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Intervall.",[560,1083,1085],{"id":1084},"beispiele","Beispiele",[565,1087,1088,1089,1174,1175,1250,1251,1317,1318,1514,1515,1789,1790,1818],{},"Gegeben ist ",[577,1090,1092,1119],{"className":1091},[580],[577,1093,1095],{"className":1094},[584],[586,1096,1097],{"xmlns":588},[590,1098,1099,1116],{},[593,1100,1101,1103,1105,1107,1109,1111,1114],{},[596,1102,598],{},[681,1104,684],{"stretchy":683},[596,1106,687],{},[681,1108,690],{"stretchy":683},[681,1110,836],{},[695,1112,1113],{},"0,5",[596,1115,687],{},[600,1117,1118],{"encoding":602},"f(x) = 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",[577,1176,1178,1201],{"className":1177},[580],[577,1179,1181],{"className":1180},[584],[586,1182,1183],{"xmlns":588},[590,1184,1185,1198],{},[593,1186,1187,1189,1191,1193,1195],{},[695,1188,697],{},[681,1190,954],{},[596,1192,687],{},[681,1194,954],{},[695,1196,1197],{},"2",[600,1199,1200],{"encoding":602},"0 \\leq x \\leq 2",[577,1202,1204,1223,1241],{"className":1203,"ariaHidden":607},[606],[577,1205,1207,1211,1214,1217,1220],{"className":1206},[611],[577,1208],{"className":1209,"style":1210},[615],"height:0.7804em;vertical-align:-0.136em;",[577,1212,697],{"className":1213},[620],[577,1215],{"className":1216,"style":729},[728],[577,1218,954],{"className":1219},[733],[577,1221],{"className":1222,"style":729},[728],[577,1224,1226,1229,1232,1235,1238],{"className":1225},[611],[577,1227],{"className":1228,"style":967},[615],[577,1230,687],{"className":1231},[620,621],[577,1233],{"className":1234,"style":729},[728],[577,1236,954],{"className":1237},[733],[577,1239],{"className":1240,"style":729},[728],[577,1242,1244,1247],{"className":1243},[611],[577,1245],{"className":1246,"style":743},[615],[577,1248,1197],{"className":1249},[620]," und ",[577,1252,1254,1278],{"className":1253},[580],[577,1255,1257],{"className":1256},[584],[586,1258,1259],{"xmlns":588},[590,1260,1261,1275],{},[593,1262,1263,1265,1267,1269,1271,1273],{},[596,1264,598],{},[681,1266,684],{"stretchy":683},[596,1268,687],{},[681,1270,690],{"stretchy":683},[681,1272,836],{},[695,1274,697],{},[600,1276,1277],{"encoding":602},"f(x) = 0",[577,1279,1281,1308],{"className":1280,"ariaHidden":607},[606],[577,1282,1284,1287,1290,1293,1296,1299,1302,1305],{"className":1283},[611],[577,1285],{"className":1286,"style":710},[615],[577,1288,598],{"className":1289,"style":622},[620,621],[577,1291,684],{"className":1292},[717],[577,1294,687],{"className":1295},[620,621],[577,1297,690],{"className":1298},[724],[577,1300],{"className":1301,"style":729},[728],[577,1303,836],{"className":1304},[733],[577,1306],{"className":1307,"style":729},[728],[577,1309,1311,1314],{"className":1310},[611],[577,1312],{"className":1313,"style":743},[615],[577,1315,697],{"className":1316},[620]," sonst. Eine Stammfunktion ist ",[577,1319,1321,1357],{"className":1320},[580],[577,1322,1324],{"className":1323},[584],[586,1325,1326],{"xmlns":588},[590,1327,1328,1354],{},[593,1329,1330,1333,1335,1337,1339,1341],{},[596,1331,1332],{},"F",[681,1334,684],{"stretchy":683},[596,1336,687],{},[681,1338,690],{"stretchy":683},[681,1340,836],{},[1342,1343,1344,1351],"mfrac",{},[1345,1346,1347,1349],"msup",{},[596,1348,687],{},[695,1350,1197],{},[695,1352,1353],{},"4",[600,1355,1356],{"encoding":602},"F(x) = \\frac{x^2}{4}",[577,1358,1360,1387],{"className":1359,"ariaHidden":607},[606],[577,1361,1363,1366,1369,1372,1375,1378,1381,1384],{"className":1362},[611],[577,1364],{"className":1365,"style":710},[615],[577,1367,1332],{"className":1368,"style":861},[620,621],[577,1370,684],{"className":1371},[717],[577,1373,687],{"className":1374},[620,621],[577,1376,690],{"className":1377},[724],[577,1379],{"className":1380,"style":729},[728],[577,1382,836],{"className":1383},[733],[577,1385],{"className":1386,"style":729},[728],[577,1388,1390,1394],{"className":1389},[611],[577,1391],{"className":1392,"style":1393},[615],"height:1.3629em;vertical-align:-0.345em;",[577,1395,1397,1401,1511],{"className":1396},[620],[577,1398],{"className":1399},[717,1400],"nulldelimiter",[577,1402,1404],{"className":1403},[1342],[577,1405,1409,1502],{"className":1406},[1407,1408],"vlist-t","vlist-t2",[577,1410,1413,1497],{"className":1411},[1412],"vlist-r",[577,1414,1418,1439,1450],{"className":1415,"style":1417},[1416],"vlist","height:1.0179em;",[577,1419,1421,1426],{"style":1420},"top:-2.655em;",[577,1422],{"className":1423,"style":1425},[1424],"pstrut","height:3em;",[577,1427,1433],{"className":1428},[1429,1430,1431,1432],"sizing","reset-size6","size3","mtight",[577,1434,1436],{"className":1435},[620,1432],[577,1437,1353],{"className":1438},[620,1432],[577,1440,1442,1445],{"style":1441},"top:-3.23em;",[577,1443],{"className":1444,"style":1425},[1424],[577,1446],{"className":1447,"style":1449},[1448],"frac-line","border-bottom-width:0.04em;",[577,1451,1453,1456],{"style":1452},"top:-3.394em;",[577,1454],{"className":1455,"style":1425},[1424],[577,1457,1459],{"className":1458},[1429,1430,1431,1432],[577,1460,1462],{"className":1461},[620,1432],[577,1463,1465,1468],{"className":1464},[620,1432],[577,1466,687],{"className":1467},[620,621,1432],[577,1469,1472],{"className":1470},[1471],"msupsub",[577,1473,1475],{"className":1474},[1407],[577,1476,1478],{"className":1477},[1412],[577,1479,1482],{"className":1480,"style":1481},[1416],"height:0.8913em;",[577,1483,1485,1489],{"style":1484},"top:-2.931em;margin-right:0.0714em;",[577,1486],{"className":1487,"style":1488},[1424],"height:2.5em;",[577,1490,1494],{"className":1491},[1429,1492,1493,1432],"reset-size3","size1",[577,1495,1197],{"className":1496},[620,1432],[577,1498,1501],{"className":1499},[1500],"vlist-s","​",[577,1503,1505],{"className":1504},[1412],[577,1506,1509],{"className":1507,"style":1508},[1416],"height:0.345em;",[577,1510],{},[577,1512],{"className":1513},[724,1400],". Die Fläche ist ",[577,1516,1518,1557],{"className":1517},[580],[577,1519,1521],{"className":1520},[584],[586,1522,1523],{"xmlns":588},[590,1524,1525,1554],{},[593,1526,1527,1537,1540,1550,1552],{},[1342,1528,1529,1535],{},[1345,1530,1531,1533],{},[695,1532,1197],{},[695,1534,1197],{},[695,1536,1353],{},[681,1538,1539],{},"−",[1342,1541,1542,1548],{},[1345,1543,1544,1546],{},[695,1545,697],{},[695,1547,1197],{},[695,1549,1353],{},[681,1551,836],{},[695,1553,795],{},[600,1555,1556],{"encoding":602},"\\frac{2^2}{4} - \\frac{0^2}{4} = 1",[577,1558,1560,1671,1780],{"className":1559,"ariaHidden":607},[606],[577,1561,1563,1566,1660,1664,1668],{"className":1562},[611],[577,1564],{"className":1565,"style":1393},[615],[577,1567,1569,1572,1657],{"className":1568},[620],[577,1570],{"className":1571},[717,1400],[577,1573,1575],{"className":1574},[1342],[577,1576,1578,1649],{"className":1577},[1407,1408],[577,1579,1581,1646],{"className":1580},[1412],[577,1582,1584,1598,1606],{"className":1583,"style":1417},[1416],[577,1585,1586,1589],{"style":1420},[577,1587],{"className":1588,"style":1425},[1424],[577,1590,1592],{"className":1591},[1429,1430,1431,1432],[577,1593,1595],{"className":1594},[620,1432],[577,1596,1353],{"className":1597},[620,1432],[577,1599,1600,1603],{"style":1441},[577,1601],{"className":1602,"style":1425},[1424],[577,1604],{"className":1605,"style":1449},[1448],[577,1607,1608,1611],{"style":1452},[577,1609],{"className":1610,"style":1425},[1424],[577,1612,1614],{"className":1613},[1429,1430,1431,1432],[577,1615,1617],{"className":1616},[620,1432],[577,1618,1620,1623],{"className":1619},[620,1432],[577,1621,1197],{"className":1622},[620,1432],[577,1624,1626],{"className":1625},[1471],[577,1627,1629],{"className":1628},[1407],[577,1630,1632],{"className":1631},[1412],[577,1633,1635],{"className":1634,"style":1481},[1416],[577,1636,1637,1640],{"style":1484},[577,1638],{"className":1639,"style":1488},[1424],[577,1641,1643],{"className":1642},[1429,1492,1493,1432],[577,1644,1197],{"className":1645},[620,1432],[577,1647,1501],{"className":1648},[1500],[577,1650,1652],{"className":1651},[1412],[577,1653,1655],{"className":1654,"style":1508},[1416],[577,1656],{},[577,1658],{"className":1659},[724,1400],[577,1661],{"className":1662,"style":1663},[728],"margin-right:0.2222em;",[577,1665,1539],{"className":1666},[1667],"mbin",[577,1669],{"className":1670,"style":1663},[728],[577,1672,1674,1677,1771,1774,1777],{"className":1673},[611],[577,1675],{"className":1676,"style":1393},[615],[577,1678,1680,1683,1768],{"className":1679},[620],[577,1681],{"className":1682},[717,1400],[577,1684,1686],{"className":1685},[1342],[577,1687,1689,1760],{"className":1688},[1407,1408],[577,1690,1692,1757],{"className":1691},[1412],[577,1693,1695,1709,1717],{"className":1694,"style":1417},[1416],[577,1696,1697,1700],{"style":1420},[577,1698],{"className":1699,"style":1425},[1424],[577,1701,1703],{"className":1702},[1429,1430,1431,1432],[577,1704,1706],{"className":1705},[620,1432],[577,1707,1353],{"className":1708},[620,1432],[577,1710,1711,1714],{"style":1441},[577,1712],{"className":1713,"style":1425},[1424],[577,1715],{"className":1716,"style":1449},[1448],[577,1718,1719,1722],{"style":1452},[577,1720],{"className":1721,"style":1425},[1424],[577,1723,1725],{"className":1724},[1429,1430,1431,1432],[577,1726,1728],{"className":1727},[620,1432],[577,1729,1731,1734],{"className":1730},[620,1432],[577,1732,697],{"className":1733},[620,1432],[577,1735,1737],{"className":1736},[1471],[577,1738,1740],{"className":1739},[1407],[577,1741,1743],{"className":1742},[1412],[577,1744,1746],{"className":1745,"style":1481},[1416],[577,1747,1748,1751],{"style":1484},[577,1749],{"className":1750,"style":1488},[1424],[577,1752,1754],{"className":1753},[1429,1492,1493,1432],[577,1755,1197],{"className":1756},[620,1432],[577,1758,1501],{"className":1759},[1500],[577,1761,1763],{"className":1762},[1412],[577,1764,1766],{"className":1765,"style":1508},[1416],[577,1767],{},[577,1769],{"className":1770},[724,1400],[577,1772],{"className":1773,"style":729},[728],[577,1775,836],{"className":1776},[733],[577,1778],{"className":1779,"style":729},[728],[577,1781,1783,1786],{"className":1782},[611],[577,1784],{"className":1785,"style":743},[615],[577,1787,795],{"className":1788},[620],", und ",[577,1791,1793,1806],{"className":1792},[580],[577,1794,1796],{"className":1795},[584],[586,1797,1798],{"xmlns":588},[590,1799,1800,1804],{},[593,1801,1802],{},[596,1803,598],{},[600,1805,598],{"encoding":602},[577,1807,1809],{"className":1808,"ariaHidden":607},[606],[577,1810,1812,1815],{"className":1811},[611],[577,1813],{"className":1814,"style":616},[615],[577,1816,598],{"className":1817,"style":622},[620,621]," ist nicht negativ, also eine Dichte.",[577,1820,1823],{"className":1821},[1822],"katex-display",[577,1824,1826,1884],{"className":1825},[580],[577,1827,1829],{"className":1828},[584],[586,1830,1832],{"xmlns":588,"display":1831},"block",[590,1833,1834,1881],{},[593,1835,1836,1838,1840,1842,1844,1846,1848,1851,1853,1855,1865,1867,1877,1879],{},[596,1837,828],{},[681,1839,684],{"stretchy":683},[695,1841,1113],{},[681,1843,954],{},[596,1845,833],{},[681,1847,954],{},[695,1849,1850],{},"1,5",[681,1852,690],{"stretchy":683},[681,1854,836],{},[1342,1856,1857,1863],{},[1345,1858,1859,1861],{},[695,1860,1850],{},[695,1862,1197],{},[695,1864,1353],{},[681,1866,1539],{},[1342,1868,1869,1875],{},[1345,1870,1871,1873],{},[695,1872,1113],{},[695,1874,1197],{},[695,1876,1353],{},[681,1878,836],{},[695,1880,1113],{},[600,1882,1883],{"encoding":602},"P(0{,}5 \\leq X \\leq 1{,}5) = \\frac{1{,}5^2}{4} - \\frac{0{,}5^2}{4} = 0{,}5",[577,1885,1887,1920,1939,1969,2089,2201],{"className":1886,"ariaHidden":607},[606],[577,1888,1890,1893,1896,1899,1902,1908,1911,1914,1917],{"className":1889},[611],[577,1891],{"className":1892,"style":710},[615],[577,1894,828],{"className":1895,"style":861},[620,621],[577,1897,684],{"className":1898},[717],[577,1900,697],{"className":1901},[620],[577,1903,1905],{"className":1904},[620],[577,1906,1166],{"className":1907},[1165],[577,1909,1170],{"className":1910},[620],[577,1912],{"className":1913,"style":729},[728],[577,1915,954],{"className":1916},[733],[577,1918],{"className":1919,"style":729},[728],[577,1921,1923,1927,1930,1933,1936],{"className":1922},[611],[577,1924],{"className":1925,"style":1926},[615],"height:0.8193em;vertical-align:-0.136em;",[577,1928,833],{"className":1929,"style":868},[620,621],[577,1931],{"className":1932,"style":729},[728],[577,1934,954],{"className":1935},[733],[577,1937],{"className":1938,"style":729},[728],[577,1940,1942,1945,1948,1954,1957,1960,1963,1966],{"className":1941},[611],[577,1943],{"className":1944,"style":710},[615],[577,1946,795],{"className":1947},[620],[577,1949,1951],{"className":1950},[620],[577,1952,1166],{"className":1953},[1165],[577,1955,1170],{"className":1956},[620],[577,1958,690],{"className":1959},[724],[577,1961],{"className":1962,"style":729},[728],[577,1964,836],{"className":1965},[733],[577,1967],{"className":1968,"style":729},[728],[577,1970,1972,1976,2080,2083,2086],{"className":1971},[611],[577,1973],{"className":1974,"style":1975},[615],"height:2.1771em;vertical-align:-0.686em;",[577,1977,1979,1982,2077],{"className":1978},[620],[577,1980],{"className":1981},[717,1400],[577,1983,1985],{"className":1984},[1342],[577,1986,1988,2068],{"className":1987},[1407,1408],[577,1989,1991,2065],{"className":1990},[1412],[577,1992,1995,2007,2015],{"className":1993,"style":1994},[1416],"height:1.4911em;",[577,1996,1998,2001],{"style":1997},"top:-2.314em;",[577,1999],{"className":2000,"style":1425},[1424],[577,2002,2004],{"className":2003},[620],[577,2005,1353],{"className":2006},[620],[577,2008,2009,2012],{"style":1441},[577,2010],{"className":2011,"style":1425},[1424],[577,2013],{"className":2014,"style":1449},[1448],[577,2016,2018,2021],{"style":2017},"top:-3.677em;",[577,2019],{"className":2020,"style":1425},[1424],[577,2022,2024,2027,2033],{"className":2023},[620],[577,2025,795],{"className":2026},[620],[577,2028,2030],{"className":2029},[620],[577,2031,1166],{"className":2032},[1165],[577,2034,2036,2039],{"className":2035},[620],[577,2037,1170],{"className":2038},[620],[577,2040,2042],{"className":2041},[1471],[577,2043,2045],{"className":2044},[1407],[577,2046,2048],{"className":2047},[1412],[577,2049,2052],{"className":2050,"style":2051},[1416],"height:0.8141em;",[577,2053,2055,2059],{"style":2054},"top:-3.063em;margin-right:0.05em;",[577,2056],{"className":2057,"style":2058},[1424],"height:2.7em;",[577,2060,2062],{"className":2061},[1429,1430,1431,1432],[577,2063,1197],{"className":2064},[620,1432],[577,2066,1501],{"className":2067},[1500],[577,2069,2071],{"className":2070},[1412],[577,2072,2075],{"className":2073,"style":2074},[1416],"height:0.686em;",[577,2076],{},[577,2078],{"className":2079},[724,1400],[577,2081],{"className":2082,"style":1663},[728],[577,2084,1539],{"className":2085},[1667],[577,2087],{"className":2088,"style":1663},[728],[577,2090,2092,2095,2192,2195,2198],{"className":2091},[611],[577,2093],{"className":2094,"style":1975},[615],[577,2096,2098,2101,2189],{"className":2097},[620],[577,2099],{"className":2100},[717,1400],[577,2102,2104],{"className":2103},[1342],[577,2105,2107,2181],{"className":2106},[1407,1408],[577,2108,2110,2178],{"className":2109},[1412],[577,2111,2113,2124,2132],{"className":2112,"style":1994},[1416],[577,2114,2115,2118],{"style":1997},[577,2116],{"className":2117,"style":1425},[1424],[577,2119,2121],{"className":2120},[620],[577,2122,1353],{"className":2123},[620],[577,2125,2126,2129],{"style":1441},[577,2127],{"className":2128,"style":1425},[1424],[577,2130],{"className":2131,"style":1449},[1448],[577,2133,2134,2137],{"style":2017},[577,2135],{"className":2136,"style":1425},[1424],[577,2138,2140,2143,2149],{"className":2139},[620],[577,2141,697],{"className":2142},[620],[577,2144,2146],{"className":2145},[620],[577,2147,1166],{"className":2148},[1165],[577,2150,2152,2155],{"className":2151},[620],[577,2153,1170],{"className":2154},[620],[577,2156,2158],{"className":2157},[1471],[577,2159,2161],{"className":2160},[1407],[577,2162,2164],{"className":2163},[1412],[577,2165,2167],{"className":2166,"style":2051},[1416],[577,2168,2169,2172],{"style":2054},[577,2170],{"className":2171,"style":2058},[1424],[577,2173,2175],{"className":2174},[1429,1430,1431,1432],[577,2176,1197],{"className":2177},[620,1432],[577,2179,1501],{"className":2180},[1500],[577,2182,2184],{"className":2183},[1412],[577,2185,2187],{"className":2186,"style":2074},[1416],[577,2188],{},[577,2190],{"className":2191},[724,1400],[577,2193],{"className":2194,"style":729},[728],[577,2196,836],{"className":2197},[733],[577,2199],{"className":2200,"style":729},[728],[577,2202,2204,2207,2210,2216],{"className":2203},[611],[577,2205],{"className":2206,"style":1155},[615],[577,2208,697],{"className":2209},[620],[577,2211,2213],{"className":2212},[620],[577,2214,1166],{"className":2215},[1165],[577,2217,1170],{"className":2218},[620],[565,2220,2221,2222,2251,2252,2353,2354,2411,2412,2440,2441,2469],{},"Für welches ",[577,2223,2225,2239],{"className":2224},[580],[577,2226,2228],{"className":2227},[584],[586,2229,2230],{"xmlns":588},[590,2231,2232,2237],{},[593,2233,2234],{},[596,2235,2236],{},"c",[600,2238,2236],{"encoding":602},[577,2240,2242],{"className":2241,"ariaHidden":607},[606],[577,2243,2245,2248],{"className":2244},[611],[577,2246],{"className":2247,"style":773},[615],[577,2249,2236],{"className":2250},[620,621]," ist ",[577,2253,2255,2285],{"className":2254},[580],[577,2256,2258],{"className":2257},[584],[586,2259,2260],{"xmlns":588},[590,2261,2262,2282],{},[593,2263,2264,2266,2268,2270,2272,2274,2276],{},[596,2265,598],{},[681,2267,684],{"stretchy":683},[596,2269,687],{},[681,2271,690],{"stretchy":683},[681,2273,836],{},[596,2275,2236],{},[1345,2277,2278,2280],{},[596,2279,687],{},[695,2281,1197],{},[600,2283,2284],{"encoding":602},"f(x) = c x^2",[577,2286,2288,2315],{"className":2287,"ariaHidden":607},[606],[577,2289,2291,2294,2297,2300,2303,2306,2309,2312],{"className":2290},[611],[577,2292],{"className":2293,"style":710},[615],[577,2295,598],{"className":2296,"style":622},[620,621],[577,2298,684],{"className":2299},[717],[577,2301,687],{"className":2302},[620,621],[577,2304,690],{"className":2305},[724],[577,2307],{"className":2308,"style":729},[728],[577,2310,836],{"className":2311},[733],[577,2313],{"className":2314,"style":729},[728],[577,2316,2318,2321,2324],{"className":2317},[611],[577,2319],{"className":2320,"style":2051},[615],[577,2322,2236],{"className":2323},[620,621],[577,2325,2327,2330],{"className":2326},[620],[577,2328,687],{"className":2329},[620,621],[577,2331,2333],{"className":2332},[1471],[577,2334,2336],{"className":2335},[1407],[577,2337,2339],{"className":2338},[1412],[577,2340,2342],{"className":2341,"style":2051},[1416],[577,2343,2344,2347],{"style":2054},[577,2345],{"className":2346,"style":2058},[1424],[577,2348,2350],{"className":2349},[1429,1430,1431,1432],[577,2351,1197],{"className":2352},[620,1432]," auf ",[577,2355,2357,2383],{"className":2356},[580],[577,2358,2360],{"className":2359},[584],[586,2361,2362],{"xmlns":588},[590,2363,2364,2380],{},[593,2365,2366,2369,2371,2374,2377],{},[681,2367,2368],{"stretchy":683},"[",[695,2370,697],{},[681,2372,2373],{"separator":607},";",[695,2375,2376],{},"3",[681,2378,2379],{"stretchy":683},"]",[600,2381,2382],{"encoding":602},"[0; 3]",[577,2384,2386],{"className":2385,"ariaHidden":607},[606],[577,2387,2389,2392,2395,2398,2401,2405,2408],{"className":2388},[611],[577,2390],{"className":2391,"style":710},[615],[577,2393,2368],{"className":2394},[717],[577,2396,697],{"className":2397},[620],[577,2399,2373],{"className":2400},[1165],[577,2402],{"className":2403,"style":2404},[728],"margin-right:0.1667em;",[577,2406,2376],{"className":2407},[620],[577,2409,2379],{"className":2410},[724]," (sonst ",[577,2413,2415,2428],{"className":2414},[580],[577,2416,2418],{"className":2417},[584],[586,2419,2420],{"xmlns":588},[590,2421,2422,2426],{},[593,2423,2424],{},[695,2425,697],{},[600,2427,697],{"encoding":602},[577,2429,2431],{"className":2430,"ariaHidden":607},[606],[577,2432,2434,2437],{"className":2433},[611],[577,2435],{"className":2436,"style":743},[615],[577,2438,697],{"className":2439},[620],") eine Dichte? Die Fläche muss ",[577,2442,2444,2457],{"className":2443},[580],[577,2445,2447],{"className":2446},[584],[586,2448,2449],{"xmlns":588},[590,2450,2451,2455],{},[593,2452,2453],{},[695,2454,795],{},[600,2456,795],{"encoding":602},[577,2458,2460],{"className":2459,"ariaHidden":607},[606],[577,2461,2463,2466],{"className":2462},[611],[577,2464],{"className":2465,"style":743},[615],[577,2467,795],{"className":2468},[620]," sein:",[577,2471,2473],{"className":2472},[1822],[577,2474,2476,2562],{"className":2475},[580],[577,2477,2479],{"className":2478},[584],[586,2480,2481],{"xmlns":588,"display":1831},[590,2482,2483,2559],{},[593,2484,2485,2495,2497,2503,2507,2511,2513,2515,2517,2520,2530,2532,2535,2537,2539,2541,2544,2547,2549,2551,2553],{},[2486,2487,2488,2491,2493],"msubsup",{},[681,2489,2490],{},"∫",[695,2492,697],{},[695,2494,2376],{},[596,2496,2236],{},[1345,2498,2499,2501],{},[596,2500,687],{},[695,2502,1197],{},[2504,2505,2506],"mtext",{}," ",[596,2508,2510],{"mathvariant":2509},"normal","d",[596,2512,687],{},[681,2514,836],{},[596,2516,2236],{},[681,2518,2519],{},"⋅",[1342,2521,2522,2528],{},[1345,2523,2524,2526],{},[695,2525,2376],{},[695,2527,2376],{},[695,2529,2376],{},[681,2531,836],{},[695,2533,2534],{},"9",[596,2536,2236],{},[681,2538,836],{},[695,2540,795],{},[728,2542],{"width":2543},"1em",[681,2545,2546],{},"⇒",[728,2548],{"width":2543},[596,2550,2236],{},[681,2552,836],{},[1342,2554,2555,2557],{},[695,2556,795],{},[695,2558,2534],{},[600,2560,2561],{"encoding":602},"\\int_0^3 c x^2\\,\\mathrm{d}x = c \\cdot \\frac{3^3}{3} = 9c = 1 \\quad\\Rightarrow\\quad c = \\frac{1}{9}",[577,2563,2565,2687,2706,2809,2830,2855,2873],{"className":2564,"ariaHidden":607},[606],[577,2566,2568,2572,2631,2634,2637,2668,2671,2675,2678,2681,2684],{"className":2567},[611],[577,2569],{"className":2570,"style":2571},[615],"height:2.476em;vertical-align:-0.9119em;",[577,2573,2576,2582],{"className":2574},[2575],"mop",[577,2577,2490],{"className":2578,"style":2581},[2575,2579,2580],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[577,2583,2585],{"className":2584},[1471],[577,2586,2588,2622],{"className":2587},[1407,1408],[577,2589,2591,2619],{"className":2590},[1412],[577,2592,2595,2607],{"className":2593,"style":2594},[1416],"height:1.564em;",[577,2596,2598,2601],{"style":2597},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[577,2599],{"className":2600,"style":2058},[1424],[577,2602,2604],{"className":2603},[1429,1430,1431,1432],[577,2605,697],{"className":2606},[620,1432],[577,2608,2610,2613],{"style":2609},"top:-3.8129em;margin-right:0.05em;",[577,2611],{"className":2612,"style":2058},[1424],[577,2614,2616],{"className":2615},[1429,1430,1431,1432],[577,2617,2376],{"className":2618},[620,1432],[577,2620,1501],{"className":2621},[1500],[577,2623,2625],{"className":2624},[1412],[577,2626,2629],{"className":2627,"style":2628},[1416],"height:0.9119em;",[577,2630],{},[577,2632],{"className":2633,"style":2404},[728],[577,2635,2236],{"className":2636},[620,621],[577,2638,2640,2643],{"className":2639},[620],[577,2641,687],{"className":2642},[620,621],[577,2644,2646],{"className":2645},[1471],[577,2647,2649],{"className":2648},[1407],[577,2650,2652],{"className":2651},[1412],[577,2653,2656],{"className":2654,"style":2655},[1416],"height:0.8641em;",[577,2657,2659,2662],{"style":2658},"top:-3.113em;margin-right:0.05em;",[577,2660],{"className":2661,"style":2058},[1424],[577,2663,2665],{"className":2664},[1429,1430,1431,1432],[577,2666,1197],{"className":2667},[620,1432],[577,2669],{"className":2670,"style":2404},[728],[577,2672,2510],{"className":2673},[620,2674],"mathrm",[577,2676,687],{"className":2677},[620,621],[577,2679],{"className":2680,"style":729},[728],[577,2682,836],{"className":2683},[733],[577,2685],{"className":2686,"style":729},[728],[577,2688,2690,2694,2697,2700,2703],{"className":2689},[611],[577,2691],{"className":2692,"style":2693},[615],"height:0.4445em;",[577,2695,2236],{"className":2696},[620,621],[577,2698],{"className":2699,"style":1663},[728],[577,2701,2519],{"className":2702},[1667],[577,2704],{"className":2705,"style":1663},[728],[577,2707,2709,2712,2800,2803,2806],{"className":2708},[611],[577,2710],{"className":2711,"style":1975},[615],[577,2713,2715,2718,2797],{"className":2714},[620],[577,2716],{"className":2717},[717,1400],[577,2719,2721],{"className":2720},[1342],[577,2722,2724,2789],{"className":2723},[1407,1408],[577,2725,2727,2786],{"className":2726},[1412],[577,2728,2730,2741,2749],{"className":2729,"style":1994},[1416],[577,2731,2732,2735],{"style":1997},[577,2733],{"className":2734,"style":1425},[1424],[577,2736,2738],{"className":2737},[620],[577,2739,2376],{"className":2740},[620],[577,2742,2743,2746],{"style":1441},[577,2744],{"className":2745,"style":1425},[1424],[577,2747],{"className":2748,"style":1449},[1448],[577,2750,2751,2754],{"style":2017},[577,2752],{"className":2753,"style":1425},[1424],[577,2755,2757],{"className":2756},[620],[577,2758,2760,2763],{"className":2759},[620],[577,2761,2376],{"className":2762},[620],[577,2764,2766],{"className":2765},[1471],[577,2767,2769],{"className":2768},[1407],[577,2770,2772],{"className":2771},[1412],[577,2773,2775],{"className":2774,"style":2051},[1416],[577,2776,2777,2780],{"style":2054},[577,2778],{"className":2779,"style":2058},[1424],[577,2781,2783],{"className":2782},[1429,1430,1431,1432],[577,2784,2376],{"className":2785},[620,1432],[577,2787,1501],{"className":2788},[1500],[577,2790,2792],{"className":2791},[1412],[577,2793,2795],{"className":2794,"style":2074},[1416],[577,2796],{},[577,2798],{"className":2799},[724,1400],[577,2801],{"className":2802,"style":729},[728],[577,2804,836],{"className":2805},[733],[577,2807],{"className":2808,"style":729},[728],[577,2810,2812,2815,2818,2821,2824,2827],{"className":2811},[611],[577,2813],{"className":2814,"style":743},[615],[577,2816,2534],{"className":2817},[620],[577,2819,2236],{"className":2820},[620,621],[577,2822],{"className":2823,"style":729},[728],[577,2825,836],{"className":2826},[733],[577,2828],{"className":2829,"style":729},[728],[577,2831,2833,2836,2839,2843,2846,2849,2852],{"className":2832},[611],[577,2834],{"className":2835,"style":743},[615],[577,2837,795],{"className":2838},[620],[577,2840],{"className":2841,"style":2842},[728],"margin-right:1em;",[577,2844],{"className":2845,"style":729},[728],[577,2847,2546],{"className":2848},[733],[577,2850],{"className":2851,"style":2842},[728],[577,2853],{"className":2854,"style":729},[728],[577,2856,2858,2861,2864,2867,2870],{"className":2857},[611],[577,2859],{"className":2860,"style":773},[615],[577,2862,2236],{"className":2863},[620,621],[577,2865],{"className":2866,"style":729},[728],[577,2868,836],{"className":2869},[733],[577,2871],{"className":2872,"style":729},[728],[577,2874,2876,2880],{"className":2875},[611],[577,2877],{"className":2878,"style":2879},[615],"height:2.0074em;vertical-align:-0.686em;",[577,2881,2883,2886,2940],{"className":2882},[620],[577,2884],{"className":2885},[717,1400],[577,2887,2889],{"className":2888},[1342],[577,2890,2892,2932],{"className":2891},[1407,1408],[577,2893,2895,2929],{"className":2894},[1412],[577,2896,2899,2910,2918],{"className":2897,"style":2898},[1416],"height:1.3214em;",[577,2900,2901,2904],{"style":1997},[577,2902],{"className":2903,"style":1425},[1424],[577,2905,2907],{"className":2906},[620],[577,2908,2534],{"className":2909},[620],[577,2911,2912,2915],{"style":1441},[577,2913],{"className":2914,"style":1425},[1424],[577,2916],{"className":2917,"style":1449},[1448],[577,2919,2920,2923],{"style":2017},[577,2921],{"className":2922,"style":1425},[1424],[577,2924,2926],{"className":2925},[620],[577,2927,795],{"className":2928},[620],[577,2930,1501],{"className":2931},[1500],[577,2933,2935],{"className":2934},[1412],[577,2936,2938],{"className":2937,"style":2074},[1416],[577,2939],{},[577,2941],{"className":2942},[724,1400],[565,2944,2945,2946,3352],{},"Damit ist ",[577,2947,2949,3008],{"className":2948},[580],[577,2950,2952],{"className":2951},[584],[586,2953,2954],{"xmlns":588},[590,2955,2956,3005],{},[593,2957,2958,2960,2962,2964,2966,2968,2970,2972,2978,2980,2990,2992,2999,3002],{},[596,2959,828],{},[681,2961,684],{"stretchy":683},[596,2963,833],{},[681,2965,954],{},[695,2967,795],{},[681,2969,690],{"stretchy":683},[681,2971,836],{},[1342,2973,2974,2976],{},[695,2975,795],{},[695,2977,2534],{},[681,2979,2519],{},[1342,2981,2982,2988],{},[1345,2983,2984,2986],{},[695,2985,795],{},[695,2987,2376],{},[695,2989,2376],{},[681,2991,836],{},[1342,2993,2994,2996],{},[695,2995,795],{},[695,2997,2998],{},"27",[681,3000,3001],{},"≈",[695,3003,3004],{},"0,037",[600,3006,3007],{"encoding":602},"P(X \\leq 1) = \\frac{1}{9} \\cdot \\frac{1^3}{3} = \\frac{1}{27} \\approx 0{,}037",[577,3009,3011,3035,3056,3141,3250,3333],{"className":3010,"ariaHidden":607},[606],[577,3012,3014,3017,3020,3023,3026,3029,3032],{"className":3013},[611],[577,3015],{"className":3016,"style":710},[615],[577,3018,828],{"className":3019,"style":861},[620,621],[577,3021,684],{"className":3022},[717],[577,3024,833],{"className":3025,"style":868},[620,621],[577,3027],{"className":3028,"style":729},[728],[577,3030,954],{"className":3031},[733],[577,3033],{"className":3034,"style":729},[728],[577,3036,3038,3041,3044,3047,3050,3053],{"className":3037},[611],[577,3039],{"className":3040,"style":710},[615],[577,3042,795],{"className":3043},[620],[577,3045,690],{"className":3046},[724],[577,3048],{"className":3049,"style":729},[728],[577,3051,836],{"className":3052},[733],[577,3054],{"className":3055,"style":729},[728],[577,3057,3059,3063,3132,3135,3138],{"className":3058},[611],[577,3060],{"className":3061,"style":3062},[615],"height:1.1901em;vertical-align:-0.345em;",[577,3064,3066,3069,3129],{"className":3065},[620],[577,3067],{"className":3068},[717,1400],[577,3070,3072],{"className":3071},[1342],[577,3073,3075,3121],{"className":3074},[1407,1408],[577,3076,3078,3118],{"className":3077},[1412],[577,3079,3082,3096,3104],{"className":3080,"style":3081},[1416],"height:0.8451em;",[577,3083,3084,3087],{"style":1420},[577,3085],{"className":3086,"style":1425},[1424],[577,3088,3090],{"className":3089},[1429,1430,1431,1432],[577,3091,3093],{"className":3092},[620,1432],[577,3094,2534],{"className":3095},[620,1432],[577,3097,3098,3101],{"style":1441},[577,3099],{"className":3100,"style":1425},[1424],[577,3102],{"className":3103,"style":1449},[1448],[577,3105,3106,3109],{"style":1452},[577,3107],{"className":3108,"style":1425},[1424],[577,3110,3112],{"className":3111},[1429,1430,1431,1432],[577,3113,3115],{"className":3114},[620,1432],[577,3116,795],{"className":3117},[620,1432],[577,3119,1501],{"className":3120},[1500],[577,3122,3124],{"className":3123},[1412],[577,3125,3127],{"className":3126,"style":1508},[1416],[577,3128],{},[577,3130],{"className":3131},[724,1400],[577,3133],{"className":3134,"style":1663},[728],[577,3136,2519],{"className":3137},[1667],[577,3139],{"className":3140,"style":1663},[728],[577,3142,3144,3147,3241,3244,3247],{"className":3143},[611],[577,3145],{"className":3146,"style":1393},[615],[577,3148,3150,3153,3238],{"className":3149},[620],[577,3151],{"className":3152},[717,1400],[577,3154,3156],{"className":3155},[1342],[577,3157,3159,3230],{"className":3158},[1407,1408],[577,3160,3162,3227],{"className":3161},[1412],[577,3163,3165,3179,3187],{"className":3164,"style":1417},[1416],[577,3166,3167,3170],{"style":1420},[577,3168],{"className":3169,"style":1425},[1424],[577,3171,3173],{"className":3172},[1429,1430,1431,1432],[577,3174,3176],{"className":3175},[620,1432],[577,3177,2376],{"className":3178},[620,1432],[577,3180,3181,3184],{"style":1441},[577,3182],{"className":3183,"style":1425},[1424],[577,3185],{"className":3186,"style":1449},[1448],[577,3188,3189,3192],{"style":1452},[577,3190],{"className":3191,"style":1425},[1424],[577,3193,3195],{"className":3194},[1429,1430,1431,1432],[577,3196,3198],{"className":3197},[620,1432],[577,3199,3201,3204],{"className":3200},[620,1432],[577,3202,795],{"className":3203},[620,1432],[577,3205,3207],{"className":3206},[1471],[577,3208,3210],{"className":3209},[1407],[577,3211,3213],{"className":3212},[1412],[577,3214,3216],{"className":3215,"style":1481},[1416],[577,3217,3218,3221],{"style":1484},[577,3219],{"className":3220,"style":1488},[1424],[577,3222,3224],{"className":3223},[1429,1492,1493,1432],[577,3225,2376],{"className":3226},[620,1432],[577,3228,1501],{"className":3229},[1500],[577,3231,3233],{"className":3232},[1412],[577,3234,3236],{"className":3235,"style":1508},[1416],[577,3237],{},[577,3239],{"className":3240},[724,1400],[577,3242],{"className":3243,"style":729},[728],[577,3245,836],{"className":3246},[733],[577,3248],{"className":3249,"style":729},[728],[577,3251,3253,3256,3324,3327,3330],{"className":3252},[611],[577,3254],{"className":3255,"style":3062},[615],[577,3257,3259,3262,3321],{"className":3258},[620],[577,3260],{"className":3261},[717,1400],[577,3263,3265],{"className":3264},[1342],[577,3266,3268,3313],{"className":3267},[1407,1408],[577,3269,3271,3310],{"className":3270},[1412],[577,3272,3274,3288,3296],{"className":3273,"style":3081},[1416],[577,3275,3276,3279],{"style":1420},[577,3277],{"className":3278,"style":1425},[1424],[577,3280,3282],{"className":3281},[1429,1430,1431,1432],[577,3283,3285],{"className":3284},[620,1432],[577,3286,2998],{"className":3287},[620,1432],[577,3289,3290,3293],{"style":1441},[577,3291],{"className":3292,"style":1425},[1424],[577,3294],{"className":3295,"style":1449},[1448],[577,3297,3298,3301],{"style":1452},[577,3299],{"className":3300,"style":1425},[1424],[577,3302,3304],{"className":3303},[1429,1430,1431,1432],[577,3305,3307],{"className":3306},[620,1432],[577,3308,795],{"className":3309},[620,1432],[577,3311,1501],{"className":3312},[1500],[577,3314,3316],{"className":3315},[1412],[577,3317,3319],{"className":3318,"style":1508},[1416],[577,3320],{},[577,3322],{"className":3323},[724,1400],[577,3325],{"className":3326,"style":729},[728],[577,3328,3001],{"className":3329},[733],[577,3331],{"className":3332,"style":729},[728],[577,3334,3336,3339,3342,3348],{"className":3335},[611],[577,3337],{"className":3338,"style":1155},[615],[577,3340,697],{"className":3341},[620],[577,3343,3345],{"className":3344},[620],[577,3346,1166],{"className":3347},[1165],[577,3349,3351],{"className":3350},[620],"037",".",[560,3354,3356],{"id":3355},"typische-fehler","Typische Fehler",[661,3358,3359,3482,3485],{},[664,3360,3361,3362,3428,3429,3481],{},"Den Funktionswert als Wahrscheinlichkeit angeben. ",[577,3363,3365,3389],{"className":3364},[580],[577,3366,3368],{"className":3367},[584],[586,3369,3370],{"xmlns":588},[590,3371,3372,3386],{},[593,3373,3374,3376,3378,3380,3382,3384],{},[596,3375,598],{},[681,3377,684],{"stretchy":683},[695,3379,1197],{},[681,3381,690],{"stretchy":683},[681,3383,836],{},[695,3385,795],{},[600,3387,3388],{"encoding":602},"f(2) = 1",[577,3390,3392,3419],{"className":3391,"ariaHidden":607},[606],[577,3393,3395,3398,3401,3404,3407,3410,3413,3416],{"className":3394},[611],[577,3396],{"className":3397,"style":710},[615],[577,3399,598],{"className":3400,"style":622},[620,621],[577,3402,684],{"className":3403},[717],[577,3405,1197],{"className":3406},[620],[577,3408,690],{"className":3409},[724],[577,3411],{"className":3412,"style":729},[728],[577,3414,836],{"className":3415},[733],[577,3417],{"className":3418,"style":729},[728],[577,3420,3422,3425],{"className":3421},[611],[577,3423],{"className":3424,"style":743},[615],[577,3426,795],{"className":3427},[620]," im ersten Beispiel heißt nicht, dass ",[577,3430,3432,3450],{"className":3431},[580],[577,3433,3435],{"className":3434},[584],[586,3436,3437],{"xmlns":588},[590,3438,3439,3447],{},[593,3440,3441,3443,3445],{},[596,3442,833],{},[681,3444,836],{},[695,3446,1197],{},[600,3448,3449],{"encoding":602},"X = 2",[577,3451,3453,3472],{"className":3452,"ariaHidden":607},[606],[577,3454,3456,3460,3463,3466,3469],{"className":3455},[611],[577,3457],{"className":3458,"style":3459},[615],"height:0.6833em;",[577,3461,833],{"className":3462,"style":868},[620,621],[577,3464],{"className":3465,"style":729},[728],[577,3467,836],{"className":3468},[733],[577,3470],{"className":3471,"style":729},[728],[577,3473,3475,3478],{"className":3474},[611],[577,3476],{"className":3477,"style":743},[615],[577,3479,1197],{"className":3480},[620]," sicher ist.",[664,3483,3484],{},"Nur die Fläche prüfen. Eine Dichte darf außerdem nirgends negativ sein.",[664,3486,3487,3488,3516,3517,3545,3546,810],{},"Über den ganzen Zahlenstrahl mit der Formel von ",[577,3489,3491,3504],{"className":3490},[580],[577,3492,3494],{"className":3493},[584],[586,3495,3496],{"xmlns":588},[590,3497,3498,3502],{},[593,3499,3500],{},[596,3501,598],{},[600,3503,598],{"encoding":602},[577,3505,3507],{"className":3506,"ariaHidden":607},[606],[577,3508,3510,3513],{"className":3509},[611],[577,3511],{"className":3512,"style":616},[615],[577,3514,598],{"className":3515,"style":622},[620,621]," integrieren, obwohl ",[577,3518,3520,3533],{"className":3519},[580],[577,3521,3523],{"className":3522},[584],[586,3524,3525],{"xmlns":588},[590,3526,3527,3531],{},[593,3528,3529],{},[596,3530,598],{},[600,3532,598],{"encoding":602},[577,3534,3536],{"className":3535,"ariaHidden":607},[606],[577,3537,3539,3542],{"className":3538},[611],[577,3540],{"className":3541,"style":616},[615],[577,3543,598],{"className":3544,"style":622},[620,621]," außerhalb des Intervalls ",[577,3547,3549,3562],{"className":3548},[580],[577,3550,3552],{"className":3551},[584],[586,3553,3554],{"xmlns":588},[590,3555,3556,3560],{},[593,3557,3558],{},[695,3559,697],{},[600,3561,697],{"encoding":602},[577,3563,3565],{"className":3564,"ariaHidden":607},[606],[577,3566,3568,3571],{"className":3567},[611],[577,3569],{"className":3570,"style":743},[615],[577,3572,697],{"className":3573},[620],{"title":3575,"searchDepth":3576,"depth":3576,"links":3577},"",2,[3578,3579,3580],{"id":562,"depth":3576,"text":563},{"id":1084,"depth":3576,"text":1085},{"id":3355,"depth":3576,"text":3356},[3582,3584,3587,3589,3591,3593,3596],{"lhs":3583,"rhs":795},"2^2\u002F4 - 0^2\u002F4",{"lhs":3585,"rhs":3586},"1.5^2\u002F4 - 0.5^2\u002F4","0.5",{"lhs":3588,"rhs":3586},"round(sum(map(0:999, f(k) = 0.5*(0.5 + (k + 0.5)\u002F1000))) \u002F 1000, 4)",{"lhs":3590,"rhs":2534},"3^3\u002F3",{"lhs":3592,"rhs":795},"round(sum(map(0:999, f(k) = ((k + 0.5)*3\u002F1000)^2 \u002F 9)) * 3\u002F1000, 4)",{"lhs":3594,"rhs":3595},"1^3\u002F27","1\u002F27",{"lhs":3597,"rhs":3598},"round(1\u002F27, 3)","0.037","f(x) \\geq 0 \\text{ für alle } x,\\ \\int_{-\\infty}^{\\infty} f(x)\\,\\mathrm{d}x = 1,\\ a \\leq b","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f(x) \\geq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height: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:0.2778em;\">\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">für alle\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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>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>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\int_{-\\infty}^{\\infty} f(x)\\,\\mathrm{d}x = 1,\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 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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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>a\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\leq b\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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","probability-density","P(a \\leq X \\leq b) = \\int_a^b 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>P\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>X\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmsubsup>\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\">P(a \\leq X \\leq b) = \\int_a^b f(x)\\,\\mathrm{d}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:0.1389em;\">P\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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:0.8193em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.511em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" 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:1.599em;\">\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 mathnormal mtight\">a\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 mathnormal mtight\">b\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:0.9119em;\">\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\" 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\u002Fdichtefunktion",[],[3612,3613,3614,3615],"cumulative-distribution","expected-value-continuous","normal-distribution","uniform-distribution-continuous",{"title":548,"description":3575},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fdichtefunktion","Bei einer stetigen Zufallsgröße ist die Wahrscheinlichkeit für ein Intervall die Fläche unter der Dichtefunktion.",[3620,3621,3622,3623,3624],"wahrscheinlichkeitsdichte","stetige zufallsgröße","integral","fläche","stetige verteilung",[3626,3628,3631,3635],{"symbol":833,"meaning":554,"symbolHtml":3627},"\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":598,"meaning":3629,"symbolHtml":3630},"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 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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3632,"meaning":3633,"symbolHtml":3634},"a,\\ b","Grenzen des Intervalls, für das die Wahrscheinlichkeit gesucht ist","\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>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a,\\ b\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\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":687,"meaning":3636,"symbolHtml":3637},"Integrationsvariable","\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","d9RhQeyvuezTzhfU4Xb11u0ZxNn8wB1GkdLPGdNH-Vg",[3640,3643,3646,3649],{"stem":3641,"title":3642,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Ferwartungswert-stetige-zufallsgroesse","Erwartungswert einer stetigen Zufallsgröße",{"stem":3644,"title":3645,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fnormalverteilung","Normalverteilung",{"stem":3647,"title":3648,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstetige-gleichverteilung","Stetige Gleichverteilung",{"stem":3650,"title":3651,"category":441},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fverteilungsfunktion","Verteilungsfunktion",1793824284936]