{"className":1710},[664],[573,1712,601],{"className":1713},[664,668],[573,1715,1691],{"className":1716},[664]," sorgt dafür, dass das Integral existiert; bei Dichten auf einem beschränkten Intervall ist sie immer erfüllt.",[559,1719,1721],{"id":1720},"beispiele","Beispiele",[564,1723,1724,1753,1754,1838,1839,1891,1892,1921],{},[573,1725,1727,1740],{"className":1726},[576],[573,1728,1730],{"className":1729},[580],[582,1731,1732],{"xmlns":584},[586,1733,1734,1738],{},[589,1735,1736],{},[599,1737,617],{},[631,1739,617],{"encoding":633},[573,1741,1743],{"className":1742,"ariaHidden":639},[638],[573,1744,1746,1750],{"className":1745},[643],[573,1747],{"className":1748,"style":1749},[647],"height:0.6833em;",[573,1751,617],{"className":1752,"style":747},[664,668]," habe die Dichte ",[573,1755,1757,1784],{"className":1756},[576],[573,1758,1760],{"className":1759},[580],[582,1761,1762],{"xmlns":584},[586,1763,1764,1781],{},[589,1765,1766,1768,1770,1772,1774,1776,1779],{},[599,1767,824],{},[592,1769,614],{"stretchy":613},[599,1771,601],{},[592,1773,629],{"stretchy":613},[592,1775,620],{},[974,1777,1778],{},"0,5",[599,1780,601],{},[631,1782,1783],{"encoding":633},"f(x) = 0{,}5x",[573,1785,1787,1814],{"className":1786,"ariaHidden":639},[638],[573,1788,1790,1793,1796,1799,1802,1805,1808,1811],{"className":1789},[643],[573,1791],{"className":1792,"style":648},[647],[573,1794,824],{"className":1795,"style":846},[664,668],[573,1797,614],{"className":1798},[743],[573,1800,601],{"className":1801},[664,668],[573,1803,629],{"className":1804},[808],[573,1806],{"className":1807,"style":751},[659],[573,1809,620],{"className":1810},[755],[573,1812],{"className":1813,"style":751},[659],[573,1815,1817,1821,1825,1831,1835],{"className":1816},[643],[573,1818],{"className":1819,"style":1820},[647],"height:0.8389em;vertical-align:-0.1944em;",[573,1822,1824],{"className":1823},[664],"0",[573,1826,1828],{"className":1827},[664],[573,1829,1018],{"className":1830},[1352],[573,1832,1834],{"className":1833},[664],"5",[573,1836,601],{"className":1837},[664,668]," auf ",[573,1840,1842,1864],{"className":1841},[576],[573,1843,1845],{"className":1844},[580],[582,1846,1847],{"xmlns":584},[586,1848,1849,1861],{},[589,1850,1851,1853,1855,1857,1859],{},[592,1852,1573],{"stretchy":613},[974,1854,1824],{},[592,1856,1579],{"separator":639},[974,1858,976],{},[592,1860,1585],{"stretchy":613},[631,1862,1863],{"encoding":633},"[0; 2]",[573,1865,1867],{"className":1866,"ariaHidden":639},[638],[573,1868,1870,1873,1876,1879,1882,1885,1888],{"className":1869},[643],[573,1871],{"className":1872,"style":648},[647],[573,1874,1573],{"className":1875},[743],[573,1877,1824],{"className":1878},[664],[573,1880,1579],{"className":1881},[1352],[573,1883],{"className":1884,"style":660},[659],[573,1886,976],{"className":1887},[664],[573,1889,1585],{"className":1890},[808],", sonst ",[573,1893,1895,1908],{"className":1894},[576],[573,1896,1898],{"className":1897},[580],[582,1899,1900],{"xmlns":584},[586,1901,1902,1906],{},[589,1903,1904],{},[974,1905,1824],{},[631,1907,1824],{"encoding":633},[573,1909,1911],{"className":1910,"ariaHidden":639},[638],[573,1912,1914,1918],{"className":1913},[643],[573,1915],{"className":1916,"style":1917},[647],"height:0.6444em;",[573,1919,1824],{"className":1920},[664],":",[573,1923,1925],{"className":1924},[917],[573,1926,1928,2023],{"className":1927},[576],[573,1929,1931],{"className":1930},[580],[582,1932,1933],{"xmlns":584,"display":926},[586,1934,1935,2020],{},[589,1936,1937,1939,1941,1943,1945,1947,1955,1957,1959,1961,1963,1965,1967,1969,1971,1996,1998,2005,2007,2014,2017],{},[599,1938,874],{},[592,1940,614],{"stretchy":613},[599,1942,617],{},[592,1944,629],{"stretchy":613},[592,1946,620],{},[943,1948,1949,1951,1953],{},[592,1950,947],{},[974,1952,1824],{},[974,1954,976],{},[599,1956,601],{},[592,1958,607],{},[974,1960,1778],{},[599,1962,601],{},[986,1964,988],{},[599,1966,991],{"mathvariant":955},[599,1968,601],{},[592,1970,620],{},[943,1972,1973,1992,1994],{},[589,1974,1975,1977,1990],{},[592,1976,1573],{"fence":639},[1978,1979,1980,1987],"mfrac",{},[969,1981,1982,1984],{},[599,1983,601],{},[974,1985,1986],{},"3",[974,1988,1989],{},"6",[592,1991,1585],{"fence":639},[974,1993,1824],{},[974,1995,976],{},[592,1997,620],{},[1978,1999,2000,2003],{},[974,2001,2002],{},"8",[974,2004,1989],{},[592,2006,620],{},[1978,2008,2009,2012],{},[974,2010,2011],{},"4",[974,2013,1986],{},[592,2015,2016],{},"≈",[974,2018,2019],{},"1,33",[631,2021,2022],{"encoding":633},"E(X) = \\int_0^2 x \\cdot 0{,}5x\\,\\mathrm{d}x = \\left[\\frac{x^3}{6}\\right]_0^2 = \\frac{8}{6} = \\frac{4}{3} \\approx 1{,}33",[573,2024,2026,2053,2128,2167,2353,2432,2509],{"className":2025,"ariaHidden":639},[638],[573,2027,2029,2032,2035,2038,2041,2044,2047,2050],{"className":2028},[643],[573,2030],{"className":2031,"style":648},[647],[573,2033,874],{"className":2034,"style":896},[664,668],[573,2036,614],{"className":2037},[743],[573,2039,617],{"className":2040,"style":747},[664,668],[573,2042,629],{"className":2043},[808],[573,2045],{"className":2046,"style":751},[659],[573,2048,620],{"className":2049},[755],[573,2051],{"className":2052,"style":751},[659],[573,2054,2056,2060,2113,2116,2119,2122,2125],{"className":2055},[643],[573,2057],{"className":2058,"style":2059},[647],"height:2.476em;vertical-align:-0.9119em;",[573,2061,2063,2066],{"className":2062},[652],[573,2064,947],{"className":2065,"style":1115},[652,653,1114],[573,2067,2069],{"className":2068},[672],[573,2070,2072,2104],{"className":2071},[676,677],[573,2073,2075,2101],{"className":2074},[681],[573,2076,2079,2090],{"className":2077,"style":2078},[685],"height:1.564em;",[573,2080,2081,2084],{"style":1131},[573,2082],{"className":2083,"style":694},[693],[573,2085,2087],{"className":2086},[698,699,700,701],[573,2088,1824],{"className":2089},[664,701],[573,2091,2092,2095],{"style":1149},[573,2093],{"className":2094,"style":694},[693],[573,2096,2098],{"className":2097},[698,699,700,701],[573,2099,976],{"className":2100},[664,701],[573,2102,709],{"className":2103},[708],[573,2105,2107],{"className":2106},[681],[573,2108,2111],{"className":2109,"style":2110},[685],"height:0.9119em;",[573,2112],{},[573,2114],{"className":2115,"style":660},[659],[573,2117,601],{"className":2118},[664,668],[573,2120],{"className":2121,"style":722},[659],[573,2123,607],{"className":2124},[726],[573,2126],{"className":2127,"style":722},[659],[573,2129,2131,2134,2137,2143,2146,2149,2152,2155,2158,2161,2164],{"className":2130},[643],[573,2132],{"className":2133,"style":1554},[647],[573,2135,1824],{"className":2136},[664],[573,2138,2140],{"className":2139},[664],[573,2141,1018],{"className":2142},[1352],[573,2144,1834],{"className":2145},[664],[573,2147,601],{"className":2148},[664,668],[573,2150],{"className":2151,"style":660},[659],[573,2153,991],{"className":2154},[664,1248],[573,2156,601],{"className":2157},[664,668],[573,2159],{"className":2160,"style":751},[659],[573,2162,620],{"className":2163},[755],[573,2165],{"className":2166,"style":751},[659],[573,2168,2170,2174,2344,2347,2350],{"className":2169},[643],[573,2171],{"className":2172,"style":2173},[647],"height:2.6948em;vertical-align:-0.9997em;",[573,2175,2178,2295],{"className":2176},[2177],"minner",[573,2179,2181,2190,2289],{"className":2180},[2177],[573,2182,2186],{"className":2183,"style":2185},[743,2184],"delimcenter","top:0em;",[573,2187,1573],{"className":2188},[2189,700],"delimsizing",[573,2191,2193,2197,2286],{"className":2192},[664],[573,2194],{"className":2195},[743,2196],"nulldelimiter",[573,2198,2200],{"className":2199},[1978],[573,2201,2203,2277],{"className":2202},[676,677],[573,2204,2206,2274],{"className":2205},[681],[573,2207,2210,2223,2234],{"className":2208,"style":2209},[685],"height:1.4911em;",[573,2211,2213,2217],{"style":2212},"top:-2.314em;",[573,2214],{"className":2215,"style":2216},[693],"height:3em;",[573,2218,2220],{"className":2219},[664],[573,2221,1989],{"className":2222},[664],[573,2224,2226,2229],{"style":2225},"top:-3.23em;",[573,2227],{"className":2228,"style":2216},[693],[573,2230],{"className":2231,"style":2233},[2232],"frac-line","border-bottom-width:0.04em;",[573,2235,2237,2240],{"style":2236},"top:-3.677em;",[573,2238],{"className":2239,"style":2216},[693],[573,2241,2243],{"className":2242},[664],[573,2244,2246,2249],{"className":2245},[664],[573,2247,601],{"className":2248},[664,668],[573,2250,2252],{"className":2251},[672],[573,2253,2255],{"className":2254},[676],[573,2256,2258],{"className":2257},[681],[573,2259,2262],{"className":2260,"style":2261},[685],"height:0.8141em;",[573,2263,2265,2268],{"style":2264},"top:-3.063em;margin-right:0.05em;",[573,2266],{"className":2267,"style":694},[693],[573,2269,2271],{"className":2270},[698,699,700,701],[573,2272,1986],{"className":2273},[664,701],[573,2275,709],{"className":2276},[708],[573,2278,2280],{"className":2279},[681],[573,2281,2284],{"className":2282,"style":2283},[685],"height:0.686em;",[573,2285],{},[573,2287],{"className":2288},[808,2196],[573,2290,2292],{"className":2291,"style":2185},[808,2184],[573,2293,1585],{"className":2294},[2189,700],[573,2296,2298],{"className":2297},[672],[573,2299,2301,2335],{"className":2300},[676,677],[573,2302,2304,2332],{"className":2303},[681],[573,2305,2308,2320],{"className":2306,"style":2307},[685],"height:1.6951em;",[573,2309,2311,2314],{"style":2310},"top:-1.7003em;margin-right:0.05em;",[573,2312],{"className":2313,"style":694},[693],[573,2315,2317],{"className":2316},[698,699,700,701],[573,2318,1824],{"className":2319},[664,701],[573,2321,2323,2326],{"style":2322},"top:-3.944em;margin-right:0.05em;",[573,2324],{"className":2325,"style":694},[693],[573,2327,2329],{"className":2328},[698,699,700,701],[573,2330,976],{"className":2331},[664,701],[573,2333,709],{"className":2334},[708],[573,2336,2338],{"className":2337},[681],[573,2339,2342],{"className":2340,"style":2341},[685],"height:0.9997em;",[573,2343],{},[573,2345],{"className":2346,"style":751},[659],[573,2348,620],{"className":2349},[755],[573,2351],{"className":2352,"style":751},[659],[573,2354,2356,2360,2423,2426,2429],{"className":2355},[643],[573,2357],{"className":2358,"style":2359},[647],"height:2.0074em;vertical-align:-0.686em;",[573,2361,2363,2366,2420],{"className":2362},[664],[573,2364],{"className":2365},[743,2196],[573,2367,2369],{"className":2368},[1978],[573,2370,2372,2412],{"className":2371},[676,677],[573,2373,2375,2409],{"className":2374},[681],[573,2376,2379,2390,2398],{"className":2377,"style":2378},[685],"height:1.3214em;",[573,2380,2381,2384],{"style":2212},[573,2382],{"className":2383,"style":2216},[693],[573,2385,2387],{"className":2386},[664],[573,2388,1989],{"className":2389},[664],[573,2391,2392,2395],{"style":2225},[573,2393],{"className":2394,"style":2216},[693],[573,2396],{"className":2397,"style":2233},[2232],[573,2399,2400,2403],{"style":2236},[573,2401],{"className":2402,"style":2216},[693],[573,2404,2406],{"className":2405},[664],[573,2407,2002],{"className":2408},[664],[573,2410,709],{"className":2411},[708],[573,2413,2415],{"className":2414},[681],[573,2416,2418],{"className":2417,"style":2283},[685],[573,2419],{},[573,2421],{"className":2422},[808,2196],[573,2424],{"className":2425,"style":751},[659],[573,2427,620],{"className":2428},[755],[573,2430],{"className":2431,"style":751},[659],[573,2433,2435,2438,2500,2503,2506],{"className":2434},[643],[573,2436],{"className":2437,"style":2359},[647],[573,2439,2441,2444,2497],{"className":2440},[664],[573,2442],{"className":2443},[743,2196],[573,2445,2447],{"className":2446},[1978],[573,2448,2450,2489],{"className":2449},[676,677],[573,2451,2453,2486],{"className":2452},[681],[573,2454,2456,2467,2475],{"className":2455,"style":2378},[685],[573,2457,2458,2461],{"style":2212},[573,2459],{"className":2460,"style":2216},[693],[573,2462,2464],{"className":2463},[664],[573,2465,1986],{"className":2466},[664],[573,2468,2469,2472],{"style":2225},[573,2470],{"className":2471,"style":2216},[693],[573,2473],{"className":2474,"style":2233},[2232],[573,2476,2477,2480],{"style":2236},[573,2478],{"className":2479,"style":2216},[693],[573,2481,2483],{"className":2482},[664],[573,2484,2011],{"className":2485},[664],[573,2487,709],{"className":2488},[708],[573,2490,2492],{"className":2491},[681],[573,2493,2495],{"className":2494,"style":2283},[685],[573,2496],{},[573,2498],{"className":2499},[808,2196],[573,2501],{"className":2502,"style":751},[659],[573,2504,2016],{"className":2505},[755],[573,2507],{"className":2508,"style":751},[659],[573,2510,2512,2515,2519,2525],{"className":2511},[643],[573,2513],{"className":2514,"style":1820},[647],[573,2516,2518],{"className":2517},[664],"1",[573,2520,2522],{"className":2521},[664],[573,2523,1018],{"className":2524},[1352],[573,2526,2528],{"className":2527},[664],"33",[564,2530,2531,2532,2989],{},"Für die Varianz: ",[573,2533,2535,2611],{"className":2534},[576],[573,2536,2538],{"className":2537},[580],[582,2539,2540],{"xmlns":584},[586,2541,2542,2608],{},[589,2543,2544,2546,2548,2554,2556,2558,2566,2568,2574,2576,2578,2580,2582,2604,2606],{},[599,2545,874],{},[592,2547,614],{"stretchy":613},[969,2549,2550,2552],{},[599,2551,617],{},[974,2553,976],{},[592,2555,629],{"stretchy":613},[592,2557,620],{},[943,2559,2560,2562,2564],{},[592,2561,947],{},[974,2563,1824],{},[974,2565,976],{},[974,2567,1778],{},[969,2569,2570,2572],{},[599,2571,601],{},[974,2573,1986],{},[986,2575,988],{},[599,2577,991],{"mathvariant":955},[599,2579,601],{},[592,2581,620],{},[943,2583,2584,2600,2602],{},[589,2585,2586,2588,2598],{},[592,2587,1573],{"fence":639},[1978,2589,2590,2596],{},[969,2591,2592,2594],{},[599,2593,601],{},[974,2595,2011],{},[974,2597,2002],{},[592,2599,1585],{"fence":639},[974,2601,1824],{},[974,2603,976],{},[592,2605,620],{},[974,2607,976],{},[631,2609,2610],{"encoding":633},"E(X^2) = \\int_0^2 0{,}5x^3\\,\\mathrm{d}x = \\left[\\frac{x^4}{8}\\right]_0^2 = 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",[573,3624,3626,3683],{"className":3625},[576],[573,3627,3629],{"className":3628},[580],[582,3630,3631],{"xmlns":584},[586,3632,3633,3680],{},[589,3634,3635,3637,3639,3641,3643,3645,3653,3655,3657,3659,3661,3663,3665,3676,3678],{},[599,3636,874],{},[592,3638,614],{"stretchy":613},[599,3640,617],{},[592,3642,629],{"stretchy":613},[592,3644,620],{},[943,3646,3647,3649,3651],{},[592,3648,947],{},[974,3650,1824],{},[974,3652,3512],{},[974,3654,3570],{},[599,3656,601],{},[986,3658,988],{},[599,3660,991],{"mathvariant":955},[599,3662,601],{},[592,3664,620],{},[1978,3666,3667,3673],{},[969,3668,3669,3671],{},[974,3670,3512],{},[974,3672,976],{},[974,3674,3675],{},"20",[592,3677,620],{},[974,3679,1834],{},[631,3681,3682],{"encoding":633},"E(X) = \\int_0^{10} 0{,}1x\\,\\mathrm{d}x = \\frac{10^2}{20} = 5",[573,3684,3686,3713,3809,3922],{"className":3685,"ariaHidden":639},[638],[573,3687,3689,3692,3695,3698,3701,3704,3707,3710],{"className":3688},[643],[573,3690],{"className":3691,"style":648},[647],[573,3693,874],{"className":3694,"style":896},[664,668],[573,3696,614],{"className":3697},[743],[573,3699,617],{"className":3700,"style":747},[664,668],[573,3702,629],{"className":3703},[808],[573,3705],{"className":3706,"style":751},[659],[573,3708,620],{"className":3709},[755],[573,3711],{"className":3712,"style":751},[659],[573,3714,3716,3719,3773,3776,3779,3785,3788,3791,3794,3797,3800,3803,3806],{"className":3715},[643],[573,3717],{"className":3718,"style":2674},[647],[573,3720,3722,3725],{"className":3721},[652],[573,3723,947],{"className":3724,"style":2681},[652,653,654],[573,3726,3728],{"className":3727},[672],[573,3729,3731,3765],{"className":3730},[676,677],[573,3732,3734,3762],{"className":3733},[681],[573,3735,3737,3748],{"className":3736,"style":2694},[685],[573,3738,3739,3742],{"style":2697},[573,3740],{"className":3741,"style":694},[693],[573,3743,3745],{"className":3744},[698,699,700,701],[573,3746,1824],{"className":3747},[664,701],[573,3749,3750,3753],{"style":2709},[573,3751],{"className":3752,"style":694},[693],[573,3754,3756],{"className":3755},[698,699,700,701],[573,3757,3759],{"className":3758},[664,701],[573,3760,3512],{"className":3761},[664,701],[573,3763,709],{"className":3764},[708],[573,3766,3768],{"className":3767},[681],[573,3769,3771],{"className":3770,"style":2728},[685],[573,3772],{},[573,3774],{"className":3775,"style":660},[659],[573,3777,1824],{"className":3778},[664],[573,3780,3782],{"className":3781},[664],[573,3783,1018],{"className":3784},[1352],[573,3786,2518],{"className":3787},[664],[573,3789,601],{"className":3790},[664,668],[573,3792],{"className":3793,"style":660},[659],[573,3795,991],{"className":3796},[664,1248],[573,3798,601],{"className":3799},[664,668],[573,3801],{"className":3802,"style":751},[659],[573,3804,620],{"className":3805},[755],[573,3807],{"className":3808,"style":751},[659],[573,3810,3812,3816,3913,3916,3919],{"className":3811},[643],[573,3813],{"className":3814,"style":3815},[647],"height:1.3629em;vertical-align:-0.345em;",[573,3817,3819,3822,3910],{"className":3818},[664],[573,3820],{"className":3821},[743,2196],[573,3823,3825],{"className":3824},[1978],[573,3826,3828,3902],{"className":3827},[676,677],[573,3829,3831,3899],{"className":3830},[681],[573,3832,3834,3848,3856],{"className":3833,"style":2831},[685],[573,3835,3836,3839],{"style":2834},[573,3837],{"className":3838,"style":2216},[693],[573,3840,3842],{"className":3841},[698,699,700,701],[573,3843,3845],{"className":3844},[664,701],[573,3846,3675],{"className":3847},[664,701],[573,3849,3850,3853],{"style":2225},[573,3851],{"className":3852,"style":2216},[693],[573,3854],{"className":3855,"style":2233},[2232],[573,3857,3858,3861],{"style":2857},[573,3859],{"className":3860,"style":2216},[693],[573,3862,3864],{"className":3863},[698,699,700,701],[573,3865,3867,3870],{"className":3866},[664,701],[573,3868,2518],{"className":3869},[664,701],[573,3871,3873,3876],{"className":3872},[664,701],[573,3874,1824],{"className":3875},[664,701],[573,3877,3879],{"className":3878},[672],[573,3880,3882],{"className":3881},[676],[573,3883,3885],{"className":3884},[681],[573,3886,3888],{"className":3887,"style":2885},[685],[573,3889,3890,3893],{"style":2888},[573,3891],{"className":3892,"style":2892},[693],[573,3894,3896],{"className":3895},[698,2896,2897,701],[573,3897,976],{"className":3898},[664,701],[573,3900,709],{"className":3901},[708],[573,3903,3905],{"className":3904},[681],[573,3906,3908],{"className":3907,"style":2910},[685],[573,3909],{},[573,3911],{"className":3912},[808,2196],[573,3914],{"className":3915,"style":751},[659],[573,3917,620],{"className":3918},[755],[573,3920],{"className":3921,"style":751},[659],[573,3923,3925,3928],{"className":3924},[643],[573,3926],{"className":3927,"style":1917},[647],[573,3929,1834],{"className":3930},[664],[559,3932,3934],{"id":3933},"typische-fehler","Typische Fehler",[3936,3937,3938,4068,4282],"ul",{},[3939,3940,3941,3942,4010,4011,4039,4040,856],"li",{},"Nur die Dichte integrieren. ",[573,3943,3945,3973],{"className":3944},[576],[573,3946,3948],{"className":3947},[580],[582,3949,3950],{"xmlns":584},[586,3951,3952,3970],{},[589,3953,3954,3956,3958,3960,3962,3964,3966,3968],{},[592,3955,947],{},[599,3957,824],{},[592,3959,614],{"stretchy":613},[599,3961,601],{},[592,3963,629],{"stretchy":613},[986,3965,988],{},[599,3967,991],{"mathvariant":955},[599,3969,601],{},[631,3971,3972],{"encoding":633},"\\int f(x)\\,\\mathrm{d}x",[573,3974,3976],{"className":3975,"ariaHidden":639},[638],[573,3977,3979,3983,3986,3989,3992,3995,3998,4001,4004,4007],{"className":3978},[643],[573,3980],{"className":3981,"style":3982},[647],"height:1.1111em;vertical-align:-0.3061em;",[573,3984,947],{"className":3985,"style":2681},[652,653,654],[573,3987],{"className":3988,"style":660},[659],[573,3990,824],{"className":3991,"style":846},[664,668],[573,3993,614],{"className":3994},[743],[573,3996,601],{"className":3997},[664,668],[573,3999,629],{"className":4000},[808],[573,4002],{"className":4003,"style":660},[659],[573,4005,991],{"className":4006},[664,1248],[573,4008,601],{"className":4009},[664,668]," ergibt immer ",[573,4012,4014,4027],{"className":4013},[576],[573,4015,4017],{"className":4016},[580],[582,4018,4019],{"xmlns":584},[586,4020,4021,4025],{},[589,4022,4023],{},[974,4024,2518],{},[631,4026,2518],{"encoding":633},[573,4028,4030],{"className":4029,"ariaHidden":639},[638],[573,4031,4033,4036],{"className":4032},[643],[573,4034],{"className":4035,"style":1917},[647],[573,4037,2518],{"className":4038},[664],"; für den Erwartungswert braucht man den Faktor ",[573,4041,4043,4056],{"className":4042},[576],[573,4044,4046],{"className":4045},[580],[582,4047,4048],{"xmlns":584},[586,4049,4050,4054],{},[589,4051,4052],{},[599,4053,601],{},[631,4055,601],{"encoding":633},[573,4057,4059],{"className":4058,"ariaHidden":639},[638],[573,4060,4062,4065],{"className":4061},[643],[573,4063],{"className":4064,"style":1642},[647],[573,4066,601],{"className":4067},[664,668],[3939,4069,4070,4071,4145,4146,4220,4221,4281],{},"Bei der Varianz ",[573,4072,4074,4098],{"className":4073},[576],[573,4075,4077],{"className":4076},[580],[582,4078,4079],{"xmlns":584},[586,4080,4081,4095],{},[589,4082,4083,4085,4087,4089],{},[599,4084,874],{},[592,4086,614],{"stretchy":613},[599,4088,617],{},[969,4090,4091,4093],{},[592,4092,629],{"stretchy":613},[974,4094,976],{},[631,4096,4097],{"encoding":633},"E(X)^2",[573,4099,4101],{"className":4100,"ariaHidden":639},[638],[573,4102,4104,4107,4110,4113,4116],{"className":4103},[643],[573,4105],{"className":4106,"style":2620},[647],[573,4108,874],{"className":4109,"style":896},[664,668],[573,4111,614],{"className":4112},[743],[573,4114,617],{"className":4115,"style":747},[664,668],[573,4117,4119,4122],{"className":4118},[808],[573,4120,629],{"className":4121},[808],[573,4123,4125],{"className":4124},[672],[573,4126,4128],{"className":4127},[676],[573,4129,4131],{"className":4130},[681],[573,4132,4134],{"className":4133,"style":2261},[685],[573,4135,4136,4139],{"style":2264},[573,4137],{"className":4138,"style":694},[693],[573,4140,4142],{"className":4141},[698,699,700,701],[573,4143,976],{"className":4144},[664,701]," statt ",[573,4147,4149,4173],{"className":4148},[576],[573,4150,4152],{"className":4151},[580],[582,4153,4154],{"xmlns":584},[586,4155,4156,4170],{},[589,4157,4158,4160,4162,4168],{},[599,4159,874],{},[592,4161,614],{"stretchy":613},[969,4163,4164,4166],{},[599,4165,617],{},[974,4167,976],{},[592,4169,629],{"stretchy":613},[631,4171,4172],{"encoding":633},"E(X^2)",[573,4174,4176],{"className":4175,"ariaHidden":639},[638],[573,4177,4179,4182,4185,4188,4217],{"className":4178},[643],[573,4180],{"className":4181,"style":2620},[647],[573,4183,874],{"className":4184,"style":896},[664,668],[573,4186,614],{"className":4187},[743],[573,4189,4191,4194],{"className":4190},[664],[573,4192,617],{"className":4193,"style":747},[664,668],[573,4195,4197],{"className":4196},[672],[573,4198,4200],{"className":4199},[676],[573,4201,4203],{"className":4202},[681],[573,4204,4206],{"className":4205,"style":2261},[685],[573,4207,4208,4211],{"style":2264},[573,4209],{"className":4210,"style":694},[693],[573,4212,4214],{"className":4213},[698,699,700,701],[573,4215,976],{"className":4216},[664,701],[573,4218,629],{"className":4219},[808]," berechnen oder ",[573,4222,4224,4242],{"className":4223},[576],[573,4225,4227],{"className":4226},[580],[582,4228,4229],{"xmlns":584},[586,4230,4231,4239],{},[589,4232,4233],{},[969,4234,4235,4237],{},[599,4236,967],{},[974,4238,976],{},[631,4240,4241],{"encoding":633},"\\mu^2",[573,4243,4245],{"className":4244,"ariaHidden":639},[638],[573,4246,4248,4252],{"className":4247},[643],[573,4249],{"className":4250,"style":4251},[647],"height:1.0085em;vertical-align:-0.1944em;",[573,4253,4255,4258],{"className":4254},[664],[573,4256,967],{"className":4257},[664,668],[573,4259,4261],{"className":4260},[672],[573,4262,4264],{"className":4263},[676],[573,4265,4267],{"className":4266},[681],[573,4268,4270],{"className":4269,"style":2261},[685],[573,4271,4272,4275],{"style":2264},[573,4273],{"className":4274,"style":694},[693],[573,4276,4278],{"className":4277},[698,699,700,701],[573,4279,976],{"className":4280},[664,701]," vergessen.",[3939,4283,4284,4285,4313,4314,4342,4343,4371],{},"Die Grenzen falsch setzen und über Bereiche integrieren, in denen ",[573,4286,4288,4301],{"className":4287},[576],[573,4289,4291],{"className":4290},[580],[582,4292,4293],{"xmlns":584},[586,4294,4295,4299],{},[589,4296,4297],{},[599,4298,824],{},[631,4300,824],{"encoding":633},[573,4302,4304],{"className":4303,"ariaHidden":639},[638],[573,4305,4307,4310],{"className":4306},[643],[573,4308],{"className":4309,"style":1554},[647],[573,4311,824],{"className":4312,"style":846},[664,668]," gleich ",[573,4315,4317,4330],{"className":4316},[576],[573,4318,4320],{"className":4319},[580],[582,4321,4322],{"xmlns":584},[586,4323,4324,4328],{},[589,4325,4326],{},[974,4327,1824],{},[631,4329,1824],{"encoding":633},[573,4331,4333],{"className":4332,"ariaHidden":639},[638],[573,4334,4336,4339],{"className":4335},[643],[573,4337],{"className":4338,"style":1917},[647],[573,4340,1824],{"className":4341},[664]," ist, aber mit der Formel von ",[573,4344,4346,4359],{"className":4345},[576],[573,4347,4349],{"className":4348},[580],[582,4350,4351],{"xmlns":584},[586,4352,4353,4357],{},[589,4354,4355],{},[599,4356,824],{},[631,4358,824],{"encoding":633},[573,4360,4362],{"className":4361,"ariaHidden":639},[638],[573,4363,4365,4368],{"className":4364},[643],[573,4366],{"className":4367,"style":1554},[647],[573,4369,824],{"className":4370,"style":846},[664,668]," weiterrechnen.",{"title":4373,"searchDepth":4374,"depth":4374,"links":4375},"",2,[4376,4377,4378],{"id":561,"depth":4374,"text":562},{"id":1720,"depth":4374,"text":1721},{"id":3933,"depth":4374,"text":3934},[4380,4383,4386,4389,4391,4394,4397],{"lhs":4381,"rhs":4382},"2^3\u002F6","4\u002F3",{"lhs":4384,"rhs":4385},"round(4\u002F3, 2)","1.33",{"lhs":4387,"rhs":4388},"round(sum(map(0:999, f(k) = 0.5*((k + 0.5)*2\u002F1000)^2)) * 2\u002F1000, 4)","round(4\u002F3, 4)",{"lhs":4390,"rhs":976},"2^4\u002F8",{"lhs":4392,"rhs":4393},"2 - (4\u002F3)^2","2\u002F9",{"lhs":4395,"rhs":4396},"round(sqrt(2\u002F9), 2)","0.47",{"lhs":4398,"rhs":1834},"10^2\u002F20","X \\text{ stetig mit Dichte } f,\\ \\int_{-\\infty}^{\\infty} |x| \\cdot f(x)\\,\\mathrm{d}x \u003C \\infty","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig mit Dichte\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\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>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int_{-\\infty}^{\\infty} |x| \\cdot f(x)\\,\\mathrm{d}x < \\infty\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2734em;vertical-align:-0.4142em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol small-op\" style=\"margin-right:0.1945em;position:relative;top:-0.0006em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8593em;\">\u003Cspan style=\"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2579em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\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:0.4142em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathrm\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","expected-value-continuous","E(X) = \\int_{-\\infty}^{\\infty} x \\cdot f(x)\\,\\mathrm{d}x","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(X) = \\int_{-\\infty}^{\\infty} x \\cdot 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style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4143em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\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:0.9703em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathrm\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert-stetige-zufallsgroesse",[],[4412,4413,4414,4415],"expected-value","probability-density","variance-random-variable","uniform-distribution-continuous",{"title":548,"description":4373},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert-stetige-zufallsgroesse","Der Erwartungswert einer stetigen Zufallsgröße ist das Integral über x mal Dichte, der Schwerpunkt der Verteilung.",[4420,4421,4422,4423,4424],"erwartungswert","stetige zufallsgröße","dichtefunktion","integral","varianz",[4426,4429,4432,4435],{"symbol":883,"meaning":4427,"symbolHtml":4428},"Erwartungswert der Zufallsgröße X, oft auch μ geschrieben","\u003Cspan class=\"katex\">\u003Cspan 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Zufallsgröße","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>X\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">X\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":824,"meaning":4433,"symbolHtml":4434},"Dichtefunktion von X","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation 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class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","sEYPQtXVNwcU6EgDgQKnHEBq3GFs8mv9eiLoCvS8Ukk",[4440,4443,4446,4449],{"stem":4441,"title":4442,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdichtefunktion","Dichtefunktion",{"stem":4444,"title":4445,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert","Erwartungswert",{"stem":4447,"title":4448,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstetige-gleichverteilung","Stetige Gleichverteilung",{"stem":4450,"title":4451,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fvarianz-zufallsgroesse","Varianz einer Zufallsgröße",1793824285166]