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\\frac{1}{\\lambda^2}",[569,885,887,917,941,962,982,1073,1184],{"className":886,"ariaHidden":599},[598],[569,888,890,893,897,900,903,906,910,914],{"className":889},[603],[569,891],{"className":892,"style":692},[607],[569,894,783],{"className":895,"style":896},[612,613],"margin-right:0.1389em;",[569,898,674],{"className":899},[700],[569,901,788],{"className":902},[612,613],[569,904,679],{"className":905},[707],[569,907],{"className":908,"style":909},[835],"margin-right:0.2778em;",[569,911,793],{"className":912},[913],"mrel",[569,915],{"className":916,"style":909},[835],[569,918,920,923,926,929,932,935,938],{"className":919},[603],[569,921],{"className":922,"style":692},[607],[569,924,796],{"className":925,"style":896},[612,613],[569,927,674],{"className":928},[700],[569,930,590],{"className":931,"style":614},[612,613],[569,933],{"className":934,"style":909},[835],[569,936,803],{"className":937},[913],[569,939],{"className":940,"style":909},[835],[569,942,944,947,950,953,956,959],{"className":943},[603],[569,945],{"className":946,"style":692},[607],[569,948,788],{"className":949},[612,613],[569,951,679],{"className":952},[707],[569,954],{"className":955,"style":909},[835],[569,957,793],{"className":958},[913],[569,960],{"className":961,"style":909},[835],[569,963,965,969,972,975,979],{"className":964},[603],[569,966],{"className":967,"style":968},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,970,813],{"className":971},[612],[569,973],{"className":974,"style":696},[835],[569,976,816],{"className":977},[978],"mbin",[569,980],{"className":981,"style":696},[835],[569,983,985,989,1039,1043,1047,1051,1055,1058,1061,1064,1067,1070],{"className":984},[603],[569,986],{"className":987,"style":988},[607],"height:1.1491em;vertical-align:-0.25em;",[569,990,992,995],{"className":991},[612],[569,993,822],{"className":994},[612,613],[569,996,999],{"className":997},[998],"msupsub",[569,1000,1003],{"className":1001},[1002],"vlist-t",[569,1004,1007],{"className":1005},[1006],"vlist-r",[569,1008,1012],{"className":1009,"style":1011},[1010],"vlist","height:0.8991em;",[569,1013,1015,1020],{"style":1014},"top:-3.113em;margin-right:0.05em;",[569,1016],{"className":1017,"style":1019},[1018],"pstrut","height:2.7em;",[569,1021,1027],{"className":1022},[1023,1024,1025,1026],"sizing","reset-size6","size3","mtight",[569,1028,1030,1033,1036],{"className":1029},[612,1026],[569,1031,816],{"className":1032},[612,1026],[569,1034,634],{"className":1035},[612,613,1026],[569,1037,788],{"className":1038},[612,613,1026],[569,1040,833],{"className":1041},[1042],"mpunct",[569,1044],{"className":1045,"style":1046},[835],"margin-right:2em;",[569,1048],{"className":1049,"style":1050},[835],"margin-right:0.1667em;",[569,1052,840],{"className":1053,"style":1054},[612,613],"margin-right:0.0576em;",[569,1056,674],{"className":1057},[700],[569,1059,590],{"className":1060,"style":614},[612,613],[569,1062,679],{"className":1063},[707],[569,1065],{"className":1066,"style":909},[835],[569,1068,793],{"className":1069},[913],[569,1071],{"className":1072,"style":909},[835],[569,1074,1076,1080,1154,1157,1160,1163,1166,1169,1172,1175,1178,1181],{"className":1075},[603],[569,1077],{"className":1078,"style":1079},[607],"height:2.0074em;vertical-align:-0.686em;",[569,1081,1083,1087,1151],{"className":1082},[612],[569,1084],{"className":1085},[700,1086],"nulldelimiter",[569,1088,1090],{"className":1089},[850],[569,1091,1094,1142],{"className":1092},[1002,1093],"vlist-t2",[569,1095,1097,1137],{"className":1096},[1006],[569,1098,1101,1114,1125],{"className":1099,"style":1100},[1010],"height:1.3214em;",[569,1102,1104,1108],{"style":1103},"top:-2.314em;",[569,1105],{"className":1106,"style":1107},[1018],"height:3em;",[569,1109,1111],{"className":1110},[612],[569,1112,634],{"className":1113},[612,613],[569,1115,1117,1120],{"style":1116},"top:-3.23em;",[569,1118],{"className":1119,"style":1107},[1018],[569,1121],{"className":1122,"style":1124},[1123],"frac-line","border-bottom-width:0.04em;",[569,1126,1128,1131],{"style":1127},"top:-3.677em;",[569,1129],{"className":1130,"style":1107},[1018],[569,1132,1134],{"className":1133},[612],[569,1135,813],{"className":1136},[612],[569,1138,1141],{"className":1139},[1140],"vlist-s","​",[569,1143,1145],{"className":1144},[1006],[569,1146,1149],{"className":1147,"style":1148},[1010],"height:0.686em;",[569,1150],{},[569,1152],{"className":1153},[707,1086],[569,1155,833],{"className":1156},[1042],[569,1158],{"className":1159,"style":1046},[835],[569,1161],{"className":1162,"style":1050},[835],[569,1164,669],{"className":1165,"style":696},[612,613],[569,1167,674],{"className":1168},[700],[569,1170,590],{"className":1171,"style":614},[612,613],[569,1173,679],{"className":1174},[707],[569,1176],{"className":1177,"style":909},[835],[569,1179,793],{"className":1180},[913],[569,1182],{"className":1183,"style":909},[835],[569,1185,1187,1190],{"className":1186},[603],[569,1188],{"className":1189,"style":1079},[607],[569,1191,1193,1196,1277],{"className":1192},[612],[569,1194],{"className":1195},[700,1086],[569,1197,1199],{"className":1198},[850],[569,1200,1202,1269],{"className":1201},[1002,1093],[569,1203,1205,1266],{"className":1204},[1006],[569,1206,1208,1247,1255],{"className":1207,"style":1100},[1010],[569,1209,1210,1213],{"style":1103},[569,1211],{"className":1212,"style":1107},[1018],[569,1214,1216],{"className":1215},[612],[569,1217,1219,1222],{"className":1218},[612],[569,1220,634],{"className":1221},[612,613],[569,1223,1225],{"className":1224},[998],[569,1226,1228],{"className":1227},[1002],[569,1229,1231],{"className":1230},[1006],[569,1232,1235],{"className":1233,"style":1234},[1010],"height:0.7401em;",[569,1236,1238,1241],{"style":1237},"top:-2.989em;margin-right:0.05em;",[569,1239],{"className":1240,"style":1019},[1018],[569,1242,1244],{"className":1243},[1023,1024,1025,1026],[569,1245,880],{"className":1246},[612,1026],[569,1248,1249,1252],{"style":1116},[569,1250],{"className":1251,"style":1107},[1018],[569,1253],{"className":1254,"style":1124},[1123],[569,1256,1257,1260],{"style":1127},[569,1258],{"className":1259,"style":1107},[1018],[569,1261,1263],{"className":1262},[612],[569,1264,813],{"className":1265},[612],[569,1267,1141],{"className":1268},[1140],[569,1270,1272],{"className":1271},[1006],[569,1273,1275],{"className":1274,"style":1148},[1010],[569,1276],{},[569,1278],{"className":1279},[707,1086],[565,1281,1282,1283,1286,1287,1412],{},"Der ",[617,1284,1285],{},"Median"," ist ",[569,1288,1290,1315],{"className":1289},[572],[569,1291,1293],{"className":1292},[576],[578,1294,1295],{"xmlns":580},[582,1296,1297,1312],{},[585,1298,1299],{},[850,1300,1301,1310],{},[585,1302,1303,1306,1308],{},[588,1304,1305],{},"ln",[671,1307,727],{},[811,1309,880],{},[588,1311,634],{},[592,1313,1314],{"encoding":594},"\\frac{\\ln 2}{\\lambda}",[569,1316,1318],{"className":1317,"ariaHidden":599},[598],[569,1319,1321,1325],{"className":1320},[603],[569,1322],{"className":1323,"style":1324},[607],"height:1.2251em;vertical-align:-0.345em;",[569,1326,1328,1331,1409],{"className":1327},[612],[569,1329],{"className":1330},[700,1086],[569,1332,1334],{"className":1333},[850],[569,1335,1337,1400],{"className":1336},[1002,1093],[569,1338,1340,1397],{"className":1339},[1006],[569,1341,1344,1359,1367],{"className":1342,"style":1343},[1010],"height:0.8801em;",[569,1345,1347,1350],{"style":1346},"top:-2.655em;",[569,1348],{"className":1349,"style":1107},[1018],[569,1351,1353],{"className":1352},[1023,1024,1025,1026],[569,1354,1356],{"className":1355},[612,1026],[569,1357,634],{"className":1358},[612,613,1026],[569,1360,1361,1364],{"style":1116},[569,1362],{"className":1363,"style":1107},[1018],[569,1365],{"className":1366,"style":1124},[1123],[569,1368,1370,1373],{"style":1369},"top:-3.394em;",[569,1371],{"className":1372,"style":1107},[1018],[569,1374,1376],{"className":1375},[1023,1024,1025,1026],[569,1377,1379,1390,1394],{"className":1378},[612,1026],[569,1380,1382,1386],{"className":1381},[749,1026],[569,1383,1385],{"className":1384},[1026],"l",[569,1387,1389],{"className":1388},[1026],"n",[569,1391],{"className":1392,"style":1393},[835,1026],"margin-right:0.1952em;",[569,1395,880],{"className":1396},[612,1026],[569,1398,1141],{"className":1399},[1140],[569,1401,1403],{"className":1402},[1006],[569,1404,1407],{"className":1405,"style":1406},[1010],"height:0.345em;",[569,1408],{},[569,1410],{"className":1411},[707,1086],", analog zur Halbwertszeit beim radioaktiven Zerfall.",[565,1414,1415,1416,1419],{},"Die Exponentialverteilung ist ",[617,1417,1418],{},"gedächtnislos",":",[569,1421,1423],{"className":1422},[767],[569,1424,1426,1514],{"className":1425},[572],[569,1427,1429],{"className":1428},[576],[578,1430,1431],{"xmlns":580,"display":776},[582,1432,1433,1511],{},[585,1434,1435,1437,1439,1441,1444,1447,1450,1453,1456,1458,1460,1462,1464,1466,1468,1470,1472,1474,1476,1478,1481,1499,1501,1503,1505,1508],{},[588,1436,796],{},[671,1438,674],{"stretchy":673},[588,1440,590],{},[671,1442,1443],{},">",[588,1445,1446],{},"s",[671,1448,1449],{},"+",[588,1451,1452],{},"t",[671,1454,1455],{},"∣",[588,1457,590],{},[671,1459,1443],{},[588,1461,1446],{},[671,1463,679],{"stretchy":673},[671,1465,793],{},[588,1467,796],{},[671,1469,674],{"stretchy":673},[588,1471,590],{},[671,1473,1443],{},[588,1475,1452],{},[671,1477,679],{"stretchy":673},[835,1479],{"width":1480},"1em",[585,1482,1483,1487,1496],{},[1484,1485,1486],"mtext",{},"f",[1488,1489,1490,1493],"mover",{"accent":599},[1484,1491,1492],{},"u",[671,1494,1495],{},"¨",[1484,1497,1498],{},"r ",[588,1500,1446],{},[671,1502,833],{"separator":599},[588,1504,1452],{},[671,1506,1507],{},"≥",[811,1509,1510],{},"0",[592,1512,1513],{"encoding":594},"P(X > s + t \\mid X > s) = P(X > t) \\quad \\text{für } s, t \\geq 0",[569,1515,1517,1541,1560,1578,1597,1618,1642,1725],{"className":1516,"ariaHidden":599},[598],[569,1518,1520,1523,1526,1529,1532,1535,1538],{"className":1519},[603],[569,1521],{"className":1522,"style":692},[607],[569,1524,796],{"className":1525,"style":896},[612,613],[569,1527,674],{"className":1528},[700],[569,1530,590],{"className":1531,"style":614},[612,613],[569,1533],{"className":1534,"style":909},[835],[569,1536,1443],{"className":1537},[913],[569,1539],{"className":1540,"style":909},[835],[569,1542,1544,1548,1551,1554,1557],{"className":1543},[603],[569,1545],{"className":1546,"style":1547},[607],"height:0.6667em;vertical-align:-0.0833em;",[569,1549,1446],{"className":1550},[612,613],[569,1552],{"className":1553,"style":696},[835],[569,1555,1449],{"className":1556},[978],[569,1558],{"className":1559,"style":696},[835],[569,1561,1563,1566,1569,1572,1575],{"className":1562},[603],[569,1564],{"className":1565,"style":692},[607],[569,1567,1452],{"className":1568},[612,613],[569,1570],{"className":1571,"style":909},[835],[569,1573,1455],{"className":1574},[913],[569,1576],{"className":1577,"style":909},[835],[569,1579,1581,1585,1588,1591,1594],{"className":1580},[603],[569,1582],{"className":1583,"style":1584},[607],"height:0.7224em;vertical-align:-0.0391em;",[569,1586,590],{"className":1587,"style":614},[612,613],[569,1589],{"className":1590,"style":909},[835],[569,1592,1443],{"className":1593},[913],[569,1595],{"className":1596,"style":909},[835],[569,1598,1600,1603,1606,1609,1612,1615],{"className":1599},[603],[569,1601],{"className":1602,"style":692},[607],[569,1604,1446],{"className":1605},[612,613],[569,1607,679],{"className":1608},[707],[569,1610],{"className":1611,"style":909},[835],[569,1613,793],{"className":1614},[913],[569,1616],{"className":1617,"style":909},[835],[569,1619,1621,1624,1627,1630,1633,1636,1639],{"className":1620},[603],[569,1622],{"className":1623,"style":692},[607],[569,1625,796],{"className":1626,"style":896},[612,613],[569,1628,674],{"className":1629},[700],[569,1631,590],{"className":1632,"style":614},[612,613],[569,1634],{"className":1635,"style":909},[835],[569,1637,1443],{"className":1638},[913],[569,1640],{"className":1641,"style":909},[835],[569,1643,1645,1648,1651,1654,1658,1704,1707,1710,1713,1716,1719,1722],{"className":1644},[603],[569,1646],{"className":1647,"style":692},[607],[569,1649,1452],{"className":1650},[612,613],[569,1652,679],{"className":1653},[707],[569,1655],{"className":1656,"style":1657},[835],"margin-right:1em;",[569,1659,1662,1665,1701],{"className":1660},[612,1661],"text",[569,1663,1486],{"className":1664},[612],[569,1666,1669],{"className":1667},[612,1668],"accent",[569,1670,1672],{"className":1671},[1002],[569,1673,1675],{"className":1674},[1006],[569,1676,1679,1688],{"className":1677,"style":1678},[1010],"height:0.6679em;",[569,1680,1682,1685],{"style":1681},"top:-3em;",[569,1683],{"className":1684,"style":1107},[1018],[569,1686,1492],{"className":1687},[612],[569,1689,1690,1693],{"style":1681},[569,1691],{"className":1692,"style":1107},[1018],[569,1694,1698],{"className":1695,"style":1697},[1696],"accent-body","left:-0.25em;",[569,1699,1495],{"className":1700},[612],[569,1702,1498],{"className":1703},[612],[569,1705,1446],{"className":1706},[612,613],[569,1708,833],{"className":1709},[1042],[569,1711],{"className":1712,"style":1050},[835],[569,1714,1452],{"className":1715},[612,613],[569,1717],{"className":1718,"style":909},[835],[569,1720,1507],{"className":1721},[913],[569,1723],{"className":1724,"style":909},[835],[569,1726,1728,1732],{"className":1727},[603],[569,1729],{"className":1730,"style":1731},[607],"height:0.6444em;",[569,1733,1510],{"className":1734},[612],[565,1736,1737,1738,1767],{},"Ein Bauteil, das schon ",[569,1739,1741,1754],{"className":1740},[572],[569,1742,1744],{"className":1743},[576],[578,1745,1746],{"xmlns":580},[582,1747,1748,1752],{},[585,1749,1750],{},[588,1751,1446],{},[592,1753,1446],{"encoding":594},[569,1755,1757],{"className":1756,"ariaHidden":599},[598],[569,1758,1760,1764],{"className":1759},[603],[569,1761],{"className":1762,"style":1763},[607],"height:0.4306em;",[569,1765,1446],{"className":1766},[612,613]," Stunden hält, ist danach „wie neu“. Für Teile mit Verschleiß ist das Modell deshalb ungeeignet.",[565,1769,1770,1771,1799],{},"Zusammenhang mit der Poisson-Verteilung: Treten Ereignisse Poisson-verteilt mit Rate ",[569,1772,1774,1787],{"className":1773},[572],[569,1775,1777],{"className":1776},[576],[578,1778,1779],{"xmlns":580},[582,1780,1781,1785],{},[585,1782,1783],{},[588,1784,634],{},[592,1786,637],{"encoding":594},[569,1788,1790],{"className":1789,"ariaHidden":599},[598],[569,1791,1793,1796],{"className":1792},[603],[569,1794],{"className":1795,"style":647},[607],[569,1797,634],{"className":1798},[612,613]," pro Zeiteinheit auf, sind die Wartezeiten zwischen ihnen exponentialverteilt mit derselben Rate.",[560,1801,1803],{"id":1802},"beispiele","Beispiele",[565,1805,1806,1807,1836,1837,1993,1994,2023],{},"Eine Lampe hält im Mittel ",[569,1808,1810,1824],{"className":1809},[572],[569,1811,1813],{"className":1812},[576],[578,1814,1815],{"xmlns":580},[582,1816,1817,1822],{},[585,1818,1819],{},[811,1820,1821],{},"2000",[592,1823,1821],{"encoding":594},[569,1825,1827],{"className":1826,"ariaHidden":599},[598],[569,1828,1830,1833],{"className":1829},[603],[569,1831],{"className":1832,"style":1731},[607],[569,1834,1821],{"className":1835},[612]," Stunden, also ",[569,1838,1840,1867],{"className":1839},[572],[569,1841,1843],{"className":1842},[576],[578,1844,1845],{"xmlns":580},[582,1846,1847,1864],{},[585,1848,1849,1851,1853,1859,1861],{},[588,1850,634],{},[671,1852,793],{},[850,1854,1855,1857],{},[811,1856,813],{},[811,1858,1821],{},[671,1860,793],{},[811,1862,1863],{},"0,0005",[592,1865,1866],{"encoding":594},"\\lambda = \\frac{1}{2000} = 0{,}0005",[569,1868,1870,1888,1973],{"className":1869,"ariaHidden":599},[598],[569,1871,1873,1876,1879,1882,1885],{"className":1872},[603],[569,1874],{"className":1875,"style":647},[607],[569,1877,634],{"className":1878},[612,613],[569,1880],{"className":1881,"style":909},[835],[569,1883,793],{"className":1884},[913],[569,1886],{"className":1887,"style":909},[835],[569,1889,1891,1895,1964,1967,1970],{"className":1890},[603],[569,1892],{"className":1893,"style":1894},[607],"height:1.1901em;vertical-align:-0.345em;",[569,1896,1898,1901,1961],{"className":1897},[612],[569,1899],{"className":1900},[700,1086],[569,1902,1904],{"className":1903},[850],[569,1905,1907,1953],{"className":1906},[1002,1093],[569,1908,1910,1950],{"className":1909},[1006],[569,1911,1914,1928,1936],{"className":1912,"style":1913},[1010],"height:0.8451em;",[569,1915,1916,1919],{"style":1346},[569,1917],{"className":1918,"style":1107},[1018],[569,1920,1922],{"className":1921},[1023,1024,1025,1026],[569,1923,1925],{"className":1924},[612,1026],[569,1926,1821],{"className":1927},[612,1026],[569,1929,1930,1933],{"style":1116},[569,1931],{"className":1932,"style":1107},[1018],[569,1934],{"className":1935,"style":1124},[1123],[569,1937,1938,1941],{"style":1369},[569,1939],{"className":1940,"style":1107},[1018],[569,1942,1944],{"className":1943},[1023,1024,1025,1026],[569,1945,1947],{"className":1946},[612,1026],[569,1948,813],{"className":1949},[612,1026],[569,1951,1141],{"className":1952},[1140],[569,1954,1956],{"className":1955},[1006],[569,1957,1959],{"className":1958,"style":1406},[1010],[569,1960],{},[569,1962],{"className":1963},[707,1086],[569,1965],{"className":1966,"style":909},[835],[569,1968,793],{"className":1969},[913],[569,1971],{"className":1972,"style":909},[835],[569,1974,1976,1980,1983,1989],{"className":1975},[603],[569,1977],{"className":1978,"style":1979},[607],"height:0.8389em;vertical-align:-0.1944em;",[569,1981,1510],{"className":1982},[612],[569,1984,1986],{"className":1985},[612],[569,1987,833],{"className":1988},[1042],[569,1990,1992],{"className":1991},[612],"0005"," pro Stunde. Ausfall in den ersten ",[569,1995,1997,2011],{"className":1996},[572],[569,1998,2000],{"className":1999},[576],[578,2001,2002],{"xmlns":580},[582,2003,2004,2009],{},[585,2005,2006],{},[811,2007,2008],{},"1000",[592,2010,2008],{"encoding":594},[569,2012,2014],{"className":2013,"ariaHidden":599},[598],[569,2015,2017,2020],{"className":2016},[603],[569,2018],{"className":2019,"style":1731},[607],[569,2021,2008],{"className":2022},[612]," Stunden:",[569,2025,2027],{"className":2026},[767],[569,2028,2030,2098],{"className":2029},[572],[569,2031,2033],{"className":2032},[576],[578,2034,2035],{"xmlns":580,"display":776},[582,2036,2037,2095],{},[585,2038,2039,2041,2043,2045,2047,2049,2051,2053,2055,2057,2072,2074,2076,2078,2089,2092],{},[588,2040,796],{},[671,2042,674],{"stretchy":673},[588,2044,590],{},[671,2046,803],{},[811,2048,2008],{},[671,2050,679],{"stretchy":673},[671,2052,793],{},[811,2054,813],{},[671,2056,816],{},[818,2058,2059,2061],{},[588,2060,822],{},[585,2062,2063,2065,2067,2070],{},[671,2064,816],{},[811,2066,1863],{},[671,2068,2069],{},"⋅",[811,2071,2008],{},[671,2073,793],{},[811,2075,813],{},[671,2077,816],{},[818,2079,2080,2082],{},[588,2081,822],{},[585,2083,2084,2086],{},[671,2085,816],{},[811,2087,2088],{},"0,5",[671,2090,2091],{},"≈",[811,2093,2094],{},"0,3935",[592,2096,2097],{"encoding":594},"P(X \\leq 1000) = 1 - e^{-0{,}0005 \\cdot 1000} = 1 - e^{-0{,}5} \\approx 0{,}3935",[569,2099,2101,2125,2146,2164,2230,2248,2308],{"className":2100,"ariaHidden":599},[598],[569,2102,2104,2107,2110,2113,2116,2119,2122],{"className":2103},[603],[569,2105],{"className":2106,"style":692},[607],[569,2108,796],{"className":2109,"style":896},[612,613],[569,2111,674],{"className":2112},[700],[569,2114,590],{"className":2115,"style":614},[612,613],[569,2117],{"className":2118,"style":909},[835],[569,2120,803],{"className":2121},[913],[569,2123],{"className":2124,"style":909},[835],[569,2126,2128,2131,2134,2137,2140,2143],{"className":2127},[603],[569,2129],{"className":2130,"style":692},[607],[569,2132,2008],{"className":2133},[612],[569,2135,679],{"className":2136},[707],[569,2138],{"className":2139,"style":909},[835],[569,2141,793],{"className":2142},[913],[569,2144],{"className":2145,"style":909},[835],[569,2147,2149,2152,2155,2158,2161],{"className":2148},[603],[569,2150],{"className":2151,"style":968},[607],[569,2153,813],{"className":2154},[612],[569,2156],{"className":2157,"style":696},[835],[569,2159,816],{"className":2160},[978],[569,2162],{"className":2163,"style":696},[835],[569,2165,2167,2171,2221,2224,2227],{"className":2166},[603],[569,2168],{"className":2169,"style":2170},[607],"height:0.8641em;",[569,2172,2174,2177],{"className":2173},[612],[569,2175,822],{"className":2176},[612,613],[569,2178,2180],{"className":2179},[998],[569,2181,2183],{"className":2182},[1002],[569,2184,2186],{"className":2185},[1006],[569,2187,2189],{"className":2188,"style":2170},[1010],[569,2190,2191,2194],{"style":1014},[569,2192],{"className":2193,"style":1019},[1018],[569,2195,2197],{"className":2196},[1023,1024,1025,1026],[569,2198,2200,2203,2206,2212,2215,2218],{"className":2199},[612,1026],[569,2201,816],{"className":2202},[612,1026],[569,2204,1510],{"className":2205},[612,1026],[569,2207,2209],{"className":2208},[612,1026],[569,2210,833],{"className":2211},[1042,1026],[569,2213,1992],{"className":2214},[612,1026],[569,2216,2069],{"className":2217},[978,1026],[569,2219,2008],{"className":2220},[612,1026],[569,2222],{"className":2223,"style":909},[835],[569,2225,793],{"className":2226},[913],[569,2228],{"className":2229,"style":909},[835],[569,2231,2233,2236,2239,2242,2245],{"className":2232},[603],[569,2234],{"className":2235,"style":968},[607],[569,2237,813],{"className":2238},[612],[569,2240],{"className":2241,"style":696},[835],[569,2243,816],{"className":2244},[978],[569,2246],{"className":2247,"style":696},[835],[569,2249,2251,2254,2299,2302,2305],{"className":2250},[603],[569,2252],{"className":2253,"style":2170},[607],[569,2255,2257,2260],{"className":2256},[612],[569,2258,822],{"className":2259},[612,613],[569,2261,2263],{"className":2262},[998],[569,2264,2266],{"className":2265},[1002],[569,2267,2269],{"className":2268},[1006],[569,2270,2272],{"className":2271,"style":2170},[1010],[569,2273,2274,2277],{"style":1014},[569,2275],{"className":2276,"style":1019},[1018],[569,2278,2280],{"className":2279},[1023,1024,1025,1026],[569,2281,2283,2286,2289,2295],{"className":2282},[612,1026],[569,2284,816],{"className":2285},[612,1026],[569,2287,1510],{"className":2288},[612,1026],[569,2290,2292],{"className":2291},[612,1026],[569,2293,833],{"className":2294},[1042,1026],[569,2296,2298],{"className":2297},[612,1026],"5",[569,2300],{"className":2301,"style":909},[835],[569,2303,2091],{"className":2304},[913],[569,2306],{"className":2307,"style":909},[835],[569,2309,2311,2314,2317,2323],{"className":2310},[603],[569,2312],{"className":2313,"style":1979},[607],[569,2315,1510],{"className":2316},[612],[569,2318,2320],{"className":2319},[612],[569,2321,833],{"className":2322},[1042],[569,2324,2326],{"className":2325},[612],"3935",[565,2328,2329,2330,2359,2360,2604],{},"Länger als ",[569,2331,2333,2347],{"className":2332},[572],[569,2334,2336],{"className":2335},[576],[578,2337,2338],{"xmlns":580},[582,2339,2340,2345],{},[585,2341,2342],{},[811,2343,2344],{},"4000",[592,2346,2344],{"encoding":594},[569,2348,2350],{"className":2349,"ariaHidden":599},[598],[569,2351,2353,2356],{"className":2352},[603],[569,2354],{"className":2355,"style":1731},[607],[569,2357,2344],{"className":2358},[612]," Stunden hält sie mit ",[569,2361,2363,2420],{"className":2362},[572],[569,2364,2366],{"className":2365},[576],[578,2367,2368],{"xmlns":580},[582,2369,2370,2417],{},[585,2371,2372,2374,2376,2378,2380,2382,2384,2386,2400,2402,2412,2414],{},[588,2373,796],{},[671,2375,674],{"stretchy":673},[588,2377,590],{},[671,2379,1443],{},[811,2381,2344],{},[671,2383,679],{"stretchy":673},[671,2385,793],{},[818,2387,2388,2390],{},[588,2389,822],{},[585,2391,2392,2394,2396,2398],{},[671,2393,816],{},[811,2395,1863],{},[671,2397,2069],{},[811,2399,2344],{},[671,2401,793],{},[818,2403,2404,2406],{},[588,2405,822],{},[585,2407,2408,2410],{},[671,2409,816],{},[811,2411,880],{},[671,2413,2091],{},[811,2415,2416],{},"0,1353",[592,2418,2419],{"encoding":594},"P(X > 4000) = e^{-0{,}0005 \\cdot 4000} = e^{-2} \\approx 0{,}1353",[569,2421,2423,2447,2468,2535,2585],{"className":2422,"ariaHidden":599},[598],[569,2424,2426,2429,2432,2435,2438,2441,2444],{"className":2425},[603],[569,2427],{"className":2428,"style":692},[607],[569,2430,796],{"className":2431,"style":896},[612,613],[569,2433,674],{"className":2434},[700],[569,2436,590],{"className":2437,"style":614},[612,613],[569,2439],{"className":2440,"style":909},[835],[569,2442,1443],{"className":2443},[913],[569,2445],{"className":2446,"style":909},[835],[569,2448,2450,2453,2456,2459,2462,2465],{"className":2449},[603],[569,2451],{"className":2452,"style":692},[607],[569,2454,2344],{"className":2455},[612],[569,2457,679],{"className":2458},[707],[569,2460],{"className":2461,"style":909},[835],[569,2463,793],{"className":2464},[913],[569,2466],{"className":2467,"style":909},[835],[569,2469,2471,2475,2526,2529,2532],{"className":2470},[603],[569,2472],{"className":2473,"style":2474},[607],"height:0.8141em;",[569,2476,2478,2481],{"className":2477},[612],[569,2479,822],{"className":2480},[612,613],[569,2482,2484],{"className":2483},[998],[569,2485,2487],{"className":2486},[1002],[569,2488,2490],{"className":2489},[1006],[569,2491,2493],{"className":2492,"style":2474},[1010],[569,2494,2496,2499],{"style":2495},"top:-3.063em;margin-right:0.05em;",[569,2497],{"className":2498,"style":1019},[1018],[569,2500,2502],{"className":2501},[1023,1024,1025,1026],[569,2503,2505,2508,2511,2517,2520,2523],{"className":2504},[612,1026],[569,2506,816],{"className":2507},[612,1026],[569,2509,1510],{"className":2510},[612,1026],[569,2512,2514],{"className":2513},[612,1026],[569,2515,833],{"className":2516},[1042,1026],[569,2518,1992],{"className":2519},[612,1026],[569,2521,2069],{"className":2522},[978,1026],[569,2524,2344],{"className":2525},[612,1026],[569,2527],{"className":2528,"style":909},[835],[569,2530,793],{"className":2531},[913],[569,2533],{"className":2534,"style":909},[835],[569,2536,2538,2541,2576,2579,2582],{"className":2537},[603],[569,2539],{"className":2540,"style":2474},[607],[569,2542,2544,2547],{"className":2543},[612],[569,2545,822],{"className":2546},[612,613],[569,2548,2550],{"className":2549},[998],[569,2551,2553],{"className":2552},[1002],[569,2554,2556],{"className":2555},[1006],[569,2557,2559],{"className":2558,"style":2474},[1010],[569,2560,2561,2564],{"style":2495},[569,2562],{"className":2563,"style":1019},[1018],[569,2565,2567],{"className":2566},[1023,1024,1025,1026],[569,2568,2570,2573],{"className":2569},[612,1026],[569,2571,816],{"className":2572},[612,1026],[569,2574,880],{"className":2575},[612,1026],[569,2577],{"className":2578,"style":909},[835],[569,2580,2091],{"className":2581},[913],[569,2583],{"className":2584,"style":909},[835],[569,2586,2588,2591,2594,2600],{"className":2587},[603],[569,2589],{"className":2590,"style":1979},[607],[569,2592,1510],{"className":2593},[612],[569,2595,2597],{"className":2596},[612],[569,2598,833],{"className":2599},[1042],[569,2601,2603],{"className":2602},[612],"1353",".",[565,2606,2607,2608,2758,2759,2604],{},"Die Hälfte der Lampen fällt vor ",[569,2609,2611,2640],{"className":2610},[572],[569,2612,2614],{"className":2613},[576],[578,2615,2616],{"xmlns":580},[582,2617,2618,2637],{},[585,2619,2620,2632,2634],{},[850,2621,2622,2630],{},[585,2623,2624,2626,2628],{},[588,2625,1305],{},[671,2627,727],{},[811,2629,880],{},[811,2631,1863],{},[671,2633,2091],{},[811,2635,2636],{},"1386",[592,2638,2639],{"encoding":594},"\\frac{\\ln 2}{0{,}0005} \\approx 1386",[569,2641,2643,2749],{"className":2642,"ariaHidden":599},[598],[569,2644,2646,2650,2740,2743,2746],{"className":2645},[603],[569,2647],{"className":2648,"style":2649},[607],"height:1.3612em;vertical-align:-0.4811em;",[569,2651,2653,2656,2737],{"className":2652},[612],[569,2654],{"className":2655},[700,1086],[569,2657,2659],{"className":2658},[850],[569,2660,2662,2728],{"className":2661},[1002,1093],[569,2663,2665,2725],{"className":2664},[1006],[569,2666,2668,2691,2699],{"className":2667,"style":1343},[1010],[569,2669,2670,2673],{"style":1346},[569,2671],{"className":2672,"style":1107},[1018],[569,2674,2676],{"className":2675},[1023,1024,1025,1026],[569,2677,2679,2682,2688],{"className":2678},[612,1026],[569,2680,1510],{"className":2681},[612,1026],[569,2683,2685],{"className":2684},[612,1026],[569,2686,833],{"className":2687},[1042,1026],[569,2689,1992],{"className":2690},[612,1026],[569,2692,2693,2696],{"style":1116},[569,2694],{"className":2695,"style":1107},[1018],[569,2697],{"className":2698,"style":1124},[1123],[569,2700,2701,2704],{"style":1369},[569,2702],{"className":2703,"style":1107},[1018],[569,2705,2707],{"className":2706},[1023,1024,1025,1026],[569,2708,2710,2719,2722],{"className":2709},[612,1026],[569,2711,2713,2716],{"className":2712},[749,1026],[569,2714,1385],{"className":2715},[1026],[569,2717,1389],{"className":2718},[1026],[569,2720],{"className":2721,"style":1393},[835,1026],[569,2723,880],{"className":2724},[612,1026],[569,2726,1141],{"className":2727},[1140],[569,2729,2731],{"className":2730},[1006],[569,2732,2735],{"className":2733,"style":2734},[1010],"height:0.4811em;",[569,2736],{},[569,2738],{"className":2739},[707,1086],[569,2741],{"className":2742,"style":909},[835],[569,2744,2091],{"className":2745},[913],[569,2747],{"className":2748,"style":909},[835],[569,2750,2752,2755],{"className":2751},[603],[569,2753],{"className":2754,"style":1731},[607],[569,2756,2636],{"className":2757},[612]," Stunden aus, also deutlich vor dem Mittelwert ",[569,2760,2762,2775],{"className":2761},[572],[569,2763,2765],{"className":2764},[576],[578,2766,2767],{"xmlns":580},[582,2768,2769,2773],{},[585,2770,2771],{},[811,2772,1821],{},[592,2774,1821],{"encoding":594},[569,2776,2778],{"className":2777,"ariaHidden":599},[598],[569,2779,2781,2784],{"className":2780},[603],[569,2782],{"className":2783,"style":1731},[607],[569,2785,1821],{"className":2786},[612],[560,2788,2790],{"id":2789},"typische-fehler","Typische Fehler",[2792,2793,2794,2944,3021,3269],"ul",{},[2795,2796,2797,2825,2826,2854,2855,2915,2916,2604],"li",{},[569,2798,2800,2813],{"className":2799},[572],[569,2801,2803],{"className":2802},[576],[578,2804,2805],{"xmlns":580},[582,2806,2807,2811],{},[585,2808,2809],{},[588,2810,634],{},[592,2812,637],{"encoding":594},[569,2814,2816],{"className":2815,"ariaHidden":599},[598],[569,2817,2819,2822],{"className":2818},[603],[569,2820],{"className":2821,"style":647},[607],[569,2823,634],{"className":2824},[612,613]," mit der mittleren Wartezeit verwechseln. Bei einer mittleren Lebensdauer von ",[569,2827,2829,2842],{"className":2828},[572],[569,2830,2832],{"className":2831},[576],[578,2833,2834],{"xmlns":580},[582,2835,2836,2840],{},[585,2837,2838],{},[811,2839,1821],{},[592,2841,1821],{"encoding":594},[569,2843,2845],{"className":2844,"ariaHidden":599},[598],[569,2846,2848,2851],{"className":2847},[603],[569,2849],{"className":2850,"style":1731},[607],[569,2852,1821],{"className":2853},[612]," h ist ",[569,2856,2858,2876],{"className":2857},[572],[569,2859,2861],{"className":2860},[576],[578,2862,2863],{"xmlns":580},[582,2864,2865,2873],{},[585,2866,2867,2869,2871],{},[588,2868,634],{},[671,2870,793],{},[811,2872,1863],{},[592,2874,2875],{"encoding":594},"\\lambda = 0{,}0005",[569,2877,2879,2897],{"className":2878,"ariaHidden":599},[598],[569,2880,2882,2885,2888,2891,2894],{"className":2881},[603],[569,2883],{"className":2884,"style":647},[607],[569,2886,634],{"className":2887},[612,613],[569,2889],{"className":2890,"style":909},[835],[569,2892,793],{"className":2893},[913],[569,2895],{"className":2896,"style":909},[835],[569,2898,2900,2903,2906,2912],{"className":2899},[603],[569,2901],{"className":2902,"style":1979},[607],[569,2904,1510],{"className":2905},[612],[569,2907,2909],{"className":2908},[612],[569,2910,833],{"className":2911},[1042],[569,2913,1992],{"className":2914},[612],", nicht ",[569,2917,2919,2932],{"className":2918},[572],[569,2920,2922],{"className":2921},[576],[578,2923,2924],{"xmlns":580},[582,2925,2926,2930],{},[585,2927,2928],{},[811,2929,1821],{},[592,2931,1821],{"encoding":594},[569,2933,2935],{"className":2934,"ariaHidden":599},[598],[569,2936,2938,2941],{"className":2937},[603],[569,2939],{"className":2940,"style":1731},[607],[569,2942,1821],{"className":2943},[612],[2795,2945,2946,2947,2992,2993,2604],{},"Den Dichtewert ",[569,2948,2950,2970],{"className":2949},[572],[569,2951,2953],{"className":2952},[576],[578,2954,2955],{"xmlns":580},[582,2956,2957,2967],{},[585,2958,2959,2961,2963,2965],{},[588,2960,1486],{},[671,2962,674],{"stretchy":673},[588,2964,788],{},[671,2966,679],{"stretchy":673},[592,2968,2969],{"encoding":594},"f(x)",[569,2971,2973],{"className":2972,"ariaHidden":599},[598],[569,2974,2976,2979,2983,2986,2989],{"className":2975},[603],[569,2977],{"className":2978,"style":692},[607],[569,2980,1486],{"className":2981,"style":2982},[612,613],"margin-right:0.1076em;",[569,2984,674],{"className":2985},[700],[569,2987,788],{"className":2988},[612,613],[569,2990,679],{"className":2991},[707]," als Wahrscheinlichkeit lesen. Wahrscheinlichkeiten sind Flächen, also Werte von ",[569,2994,2996,3009],{"className":2995},[572],[569,2997,2999],{"className":2998},[576],[578,3000,3001],{"xmlns":580},[582,3002,3003,3007],{},[585,3004,3005],{},[588,3006,783],{},[592,3008,783],{"encoding":594},[569,3010,3012],{"className":3011,"ariaHidden":599},[598],[569,3013,3015,3018],{"className":3014},[603],[569,3016],{"className":3017,"style":608},[607],[569,3019,783],{"className":3020,"style":896},[612,613],[2795,3022,3023,3089,3090,3134,3135,2604],{},[569,3024,3026,3050],{"className":3025},[572],[569,3027,3029],{"className":3028},[576],[578,3030,3031],{"xmlns":580},[582,3032,3033,3047],{},[585,3034,3035,3037,3039,3041,3043,3045],{},[588,3036,796],{},[671,3038,674],{"stretchy":673},[588,3040,590],{},[671,3042,1443],{},[588,3044,788],{},[671,3046,679],{"stretchy":673},[592,3048,3049],{"encoding":594},"P(X > x)",[569,3051,3053,3077],{"className":3052,"ariaHidden":599},[598],[569,3054,3056,3059,3062,3065,3068,3071,3074],{"className":3055},[603],[569,3057],{"className":3058,"style":692},[607],[569,3060,796],{"className":3061,"style":896},[612,613],[569,3063,674],{"className":3064},[700],[569,3066,590],{"className":3067,"style":614},[612,613],[569,3069],{"className":3070,"style":909},[835],[569,3072,1443],{"className":3073},[913],[569,3075],{"className":3076,"style":909},[835],[569,3078,3080,3083,3086],{"className":3079},[603],[569,3081],{"className":3082,"style":692},[607],[569,3084,788],{"className":3085},[612,613],[569,3087,679],{"className":3088},[707]," mit ",[569,3091,3093,3113],{"className":3092},[572],[569,3094,3096],{"className":3095},[576],[578,3097,3098],{"xmlns":580},[582,3099,3100,3110],{},[585,3101,3102,3104,3106,3108],{},[588,3103,783],{},[671,3105,674],{"stretchy":673},[588,3107,788],{},[671,3109,679],{"stretchy":673},[592,3111,3112],{"encoding":594},"F(x)",[569,3114,3116],{"className":3115,"ariaHidden":599},[598],[569,3117,3119,3122,3125,3128,3131],{"className":3118},[603],[569,3120],{"className":3121,"style":692},[607],[569,3123,783],{"className":3124,"style":896},[612,613],[569,3126,674],{"className":3127},[700],[569,3129,788],{"className":3130},[612,613],[569,3132,679],{"className":3133},[707]," berechnen. Für „länger als“ gilt ",[569,3136,3138,3176],{"className":3137},[572],[569,3139,3141],{"className":3140},[576],[578,3142,3143],{"xmlns":580},[582,3144,3145,3173],{},[585,3146,3147,3149,3151,3153,3155,3157,3159,3161],{},[588,3148,796],{},[671,3150,674],{"stretchy":673},[588,3152,590],{},[671,3154,1443],{},[588,3156,788],{},[671,3158,679],{"stretchy":673},[671,3160,793],{},[818,3162,3163,3165],{},[588,3164,822],{},[585,3166,3167,3169,3171],{},[671,3168,816],{},[588,3170,634],{},[588,3172,788],{},[592,3174,3175],{"encoding":594},"P(X > x) = e^{-\\lambda x}",[569,3177,3179,3203,3224],{"className":3178,"ariaHidden":599},[598],[569,3180,3182,3185,3188,3191,3194,3197,3200],{"className":3181},[603],[569,3183],{"className":3184,"style":692},[607],[569,3186,796],{"className":3187,"style":896},[612,613],[569,3189,674],{"className":3190},[700],[569,3192,590],{"className":3193,"style":614},[612,613],[569,3195],{"className":3196,"style":909},[835],[569,3198,1443],{"className":3199},[913],[569,3201],{"className":3202,"style":909},[835],[569,3204,3206,3209,3212,3215,3218,3221],{"className":3205},[603],[569,3207],{"className":3208,"style":692},[607],[569,3210,788],{"className":3211},[612,613],[569,3213,679],{"className":3214},[707],[569,3216],{"className":3217,"style":909},[835],[569,3219,793],{"className":3220},[913],[569,3222],{"className":3223,"style":909},[835],[569,3225,3227,3231],{"className":3226},[603],[569,3228],{"className":3229,"style":3230},[607],"height:0.8491em;",[569,3232,3234,3237],{"className":3233},[612],[569,3235,822],{"className":3236},[612,613],[569,3238,3240],{"className":3239},[998],[569,3241,3243],{"className":3242},[1002],[569,3244,3246],{"className":3245},[1006],[569,3247,3249],{"className":3248,"style":3230},[1010],[569,3250,3251,3254],{"style":2495},[569,3252],{"className":3253,"style":1019},[1018],[569,3255,3257],{"className":3256},[1023,1024,1025,1026],[569,3258,3260,3263,3266],{"className":3259},[612,1026],[569,3261,816],{"className":3262},[612,1026],[569,3264,634],{"className":3265},[612,613,1026],[569,3267,788],{"className":3268},[612,613,1026],[2795,3270,3271],{},"Erwartungswert und Median gleichsetzen. Wegen der schiefen Verteilung ist der Median kleiner.",{"title":3273,"searchDepth":3274,"depth":3274,"links":3275},"",2,[3276,3277,3278],{"id":562,"depth":3274,"text":563},{"id":1802,"depth":3274,"text":1803},{"id":2789,"depth":3274,"text":2790},[3280,3283,3286,3289,3292,3295,3297],{"lhs":3281,"rhs":3282},"exp(-l*(s + t)) \u002F exp(-l*s)","exp(-l*t)",{"lhs":3284,"rhs":3285},"1 - exp(-l * log(2)\u002Fl)","0.5",{"lhs":3287,"rhs":3288},"1 \u002F 2000","0.0005",{"lhs":3290,"rhs":3291},"round(1 - exp(-0.0005 * 1000), 4)","0.3935",{"lhs":3293,"rhs":3294},"round(exp(-0.0005 * 4000), 4)","0.1353",{"lhs":3296,"rhs":2636},"round(log(2) \u002F 0.0005)",{"lhs":3298,"rhs":3299},"1 \u002F 0.0005^2","2000^2","\\lambda > 0,\\ x \\geq 0\\ (\\text{für } x \u003C 0 \\text{ ist } f(x) = 0)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>λ\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lambda > 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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">λ\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\">0\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>x\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmrow>\u003Cmtext>f\u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmtext>u\u003C\u002Fmtext>\u003Cmo>¨\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>r \u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmtext> ist \u003C\u002Fmtext>\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>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\geq 0\\ (\\text{für } x < 0 \\text{ ist } f(x) = 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:0.7719em;vertical-align:-0.136em;\">\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan 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