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Das macht die Regel zu einem starken Werkzeug. Man zerlegt eine komplizierte Zufallsgröße in eine Summe einfacher ",[569,1135,555],{}," ",[574,1138,1140,1177],{"className":1139},[581],[574,1141,1143],{"className":1142},[585],[587,1144,1145],{"xmlns":589},[592,1146,1147,1174],{},[595,1148,1149,1157,1160,1163,1166,1169,1171],{},[607,1150,1151,1154],{},[598,1152,1153],{},"I",[598,1155,1156],{},"j",[602,1158,1159],{},"∈",[602,1161,1162],{"stretchy":604},"{",[613,1164,1165],{},"0",[602,1167,1168],{"separator":699},",",[613,1170,615],{},[602,1172,1173],{"stretchy":604},"}",[691,1175,1176],{"encoding":693},"I_j \\in \\{0, 1\\}",[574,1178,1180,1239],{"className":1179,"ariaHidden":699},[698],[574,1181,1183,1187,1230,1233,1236],{"className":1182},[703],[574,1184],{"className":1185,"style":1186},[707],"height:0.9694em;vertical-align:-0.2861em;",[574,1188,1190,1193],{"className":1189},[712],[574,1191,1153],{"className":1192,"style":725},[712,713],[574,1194,1196],{"className":1195},[729],[574,1197,1199,1221],{"className":1198},[733,734],[574,1200,1202,1218],{"className":1201},[738],[574,1203,1206],{"className":1204,"style":1205},[742],"height:0.3117em;",[574,1207,1208,1211],{"style":746},[574,1209],{"className":1210,"style":751},[750],[574,1212,1214],{"className":1213},[755,756,757,758],[574,1215,1156],{"className":1216,"style":1217},[712,713,758],"margin-right:0.0572em;",[574,1219,766],{"className":1220},[765],[574,1222,1224],{"className":1223},[738],[574,1225,1228],{"className":1226,"style":1227},[742],"height:0.2861em;",[574,1229],{},[574,1231],{"className":1232,"style":918},[779],[574,1234,1159],{"className":1235},[922],[574,1237],{"className":1238,"style":918},[779],[574,1240,1242,1245,1248,1251,1255,1259,1262],{"className":1241},[703],[574,1243],{"className":1244,"style":708},[707],[574,1246,1162],{"className":1247},[718],[574,1249,1165],{"className":1250},[712],[574,1252,1168],{"className":1253},[1254],"mpunct",[574,1256],{"className":1257,"style":1258},[779],"margin-right:0.1667em;",[574,1260,615],{"className":1261},[712],[574,1263,1173],{"className":1264},[914]," mit ",[574,1267,1269,1312],{"className":1268},[581],[574,1270,1272],{"className":1271},[585],[587,1273,1274],{"xmlns":589},[592,1275,1276,1309],{},[595,1277,1278,1280,1282,1288,1290,1292,1295,1297,1303,1305,1307],{},[598,1279,600],{},[602,1281,605],{"stretchy":604},[607,1283,1284,1286],{},[598,1285,1153],{},[598,1287,1156],{},[602,1289,642],{"stretchy":604},[602,1291,645],{},[598,1293,1294],{},"P",[602,1296,605],{"stretchy":604},[607,1298,1299,1301],{},[598,1300,1153],{},[598,1302,1156],{},[602,1304,645],{},[613,1306,615],{},[602,1308,642],{"stretchy":604},[691,1310,1311],{"encoding":693},"E(I_j) = P(I_j = 1)",[574,1313,1315,1380,1442],{"className":1314,"ariaHidden":699},[698],[574,1316,1318,1322,1325,1328,1368,1371,1374,1377],{"className":1317},[703],[574,1319],{"className":1320,"style":1321},[707],"height:1.0361em;vertical-align:-0.2861em;",[574,1323,600],{"className":1324,"style":714},[712,713],[574,1326,605],{"className":1327},[718],[574,1329,1331,1334],{"className":1330},[712],[574,1332,1153],{"className":1333,"style":725},[712,713],[574,1335,1337],{"className":1336},[729],[574,1338,1340,1360],{"className":1339},[733,734],[574,1341,1343,1357],{"className":1342},[738],[574,1344,1346],{"className":1345,"style":1205},[742],[574,1347,1348,1351],{"style":746},[574,1349],{"className":1350,"style":751},[750],[574,1352,1354],{"className":1353},[755,756,757,758],[574,1355,1156],{"className":1356,"style":1217},[712,713,758],[574,1358,766],{"className":1359},[765],[574,1361,1363],{"className":1362},[738],[574,1364,1366],{"className":1365,"style":1227},[742],[574,1367],{},[574,1369,642],{"className":1370},[914],[574,1372],{"className":1373,"style":918},[779],[574,1375,645],{"className":1376},[922],[574,1378],{"className":1379,"style":918},[779],[574,1381,1383,1386,1390,1393,1433,1436,1439],{"className":1382},[703],[574,1384],{"className":1385,"style":1321},[707],[574,1387,1294],{"className":1388,"style":1389},[712,713],"margin-right:0.1389em;",[574,1391,605],{"className":1392},[718],[574,1394,1396,1399],{"className":1395},[712],[574,1397,1153],{"className":1398,"style":725},[712,713],[574,1400,1402],{"className":1401},[729],[574,1403,1405,1425],{"className":1404},[733,734],[574,1406,1408,1422],{"className":1407},[738],[574,1409,1411],{"className":1410,"style":1205},[742],[574,1412,1413,1416],{"style":746},[574,1414],{"className":1415,"style":751},[750],[574,1417,1419],{"className":1418},[755,756,757,758],[574,1420,1156],{"className":1421,"style":1217},[712,713,758],[574,1423,766],{"className":1424},[765],[574,1426,1428],{"className":1427},[738],[574,1429,1431],{"className":1430,"style":1227},[742],[574,1432],{},[574,1434],{"className":1435,"style":918},[779],[574,1437,645],{"className":1438},[922],[574,1440],{"className":1441,"style":918},[779],[574,1443,1445,1448,1451],{"className":1444},[703],[574,1446],{"className":1447,"style":708},[707],[574,1449,615],{"className":1450},[712],[574,1452,642],{"className":1453},[914]," und addiert deren Erwartungswerte.",[565,1456,1457],{},"Die Regel folgt direkt aus der Definition als (gewichtete) Summe bzw. Integral, weil Summe und Integral linear sind.",[560,1459,1461],{"id":1460},"beispiele","Beispiele",[565,1463,1464,1465,1582],{},"Augensumme zweier Würfel: Mit ",[574,1466,1468,1504],{"className":1467},[581],[574,1469,1471],{"className":1470},[585],[587,1472,1473],{"xmlns":589},[592,1474,1475,1501],{},[595,1476,1477,1479,1481,1483,1485,1487,1489,1491,1494,1496,1498],{},[598,1478,600],{},[602,1480,605],{"stretchy":604},[598,1482,611],{},[602,1484,642],{"stretchy":604},[602,1486,645],{},[598,1488,600],{},[602,1490,605],{"stretchy":604},[598,1492,1493],{},"Y",[602,1495,642],{"stretchy":604},[602,1497,645],{},[613,1499,1500],{},"3,5",[691,1502,1503],{"encoding":693},"E(X) = E(Y) = 3{,}5",[574,1505,1507,1534,1561],{"className":1506,"ariaHidden":699},[698],[574,1508,1510,1513,1516,1519,1522,1525,1528,1531],{"className":1509},[703],[574,1511],{"className":1512,"style":708},[707],[574,1514,600],{"className":1515,"style":714},[712,713],[574,1517,605],{"className":1518},[718],[574,1520,611],{"className":1521,"style":725},[712,713],[574,1523,642],{"className":1524},[914],[574,1526],{"className":1527,"style":918},[779],[574,1529,645],{"className":1530},[922],[574,1532],{"className":1533,"style":918},[779],[574,1535,1537,1540,1543,1546,1549,1552,1555,1558],{"className":1536},[703],[574,1538],{"className":1539,"style":708},[707],[574,1541,600],{"className":1542,"style":714},[712,713],[574,1544,605],{"className":1545},[718],[574,1547,1493],{"className":1548,"style":780},[712,713],[574,1550,642],{"className":1551},[914],[574,1553],{"className":1554,"style":918},[779],[574,1556,645],{"className":1557},[922],[574,1559],{"className":1560,"style":918},[779],[574,1562,1564,1568,1572,1578],{"className":1563},[703],[574,1565],{"className":1566,"style":1567},[707],"height:0.8389em;vertical-align:-0.1944em;",[574,1569,1571],{"className":1570},[712],"3",[574,1573,1575],{"className":1574},[712],[574,1576,1168],{"className":1577},[1254],[574,1579,1581],{"className":1580},[712],"5"," folgt ohne Verteilungstabelle",[574,1584,1586],{"className":1585},[577],[574,1587,1589,1626],{"className":1588},[581],[574,1590,1592],{"className":1591},[585],[587,1593,1594],{"xmlns":589,"display":590},[592,1595,1596,1623],{},[595,1597,1598,1600,1602,1604,1606,1608,1610,1612,1614,1616,1618,1620],{},[598,1599,600],{},[602,1601,605],{"stretchy":604},[598,1603,611],{},[602,1605,618],{},[598,1607,1493],{},[602,1609,642],{"stretchy":604},[602,1611,645],{},[613,1613,1500],{},[602,1615,618],{},[613,1617,1500],{},[602,1619,645],{},[613,1621,1622],{},"7",[691,1624,1625],{"encoding":693},"E(X + Y) = 3{,}5 + 3{,}5 = 7",[574,1627,1629,1653,1674,1701,1728],{"className":1628,"ariaHidden":699},[698],[574,1630,1632,1635,1638,1641,1644,1647,1650],{"className":1631},[703],[574,1633],{"className":1634,"style":708},[707],[574,1636,600],{"className":1637,"style":714},[712,713],[574,1639,605],{"className":1640},[718],[574,1642,611],{"className":1643,"style":725},[712,713],[574,1645],{"className":1646,"style":780},[779],[574,1648,618],{"className":1649},[784],[574,1651],{"className":1652,"style":780},[779],[574,1654,1656,1659,1662,1665,1668,1671],{"className":1655},[703],[574,1657],{"className":1658,"style":708},[707],[574,1660,1493],{"className":1661,"style":780},[712,713],[574,1663,642],{"className":1664},[914],[574,1666],{"className":1667,"style":918},[779],[574,1669,645],{"className":1670},[922],[574,1672],{"className":1673,"style":918},[779],[574,1675,1677,1680,1683,1689,1692,1695,1698],{"className":1676},[703],[574,1678],{"className":1679,"style":1567},[707],[574,1681,1571],{"className":1682},[712],[574,1684,1686],{"className":1685},[712],[574,1687,1168],{"className":1688},[1254],[574,1690,1581],{"className":1691},[712],[574,1693],{"className":1694,"style":780},[779],[574,1696,618],{"className":1697},[784],[574,1699],{"className":1700,"style":780},[779],[574,1702,1704,1707,1710,1716,1719,1722,1725],{"className":1703},[703],[574,1705],{"className":1706,"style":1567},[707],[574,1708,1571],{"className":1709},[712],[574,1711,1713],{"className":1712},[712],[574,1714,1168],{"className":1715},[1254],[574,1717,1581],{"className":1718},[712],[574,1720],{"className":1721,"style":918},[779],[574,1723,645],{"className":1724},[922],[574,1726],{"className":1727,"style":918},[779],[574,1729,1731,1735],{"className":1730},[703],[574,1732],{"className":1733,"style":1734},[707],"height:0.6444em;",[574,1736,1622],{"className":1737},[712],[565,1739,1740,1741,1799,1800,1829],{},"Ein Spiel zahlt ",[574,1742,1744,1765],{"className":1743},[581],[574,1745,1747],{"className":1746},[585],[587,1748,1749],{"xmlns":589},[592,1750,1751,1762],{},[595,1752,1753,1755,1757,1760],{},[613,1754,625],{},[598,1756,611],{},[602,1758,1759],{},"−",[613,1761,1571],{},[691,1763,1764],{"encoding":693},"2X - 3",[574,1766,1768,1790],{"className":1767,"ariaHidden":699},[698],[574,1769,1771,1775,1778,1781,1784,1787],{"className":1770},[703],[574,1772],{"className":1773,"style":1774},[707],"height:0.7667em;vertical-align:-0.0833em;",[574,1776,625],{"className":1777},[712],[574,1779,611],{"className":1780,"style":725},[712,713],[574,1782],{"className":1783,"style":780},[779],[574,1785,1759],{"className":1786},[784],[574,1788],{"className":1789,"style":780},[779],[574,1791,1793,1796],{"className":1792},[703],[574,1794],{"className":1795,"style":1734},[707],[574,1797,1571],{"className":1798},[712]," Euro, wobei ",[574,1801,1803,1816],{"className":1802},[581],[574,1804,1806],{"className":1805},[585],[587,1807,1808],{"xmlns":589},[592,1809,1810,1814],{},[595,1811,1812],{},[598,1813,611],{},[691,1815,611],{"encoding":693},[574,1817,1819],{"className":1818,"ariaHidden":699},[698],[574,1820,1822,1826],{"className":1821},[703],[574,1823],{"className":1824,"style":1825},[707],"height:0.6833em;",[574,1827,611],{"className":1828,"style":725},[712,713]," die Augenzahl eines Würfels ist:",[574,1831,1833],{"className":1832},[577],[574,1834,1836,1880],{"className":1835},[581],[574,1837,1839],{"className":1838},[585],[587,1840,1841],{"xmlns":589,"display":590},[592,1842,1843,1877],{},[595,1844,1845,1847,1849,1851,1853,1855,1857,1859,1861,1863,1866,1868,1870,1872,1874],{},[598,1846,600],{},[602,1848,605],{"stretchy":604},[613,1850,625],{},[598,1852,611],{},[602,1854,1759],{},[613,1856,1571],{},[602,1858,642],{"stretchy":604},[602,1860,645],{},[613,1862,625],{},[602,1864,1865],{},"⋅",[613,1867,1500],{},[602,1869,1759],{},[613,1871,1571],{},[602,1873,645],{},[613,1875,1876],{},"4",[691,1878,1879],{"encoding":693},"E(2X - 3) = 2 \\cdot 3{,}5 - 3 = 4",[574,1881,1883,1910,1931,1949,1976,1994],{"className":1882,"ariaHidden":699},[698],[574,1884,1886,1889,1892,1895,1898,1901,1904,1907],{"className":1885},[703],[574,1887],{"className":1888,"style":708},[707],[574,1890,600],{"className":1891,"style":714},[712,713],[574,1893,605],{"className":1894},[718],[574,1896,625],{"className":1897},[712],[574,1899,611],{"className":1900,"style":725},[712,713],[574,1902],{"className":1903,"style":780},[779],[574,1905,1759],{"className":1906},[784],[574,1908],{"className":1909,"style":780},[779],[574,1911,1913,1916,1919,1922,1925,1928],{"className":1912},[703],[574,1914],{"className":1915,"style":708},[707],[574,1917,1571],{"className":1918},[712],[574,1920,642],{"className":1921},[914],[574,1923],{"className":1924,"style":918},[779],[574,1926,645],{"className":1927},[922],[574,1929],{"className":1930,"style":918},[779],[574,1932,1934,1937,1940,1943,1946],{"className":1933},[703],[574,1935],{"className":1936,"style":1734},[707],[574,1938,625],{"className":1939},[712],[574,1941],{"className":1942,"style":780},[779],[574,1944,1865],{"className":1945},[784],[574,1947],{"className":1948,"style":780},[779],[574,1950,1952,1955,1958,1964,1967,1970,1973],{"className":1951},[703],[574,1953],{"className":1954,"style":1567},[707],[574,1956,1571],{"className":1957},[712],[574,1959,1961],{"className":1960},[712],[574,1962,1168],{"className":1963},[1254],[574,1965,1581],{"className":1966},[712],[574,1968],{"className":1969,"style":780},[779],[574,1971,1759],{"className":1972},[784],[574,1974],{"className":1975,"style":780},[779],[574,1977,1979,1982,1985,1988,1991],{"className":1978},[703],[574,1980],{"className":1981,"style":1734},[707],[574,1983,1571],{"className":1984},[712],[574,1986],{"className":1987,"style":918},[779],[574,1989,645],{"className":1990},[922],[574,1992],{"className":1993,"style":918},[779],[574,1995,1997,2000],{"className":1996},[703],[574,1998],{"className":1999,"style":1734},[707],[574,2001,1876],{"className":2002},[712],[565,2004,2005,2006,2183,2184,2276,2277,2306,2307,2415,2416,2505,2506,2590,2591,2643,2644,2704],{},"Erwartungswert der Binomialverteilung: ",[574,2007,2009,2043],{"className":2008},[581],[574,2010,2012],{"className":2011},[585],[587,2013,2014],{"xmlns":589},[592,2015,2016,2040],{},[595,2017,2018,2020,2022,2028,2030,2032,2034],{},[598,2019,611],{},[602,2021,645],{},[607,2023,2024,2026],{},[598,2025,1153],{},[613,2027,615],{},[602,2029,618],{},[602,2031,630],{},[602,2033,618],{},[607,2035,2036,2038],{},[598,2037,1153],{},[598,2039,639],{},[691,2041,2042],{"encoding":693},"X = I_1 + \\ldots + I_n",[574,2044,2046,2064,2119,2137],{"className":2045,"ariaHidden":699},[698],[574,2047,2049,2052,2055,2058,2061],{"className":2048},[703],[574,2050],{"className":2051,"style":1825},[707],[574,2053,611],{"className":2054,"style":725},[712,713],[574,2056],{"className":2057,"style":918},[779],[574,2059,645],{"className":2060},[922],[574,2062],{"className":2063,"style":918},[779],[574,2065,2067,2070,2110,2113,2116],{"className":2066},[703],[574,2068],{"className":2069,"style":794},[707],[574,2071,2073,2076],{"className":2072},[712],[574,2074,1153],{"className":2075,"style":725},[712,713],[574,2077,2079],{"className":2078},[729],[574,2080,2082,2102],{"className":2081},[733,734],[574,2083,2085,2099],{"className":2084},[738],[574,2086,2088],{"className":2087,"style":743},[742],[574,2089,2090,2093],{"style":746},[574,2091],{"className":2092,"style":751},[750],[574,2094,2096],{"className":2095},[755,756,757,758],[574,2097,615],{"className":2098},[712,758],[574,2100,766],{"className":2101},[765],[574,2103,2105],{"className":2104},[738],[574,2106,2108],{"className":2107,"style":773},[742],[574,2109],{},[574,2111],{"className":2112,"style":780},[779],[574,2114,618],{"className":2115},[784],[574,2117],{"className":2118,"style":780},[779],[574,2120,2122,2125,2128,2131,2134],{"className":2121},[703],[574,2123],{"className":2124,"style":850},[707],[574,2126,630],{"className":2127},[854],[574,2129],{"className":2130,"style":780},[779],[574,2132,618],{"className":2133},[784],[574,2135],{"className":2136,"style":780},[779],[574,2138,2140,2143],{"className":2139},[703],[574,2141],{"className":2142,"style":794},[707],[574,2144,2146,2149],{"className":2145},[712],[574,2147,1153],{"className":2148,"style":725},[712,713],[574,2150,2152],{"className":2151},[729],[574,2153,2155,2175],{"className":2154},[733,734],[574,2156,2158,2172],{"className":2157},[738],[574,2159,2161],{"className":2160,"style":888},[742],[574,2162,2163,2166],{"style":746},[574,2164],{"className":2165,"style":751},[750],[574,2167,2169],{"className":2168},[755,756,757,758],[574,2170,639],{"className":2171},[712,713,758],[574,2173,766],{"className":2174},[765],[574,2176,2178],{"className":2177},[738],[574,2179,2181],{"className":2180,"style":773},[742],[574,2182],{},", wobei ",[574,2185,2187,2209],{"className":2186},[581],[574,2188,2190],{"className":2189},[585],[587,2191,2192],{"xmlns":589},[592,2193,2194,2206],{},[595,2195,2196,2202,2204],{},[607,2197,2198,2200],{},[598,2199,1153],{},[598,2201,1156],{},[602,2203,645],{},[613,2205,615],{},[691,2207,2208],{"encoding":693},"I_j = 1",[574,2210,2212,2267],{"className":2211,"ariaHidden":699},[698],[574,2213,2215,2218,2258,2261,2264],{"className":2214},[703],[574,2216],{"className":2217,"style":1186},[707],[574,2219,2221,2224],{"className":2220},[712],[574,2222,1153],{"className":2223,"style":725},[712,713],[574,2225,2227],{"className":2226},[729],[574,2228,2230,2250],{"className":2229},[733,734],[574,2231,2233,2247],{"className":2232},[738],[574,2234,2236],{"className":2235,"style":1205},[742],[574,2237,2238,2241],{"style":746},[574,2239],{"className":2240,"style":751},[750],[574,2242,2244],{"className":2243},[755,756,757,758],[574,2245,1156],{"className":2246,"style":1217},[712,713,758],[574,2248,766],{"className":2249},[765],[574,2251,2253],{"className":2252},[738],[574,2254,2256],{"className":2255,"style":1227},[742],[574,2257],{},[574,2259],{"className":2260,"style":918},[779],[574,2262,645],{"className":2263},[922],[574,2265],{"className":2266,"style":918},[779],[574,2268,2270,2273],{"className":2269},[703],[574,2271],{"className":2272,"style":1734},[707],[574,2274,615],{"className":2275},[712]," ist, wenn der ",[574,2278,2280,2293],{"className":2279},[581],[574,2281,2283],{"className":2282},[585],[587,2284,2285],{"xmlns":589},[592,2286,2287,2291],{},[595,2288,2289],{},[598,2290,1156],{},[691,2292,1156],{"encoding":693},[574,2294,2296],{"className":2295,"ariaHidden":699},[698],[574,2297,2299,2303],{"className":2298},[703],[574,2300],{"className":2301,"style":2302},[707],"height:0.854em;vertical-align:-0.1944em;",[574,2304,1156],{"className":2305,"style":1217},[712,713],"-te Versuch ein Treffer ist. Wegen ",[574,2308,2310,2338],{"className":2309},[581],[574,2311,2313],{"className":2312},[585],[587,2314,2315],{"xmlns":589},[592,2316,2317,2335],{},[595,2318,2319,2321,2323,2329,2331,2333],{},[598,2320,600],{},[602,2322,605],{"stretchy":604},[607,2324,2325,2327],{},[598,2326,1153],{},[598,2328,1156],{},[602,2330,642],{"stretchy":604},[602,2332,645],{},[598,2334,565],{},[691,2336,2337],{"encoding":693},"E(I_j) = p",[574,2339,2341,2405],{"className":2340,"ariaHidden":699},[698],[574,2342,2344,2347,2350,2353,2393,2396,2399,2402],{"className":2343},[703],[574,2345],{"className":2346,"style":1321},[707],[574,2348,600],{"className":2349,"style":714},[712,713],[574,2351,605],{"className":2352},[718],[574,2354,2356,2359],{"className":2355},[712],[574,2357,1153],{"className":2358,"style":725},[712,713],[574,2360,2362],{"className":2361},[729],[574,2363,2365,2385],{"className":2364},[733,734],[574,2366,2368,2382],{"className":2367},[738],[574,2369,2371],{"className":2370,"style":1205},[742],[574,2372,2373,2376],{"style":746},[574,2374],{"className":2375,"style":751},[750],[574,2377,2379],{"className":2378},[755,756,757,758],[574,2380,1156],{"className":2381,"style":1217},[712,713,758],[574,2383,766],{"className":2384},[765],[574,2386,2388],{"className":2387},[738],[574,2389,2391],{"className":2390,"style":1227},[742],[574,2392],{},[574,2394,642],{"className":2395},[914],[574,2397],{"className":2398,"style":918},[779],[574,2400,645],{"className":2401},[922],[574,2403],{"className":2404,"style":918},[779],[574,2406,2408,2412],{"className":2407},[703],[574,2409],{"className":2410,"style":2411},[707],"height:0.625em;vertical-align:-0.1944em;",[574,2413,565],{"className":2414},[712,713]," ist ",[574,2417,2419,2447],{"className":2418},[581],[574,2420,2422],{"className":2421},[585],[587,2423,2424],{"xmlns":589},[592,2425,2426,2444],{},[595,2427,2428,2430,2432,2434,2436,2438,2440,2442],{},[598,2429,600],{},[602,2431,605],{"stretchy":604},[598,2433,611],{},[602,2435,642],{"stretchy":604},[602,2437,645],{},[598,2439,639],{},[602,2441,1865],{},[598,2443,565],{},[691,2445,2446],{"encoding":693},"E(X) = n \\cdot p",[574,2448,2450,2477,2496],{"className":2449,"ariaHidden":699},[698],[574,2451,2453,2456,2459,2462,2465,2468,2471,2474],{"className":2452},[703],[574,2454],{"className":2455,"style":708},[707],[574,2457,600],{"className":2458,"style":714},[712,713],[574,2460,605],{"className":2461},[718],[574,2463,611],{"className":2464,"style":725},[712,713],[574,2466,642],{"className":2467},[914],[574,2469],{"className":2470,"style":918},[779],[574,2472,645],{"className":2473},[922],[574,2475],{"className":2476,"style":918},[779],[574,2478,2480,2484,2487,2490,2493],{"className":2479},[703],[574,2481],{"className":2482,"style":2483},[707],"height:0.4445em;",[574,2485,639],{"className":2486},[712,713],[574,2488],{"className":2489,"style":780},[779],[574,2491,1865],{"className":2492},[784],[574,2494],{"className":2495,"style":780},[779],[574,2497,2499,2502],{"className":2498},[703],[574,2500],{"className":2501,"style":2411},[707],[574,2503,565],{"className":2504},[712,713],", z.B. ",[574,2507,2509,2533],{"className":2508},[581],[574,2510,2512],{"className":2511},[585],[587,2513,2514],{"xmlns":589},[592,2515,2516,2530],{},[595,2517,2518,2521,2523,2526,2528],{},[613,2519,2520],{},"10",[602,2522,1865],{},[613,2524,2525],{},"0,3",[602,2527,645],{},[613,2529,1571],{},[691,2531,2532],{"encoding":693},"10 \\cdot 0{,}3 = 3",[574,2534,2536,2554,2581],{"className":2535,"ariaHidden":699},[698],[574,2537,2539,2542,2545,2548,2551],{"className":2538},[703],[574,2540],{"className":2541,"style":1734},[707],[574,2543,2520],{"className":2544},[712],[574,2546],{"className":2547,"style":780},[779],[574,2549,1865],{"className":2550},[784],[574,2552],{"className":2553,"style":780},[779],[574,2555,2557,2560,2563,2569,2572,2575,2578],{"className":2556},[703],[574,2558],{"className":2559,"style":1567},[707],[574,2561,1165],{"className":2562},[712],[574,2564,2566],{"className":2565},[712],[574,2567,1168],{"className":2568},[1254],[574,2570,1571],{"className":2571},[712],[574,2573],{"className":2574,"style":918},[779],[574,2576,645],{"className":2577},[922],[574,2579],{"className":2580,"style":918},[779],[574,2582,2584,2587],{"className":2583},[703],[574,2585],{"className":2586,"style":1734},[707],[574,2588,1571],{"className":2589},[712]," für ",[574,2592,2594,2612],{"className":2593},[581],[574,2595,2597],{"className":2596},[585],[587,2598,2599],{"xmlns":589},[592,2600,2601,2609],{},[595,2602,2603,2605,2607],{},[598,2604,639],{},[602,2606,645],{},[613,2608,2520],{},[691,2610,2611],{"encoding":693},"n = 10",[574,2613,2615,2634],{"className":2614,"ariaHidden":699},[698],[574,2616,2618,2622,2625,2628,2631],{"className":2617},[703],[574,2619],{"className":2620,"style":2621},[707],"height:0.4306em;",[574,2623,639],{"className":2624},[712,713],[574,2626],{"className":2627,"style":918},[779],[574,2629,645],{"className":2630},[922],[574,2632],{"className":2633,"style":918},[779],[574,2635,2637,2640],{"className":2636},[703],[574,2638],{"className":2639,"style":1734},[707],[574,2641,2520],{"className":2642},[712],", ",[574,2645,2647,2665],{"className":2646},[581],[574,2648,2650],{"className":2649},[585],[587,2651,2652],{"xmlns":589},[592,2653,2654,2662],{},[595,2655,2656,2658,2660],{},[598,2657,565],{},[602,2659,645],{},[613,2661,2525],{},[691,2663,2664],{"encoding":693},"p = 0{,}3",[574,2666,2668,2686],{"className":2667,"ariaHidden":699},[698],[574,2669,2671,2674,2677,2680,2683],{"className":2670},[703],[574,2672],{"className":2673,"style":2411},[707],[574,2675,565],{"className":2676},[712,713],[574,2678],{"className":2679,"style":918},[779],[574,2681,645],{"className":2682},[922],[574,2684],{"className":2685,"style":918},[779],[574,2687,2689,2692,2695,2701],{"className":2688},[703],[574,2690],{"className":2691,"style":1567},[707],[574,2693,1165],{"className":2694},[712],[574,2696,2698],{"className":2697},[712],[574,2699,1168],{"className":2700},[1254],[574,2702,1571],{"className":2703},[712],".",[560,2706,2708],{"id":2707},"typische-fehler","Typische Fehler",[2710,2711,2712,2915,3548],"ul",{},[2713,2714,2715,2716,2856,2857,2885,2886,2914],"li",{},"Die Regel auf Produkte übertragen. ",[574,2717,2719,2763],{"className":2718},[581],[574,2720,2722],{"className":2721},[585],[587,2723,2724],{"xmlns":589},[592,2725,2726,2760],{},[595,2727,2728,2730,2732,2734,2736,2738,2740,2742,2744,2746,2748,2750,2752,2754,2756,2758],{},[598,2729,600],{},[602,2731,605],{"stretchy":604},[598,2733,611],{},[602,2735,1865],{},[598,2737,1493],{},[602,2739,642],{"stretchy":604},[602,2741,645],{},[598,2743,600],{},[602,2745,605],{"stretchy":604},[598,2747,611],{},[602,2749,642],{"stretchy":604},[602,2751,1865],{},[598,2753,600],{},[602,2755,605],{"stretchy":604},[598,2757,1493],{},[602,2759,642],{"stretchy":604},[691,2761,2762],{"encoding":693},"E(X \\cdot Y) = E(X) \\cdot E(Y)",[574,2764,2766,2790,2811,2838],{"className":2765,"ariaHidden":699},[698],[574,2767,2769,2772,2775,2778,2781,2784,2787],{"className":2768},[703],[574,2770],{"className":2771,"style":708},[707],[574,2773,600],{"className":2774,"style":714},[712,713],[574,2776,605],{"className":2777},[718],[574,2779,611],{"className":2780,"style":725},[712,713],[574,2782],{"className":2783,"style":780},[779],[574,2785,1865],{"className":2786},[784],[574,2788],{"className":2789,"style":780},[779],[574,2791,2793,2796,2799,2802,2805,2808],{"className":2792},[703],[574,2794],{"className":2795,"style":708},[707],[574,2797,1493],{"className":2798,"style":780},[712,713],[574,2800,642],{"className":2801},[914],[574,2803],{"className":2804,"style":918},[779],[574,2806,645],{"className":2807},[922],[574,2809],{"className":2810,"style":918},[779],[574,2812,2814,2817,2820,2823,2826,2829,2832,2835],{"className":2813},[703],[574,2815],{"className":2816,"style":708},[707],[574,2818,600],{"className":2819,"style":714},[712,713],[574,2821,605],{"className":2822},[718],[574,2824,611],{"className":2825,"style":725},[712,713],[574,2827,642],{"className":2828},[914],[574,2830],{"className":2831,"style":780},[779],[574,2833,1865],{"className":2834},[784],[574,2836],{"className":2837,"style":780},[779],[574,2839,2841,2844,2847,2850,2853],{"className":2840},[703],[574,2842],{"className":2843,"style":708},[707],[574,2845,600],{"className":2846,"style":714},[712,713],[574,2848,605],{"className":2849},[718],[574,2851,1493],{"className":2852,"style":780},[712,713],[574,2854,642],{"className":2855},[914]," gilt nur, wenn ",[574,2858,2860,2873],{"className":2859},[581],[574,2861,2863],{"className":2862},[585],[587,2864,2865],{"xmlns":589},[592,2866,2867,2871],{},[595,2868,2869],{},[598,2870,611],{},[691,2872,611],{"encoding":693},[574,2874,2876],{"className":2875,"ariaHidden":699},[698],[574,2877,2879,2882],{"className":2878},[703],[574,2880],{"className":2881,"style":1825},[707],[574,2883,611],{"className":2884,"style":725},[712,713]," und ",[574,2887,2889,2902],{"className":2888},[581],[574,2890,2892],{"className":2891},[585],[587,2893,2894],{"xmlns":589},[592,2895,2896,2900],{},[595,2897,2898],{},[598,2899,1493],{},[691,2901,1493],{"encoding":693},[574,2903,2905],{"className":2904,"ariaHidden":699},[698],[574,2906,2908,2911],{"className":2907},[703],[574,2909],{"className":2910,"style":1825},[707],[574,2912,1493],{"className":2913,"style":780},[712,713]," unkorreliert sind, z.B. bei Unabhängigkeit.",[2713,2916,2917,2918,3135,3136,3254,3255,2704],{},"Die Regel auf nichtlineare Funktionen übertragen. Beim Würfel ist ",[574,2919,2921,2963],{"className":2920},[581],[574,2922,2924],{"className":2923},[585],[587,2925,2926],{"xmlns":589},[592,2927,2928,2960],{},[595,2929,2930,2932,2934,2941,2943,2945,2954,2957],{},[598,2931,600],{},[602,2933,605],{"stretchy":604},[2935,2936,2937,2939],"msup",{},[598,2938,611],{},[613,2940,625],{},[602,2942,642],{"stretchy":604},[602,2944,645],{},[2946,2947,2948,2951],"mfrac",{},[613,2949,2950],{},"91",[613,2952,2953],{},"6",[602,2955,2956],{},"≈",[613,2958,2959],{},"15,17",[691,2961,2962],{"encoding":693},"E(X^2) = \\frac{91}{6} \\approx 15{,}17",[574,2964,2966,3022,3115],{"className":2965,"ariaHidden":699},[698],[574,2967,2969,2973,2976,2979,3010,3013,3016,3019],{"className":2968},[703],[574,2970],{"className":2971,"style":2972},[707],"height:1.0641em;vertical-align:-0.25em;",[574,2974,600],{"className":2975,"style":714},[712,713],[574,2977,605],{"className":2978},[718],[574,2980,2982,2985],{"className":2981},[712],[574,2983,611],{"className":2984,"style":725},[712,713],[574,2986,2988],{"className":2987},[729],[574,2989,2991],{"className":2990},[733],[574,2992,2994],{"className":2993},[738],[574,2995,2998],{"className":2996,"style":2997},[742],"height:0.8141em;",[574,2999,3001,3004],{"style":3000},"top:-3.063em;margin-right:0.05em;",[574,3002],{"className":3003,"style":751},[750],[574,3005,3007],{"className":3006},[755,756,757,758],[574,3008,625],{"className":3009},[712,758],[574,3011,642],{"className":3012},[914],[574,3014],{"className":3015,"style":918},[779],[574,3017,645],{"className":3018},[922],[574,3020],{"className":3021,"style":918},[779],[574,3023,3025,3029,3106,3109,3112],{"className":3024},[703],[574,3026],{"className":3027,"style":3028},[707],"height:1.1901em;vertical-align:-0.345em;",[574,3030,3032,3036,3103],{"className":3031},[712],[574,3033],{"className":3034},[718,3035],"nulldelimiter",[574,3037,3039],{"className":3038},[2946],[574,3040,3042,3094],{"className":3041},[733,734],[574,3043,3045,3091],{"className":3044},[738],[574,3046,3049,3065,3076],{"className":3047,"style":3048},[742],"height:0.8451em;",[574,3050,3052,3056],{"style":3051},"top:-2.655em;",[574,3053],{"className":3054,"style":3055},[750],"height:3em;",[574,3057,3059],{"className":3058},[755,756,757,758],[574,3060,3062],{"className":3061},[712,758],[574,3063,2953],{"className":3064},[712,758],[574,3066,3068,3071],{"style":3067},"top:-3.23em;",[574,3069],{"className":3070,"style":3055},[750],[574,3072],{"className":3073,"style":3075},[3074],"frac-line","border-bottom-width:0.04em;",[574,3077,3079,3082],{"style":3078},"top:-3.394em;",[574,3080],{"className":3081,"style":3055},[750],[574,3083,3085],{"className":3084},[755,756,757,758],[574,3086,3088],{"className":3087},[712,758],[574,3089,2950],{"className":3090},[712,758],[574,3092,766],{"className":3093},[765],[574,3095,3097],{"className":3096},[738],[574,3098,3101],{"className":3099,"style":3100},[742],"height:0.345em;",[574,3102],{},[574,3104],{"className":3105},[914,3035],[574,3107],{"className":3108,"style":918},[779],[574,3110,2956],{"className":3111},[922],[574,3113],{"className":3114,"style":918},[779],[574,3116,3118,3121,3125,3131],{"className":3117},[703],[574,3119],{"className":3120,"style":1567},[707],[574,3122,3124],{"className":3123},[712],"15",[574,3126,3128],{"className":3127},[712],[574,3129,1168],{"className":3130},[1254],[574,3132,3134],{"className":3133},[712],"17",", aber ",[574,3137,3139,3172],{"className":3138},[581],[574,3140,3142],{"className":3141},[585],[587,3143,3144],{"xmlns":589},[592,3145,3146,3169],{},[595,3147,3148,3150,3152,3154,3156,3158,3164,3166],{},[602,3149,605],{"stretchy":604},[598,3151,600],{},[602,3153,605],{"stretchy":604},[598,3155,611],{},[602,3157,642],{"stretchy":604},[2935,3159,3160,3162],{},[602,3161,642],{"stretchy":604},[613,3163,625],{},[602,3165,645],{},[613,3167,3168],{},"12,25",[691,3170,3171],{"encoding":693},"(E(X))^2 = 12{,}25",[574,3173,3175,3234],{"className":3174,"ariaHidden":699},[698],[574,3176,3178,3181,3184,3187,3190,3193,3196,3225,3228,3231],{"className":3177},[703],[574,3179],{"className":3180,"style":2972},[707],[574,3182,605],{"className":3183},[718],[574,3185,600],{"className":3186,"style":714},[712,713],[574,3188,605],{"className":3189},[718],[574,3191,611],{"className":3192,"style":725},[712,713],[574,3194,642],{"className":3195},[914],[574,3197,3199,3202],{"className":3198},[914],[574,3200,642],{"className":3201},[914],[574,3203,3205],{"className":3204},[729],[574,3206,3208],{"className":3207},[733],[574,3209,3211],{"className":3210},[738],[574,3212,3214],{"className":3213,"style":2997},[742],[574,3215,3216,3219],{"style":3000},[574,3217],{"className":3218,"style":751},[750],[574,3220,3222],{"className":3221},[755,756,757,758],[574,3223,625],{"className":3224},[712,758],[574,3226],{"className":3227,"style":918},[779],[574,3229,645],{"className":3230},[922],[574,3232],{"className":3233,"style":918},[779],[574,3235,3237,3240,3244,3250],{"className":3236},[703],[574,3238],{"className":3239,"style":1567},[707],[574,3241,3243],{"className":3242},[712],"12",[574,3245,3247],{"className":3246},[712],[574,3248,1168],{"className":3249},[1254],[574,3251,3253],{"className":3252},[712],"25",". Ebenso ist ",[574,3256,3258,3306],{"className":3257},[581],[574,3259,3261],{"className":3260},[585],[587,3262,3263],{"xmlns":589},[592,3264,3265,3303],{},[595,3266,3267,3269,3273,3285,3289],{},[598,3268,600],{},[3270,3271,3272],"mtext",{}," ⁣",[595,3274,3275,3277,3283],{},[602,3276,605],{"fence":699},[2946,3278,3279,3281],{},[613,3280,615],{},[598,3282,611],{},[602,3284,642],{"fence":699},[602,3286,3288],{"mathvariant":3287},"normal","≠",[2946,3290,3291,3293],{},[613,3292,615],{},[595,3294,3295,3297,3299,3301],{},[598,3296,600],{},[602,3298,605],{"stretchy":604},[598,3300,611],{},[602,3302,642],{"stretchy":604},[691,3304,3305],{"encoding":693},"E\\!\\left(\\frac{1}{X}\\right) \\neq \\frac{1}{E(X)}",[574,3307,3309,3463],{"className":3308,"ariaHidden":699},[698],[574,3310,3312,3316,3319,3323,3326,3413,3416,3460],{"className":3311},[703],[574,3313],{"className":3314,"style":3315},[707],"height:1.2em;vertical-align:-0.35em;",[574,3317,600],{"className":3318,"style":714},[712,713],[574,3320],{"className":3321,"style":3322},[779],"margin-right:-0.1667em;",[574,3324],{"className":3325,"style":1258},[779],[574,3327,3329,3339,3407],{"className":3328},[854],[574,3330,3334],{"className":3331,"style":3333},[718,3332],"delimcenter","top:0em;",[574,3335,605],{"className":3336},[3337,3338],"delimsizing","size1",[574,3340,3342,3345,3404],{"className":3341},[712],[574,3343],{"className":3344},[718,3035],[574,3346,3348],{"className":3347},[2946],[574,3349,3351,3396],{"className":3350},[733,734],[574,3352,3354,3393],{"className":3353},[738],[574,3355,3357,3371,3379],{"className":3356,"style":3048},[742],[574,3358,3359,3362],{"style":3051},[574,3360],{"className":3361,"style":3055},[750],[574,3363,3365],{"className":3364},[755,756,757,758],[574,3366,3368],{"className":3367},[712,758],[574,3369,611],{"className":3370,"style":725},[712,713,758],[574,3372,3373,3376],{"style":3067},[574,3374],{"className":3375,"style":3055},[750],[574,3377],{"className":3378,"style":3075},[3074],[574,3380,3381,3384],{"style":3078},[574,3382],{"className":3383,"style":3055},[750],[574,3385,3387],{"className":3386},[755,756,757,758],[574,3388,3390],{"className":3389},[712,758],[574,3391,615],{"className":3392},[712,758],[574,3394,766],{"className":3395},[765],[574,3397,3399],{"className":3398},[738],[574,3400,3402],{"className":3401,"style":3100},[742],[574,3403],{},[574,3405],{"className":3406},[914,3035],[574,3408,3410],{"className":3409,"style":3333},[914,3332],[574,3411,642],{"className":3412},[3337,3338],[574,3414],{"className":3415,"style":918},[779],[574,3417,3419,3453,3457],{"className":3418},[922],[574,3420,3422],{"className":3421},[922],[574,3423,3426],{"className":3424},[712,3425],"vbox",[574,3427,3430],{"className":3428},[3429],"thinbox",[574,3431,3434,3438,3449],{"className":3432},[3433],"rlap",[574,3435],{"className":3436,"style":3437},[707],"height:0.8889em;vertical-align:-0.1944em;",[574,3439,3442],{"className":3440},[3441],"inner",[574,3443,3445],{"className":3444},[712],[574,3446,3448],{"className":3447},[922],"",[574,3450],{"className":3451},[3452],"fix",[574,3454],{"className":3455},[779,3456],"nobreak",[574,3458,645],{"className":3459},[922],[574,3461],{"className":3462,"style":918},[779],[574,3464,3466,3470],{"className":3465},[703],[574,3467],{"className":3468,"style":3469},[707],"height:1.3651em;vertical-align:-0.52em;",[574,3471,3473,3476,3545],{"className":3472},[712],[574,3474],{"className":3475},[718,3035],[574,3477,3479],{"className":3478},[2946],[574,3480,3482,3536],{"className":3481},[733,734],[574,3483,3485,3533],{"className":3484},[738],[574,3486,3488,3511,3519],{"className":3487,"style":3048},[742],[574,3489,3490,3493],{"style":3051},[574,3491],{"className":3492,"style":3055},[750],[574,3494,3496],{"className":3495},[755,756,757,758],[574,3497,3499,3502,3505,3508],{"className":3498},[712,758],[574,3500,600],{"className":3501,"style":714},[712,713,758],[574,3503,605],{"className":3504},[718,758],[574,3506,611],{"className":3507,"style":725},[712,713,758],[574,3509,642],{"className":3510},[914,758],[574,3512,3513,3516],{"style":3067},[574,3514],{"className":3515,"style":3055},[750],[574,3517],{"className":3518,"style":3075},[3074],[574,3520,3521,3524],{"style":3078},[574,3522],{"className":3523,"style":3055},[750],[574,3525,3527],{"className":3526},[755,756,757,758],[574,3528,3530],{"className":3529},[712,758],[574,3531,615],{"className":3532},[712,758],[574,3534,766],{"className":3535},[765],[574,3537,3539],{"className":3538},[738],[574,3540,3543],{"className":3541,"style":3542},[742],"height:0.52em;",[574,3544],{},[574,3546],{"className":3547},[914,3035],[2713,3549,3550,3551,3691,3692,3695],{},"Glauben, für ",[574,3552,3554,3598],{"className":3553},[581],[574,3555,3557],{"className":3556},[585],[587,3558,3559],{"xmlns":589},[592,3560,3561,3595],{},[595,3562,3563,3565,3567,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587,3589,3591,3593],{},[598,3564,600],{},[602,3566,605],{"stretchy":604},[598,3568,611],{},[602,3570,618],{},[598,3572,1493],{},[602,3574,642],{"stretchy":604},[602,3576,645],{},[598,3578,600],{},[602,3580,605],{"stretchy":604},[598,3582,611],{},[602,3584,642],{"stretchy":604},[602,3586,618],{},[598,3588,600],{},[602,3590,605],{"stretchy":604},[598,3592,1493],{},[602,3594,642],{"stretchy":604},[691,3596,3597],{"encoding":693},"E(X + Y) = E(X) + E(Y)",[574,3599,3601,3625,3646,3673],{"className":3600,"ariaHidden":699},[698],[574,3602,3604,3607,3610,3613,3616,3619,3622],{"className":3603},[703],[574,3605],{"className":3606,"style":708},[707],[574,3608,600],{"className":3609,"style":714},[712,713],[574,3611,605],{"className":3612},[718],[574,3614,611],{"className":3615,"style":725},[712,713],[574,3617],{"className":3618,"style":780},[779],[574,3620,618],{"className":3621},[784],[574,3623],{"className":3624,"style":780},[779],[574,3626,3628,3631,3634,3637,3640,3643],{"className":3627},[703],[574,3629],{"className":3630,"style":708},[707],[574,3632,1493],{"className":3633,"style":780},[712,713],[574,3635,642],{"className":3636},[914],[574,3638],{"className":3639,"style":918},[779],[574,3641,645],{"className":3642},[922],[574,3644],{"className":3645,"style":918},[779],[574,3647,3649,3652,3655,3658,3661,3664,3667,3670],{"className":3648},[703],[574,3650],{"className":3651,"style":708},[707],[574,3653,600],{"className":3654,"style":714},[712,713],[574,3656,605],{"className":3657},[718],[574,3659,611],{"className":3660,"style":725},[712,713],[574,3662,642],{"className":3663},[914],[574,3665],{"className":3666,"style":780},[779],[574,3668,618],{"className":3669},[784],[574,3671],{"className":3672,"style":780},[779],[574,3674,3676,3679,3682,3685,3688],{"className":3675},[703],[574,3677],{"className":3678,"style":708},[707],[574,3680,600],{"className":3681,"style":714},[712,713],[574,3683,605],{"className":3684},[718],[574,3686,1493],{"className":3687,"style":780},[712,713],[574,3689,642],{"className":3690},[914]," brauche man Unabhängigkeit. Erst bei der ",[569,3693,3694],{},"Varianz"," einer Summe spielt die Abhängigkeit eine Rolle.",{"title":3697,"searchDepth":3698,"depth":3698,"links":3699},"",2,[3700,3701,3702],{"id":562,"depth":3698,"text":563},{"id":1460,"depth":3698,"text":1461},{"id":2707,"depth":3698,"text":2708},[3704,3707,3709,3711,3713,3715,3718,3721],{"lhs":3705,"rhs":3706},"(a*x1 + c)*p + (a*x2 + c)*(1-p)","a*(x1*p + x2*(1-p)) + c",{"lhs":3708,"rhs":1622},"3.5 + 3.5",{"lhs":3710,"rhs":1876},"2 * 3.5 - 3",{"lhs":3712,"rhs":1876},"(2*1-3 + 2*2-3 + 2*3-3 + 2*4-3 + 2*5-3 + 2*6-3) \u002F 6",{"lhs":3714,"rhs":1571},"10 * 0.3",{"lhs":3716,"rhs":3717},"(1 + 4 + 9 + 16 + 25 + 36) \u002F 6","91\u002F6",{"lhs":3719,"rhs":3720},"round(91\u002F6, 2)","15.17",{"lhs":3722,"rhs":3723},"3.5^2","12.25","a, b, c \\in \\mathbb{R},\\ E(X) \\text{ und } E(Y) \\text{ existieren}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b, c \\in \\mathbb{R},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(X)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">und\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(Y)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">existieren\u003C\u002Fspan>",null,"md","expectation-linearity","E(aX + bY + c) = a\\,E(X) + b\\,E(Y) + c","\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>a\u003C\u002Fmi>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>Y\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>c\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E(aX + bY + c) = a\\,E(X) + b\\,E(Y) + c\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">bY\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\">c\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" 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