{"id":38277,"date":"2020-11-15T00:02:04","date_gmt":"2020-11-14T22:02:04","guid":{"rendered":"https:\/\/www.lecturesbureau.gr\/1\/?p=38277"},"modified":"2020-11-15T13:30:30","modified_gmt":"2020-11-15T11:30:30","slug":"jacob-bernoulli","status":"publish","type":"post","link":"https:\/\/www.lecturesbureau.gr\/1\/jacob-bernoulli\/","title":{"rendered":"\u0397 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03b7\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 Jacob Bernoulli \u03c3\u03c4\u03b1 \u03c4\u03c5\u03c7\u03b5\u03c1\u03ac \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9\u03b1 (Lectures Bureau)"},"content":{"rendered":"<p>\u039f \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 (Jacob Bernoulli, 6 \u0399\u03b1\u03bd\u03bf\u03c5\u03b1\u03c1\u03af\u03bf\u03c5 1655 \u2013 16 \u0391\u03c5\u03b3\u03bf\u03cd\u03c3\u03c4\u03bf\u03c5 1705) \u03ae\u03c4\u03b1\u03bd \u0395\u03bb\u03b2\u03b5\u03c4\u03cc\u03c2 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\u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03cc\u03c2 \u03bf\u03c1\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c4\u03b7\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2: \u03b1\u03bd \u03ad\u03bd\u03b1 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03ad\u03c7\u03b5\u03b9 a \u03c0\u03b9\u03b8\u03b1\u03bd\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b9\u03bb\u03b5\u03b3\u03bf\u03cd\u03bd \u03bf\u03c0\u03bf\u03b9\u03b1\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 b \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03ac \u03ad\u03c4\u03c3\u03b9 \u03ce\u03c3\u03c4\u03b5 b \u2264 a, \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03b5\u03af \u03bf\u03c0\u03bf\u03b9\u03bf\u03b4\u03ae\u03c0\u03bf\u03c4\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b1 b \u03b5\u03af\u03bd\u03b1\u03b9 ba. \u03a9\u03c3\u03c4\u03cc\u03c3\u03bf \u03b7 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03c4\u03bf\u03c5 \u03b5\u03c0\u03b9\u03c1\u03c1\u03bf\u03ae \u03b4\u03b5\u03bd \u03ae\u03c4\u03b1\u03bd \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7. \u0388\u03b3\u03c1\u03b1\u03c8\u03b5 \u03bc\u03cc\u03bd\u03bf \u03ad\u03bd\u03b1 \u03b2\u03b9\u03b2\u03bb\u03af\u03bf \u03c0\u03ac\u03bd\u03c9 \u03c3\u03c4\u03bf \u03b8\u03ad\u03bc\u03b1 \u03c4\u03bf 1525 \u03bc\u03b5 \u03c4\u03af\u03c4\u03bb\u03bf Liber de ludo aleae (\u0392\u03b9\u03b2\u03bb\u03af\u03bf \u03c0\u03ac\u03bd\u03c9 \u03c3\u03c4\u03b1 \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9\u03b1 \u03c4\u03cd\u03c7\u03b7\u03c2), \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03cc\u03bc\u03c9\u03c2 \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03b8\u03b7\u03ba\u03b5 \u03bc\u03b5\u03c4\u03ac \u03c4\u03bf\u03bd \u03b8\u03ac\u03bd\u03b1\u03c4\u03cc \u03c4\u03bf\u03c5 \u03c4\u03bf 1663.<\/p>\n<p>\u0397 \u03b7\u03bc\u03b5\u03c1\u03bf\u03bc\u03b7\u03bd\u03af\u03b1 \u03c4\u03b7\u03bd \u03bf\u03c0\u03bf\u03af\u03b1 \u03b7 \u03b9\u03c3\u03c4\u03bf\u03c1\u03b9\u03ba\u03bf\u03af \u03b8\u03b5\u03c9\u03c1\u03bf\u03cd\u03bd \u03c9\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c3\u03cd\u03b3\u03c7\u03c1\u03bf\u03bd\u03b7 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf 1654, \u03c7\u03c1\u03bf\u03bd\u03b9\u03ac \u03ba\u03b1\u03c4\u03ac \u03c4\u03b7\u03bd \u03bf\u03c0\u03bf\u03af\u03b1 \u03bf \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03ba\u03b1\u03b9 \u03bf \u03a6\u03b5\u03c1\u03bc\u03ac \u03ac\u03c1\u03c7\u03b9\u03c3\u03b1\u03bd \u03bd\u03b1 \u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03b3\u03c1\u03b1\u03c6\u03bf\u03cd\u03bd \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2. \u0391\u03b9\u03c4\u03af\u03b1 \u03b3\u03b9\u03b1 \u03b1\u03c5\u03c4\u03cc \u03ae\u03c4\u03b1\u03bd \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03c7\u03b5 \u03c3\u03c4\u03b5\u03af\u03bb\u03b5\u03b9 \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03c7\u03c1\u03bf\u03bd\u03b9\u03ac \u03ad\u03bd\u03b1\u03c2 \u03c4\u03b6\u03bf\u03b3\u03b1\u03b4\u03cc\u03c1\u03bf\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf \u03a0\u03b1\u03c1\u03af\u03c3\u03b9 \u03bf\u03bd\u03cc\u03bc\u03b1\u03c4\u03b9 \u0391\u03bd\u03c4\u03bf\u03c5\u03ac\u03bd \u0393\u03ba\u03bf\u03bc\u03c0\u03cc (Antoine Gombaud) \u03c3\u03c4\u03bf\u03bd \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03ba\u03b1\u03b9 \u03ac\u03bb\u03bb\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c1\u03c9\u03c4\u03ce\u03bd\u03c4\u03b1\u03c2 \u03b4\u03b9\u03ac\u03c6\u03bf\u03c1\u03b1 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2. \u03a0\u03b9\u03bf \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b1 \u03ad\u03b8\u03b5\u03c3\u03b5 \u03c4\u03bf \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03c4\u03b7\u03c2 \u03b4\u03b9\u03b1\u03af\u03c1\u03b5\u03c3\u03b7\u03c2 \u03c4\u03bf\u03c5 \u03c3\u03c4\u03bf\u03b9\u03c7\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2, \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9 \u03b4\u03cd\u03bf \u03c0\u03b1\u03b9\u03ba\u03c4\u03ce\u03bd \u03c3\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03ba\u03b5\u03c1\u03b4\u03af\u03b6\u03b5\u03b9 \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03b4\u03cd\u03bf \u03bc\u03b5\u03c4\u03ac \u03b1\u03c0\u03cc \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b3\u03cd\u03c1\u03c9\u03bd. \u03a4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u03b1\u03c6\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03c4\u03bf\u03bd \u03b4\u03af\u03ba\u03b1\u03b9\u03bf \u03b4\u03b9\u03b1\u03bc\u03bf\u03b9\u03c1\u03b1\u03c3\u03bc\u03cc \u03c4\u03b7\u03c2 \u03b1\u03be\u03af\u03b1\u03c2 \u03c0\u03bf\u03c5 \u03b5\u03af\u03c7\u03b5 \u03c3\u03c5\u03b3\u03ba\u03b5\u03bd\u03c4\u03c1\u03c9\u03b8\u03b5\u03af \u03b1\u03bd \u03c4\u03bf \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9 \u03c3\u03c4\u03b1\u03bc\u03b1\u03c4\u03bf\u03cd\u03c3\u03b5 \u03c0\u03c1\u03cc\u03c9\u03c1\u03b1 \u03bb\u03cc\u03b3\u03c9 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b1\u03c2 \u03b5\u03be\u03c9\u03c4\u03b5\u03c1\u03b9\u03ba\u03ae\u03c2 \u03b1\u03b9\u03c4\u03af\u03b1\u03c2.<\/p>\n<p>\u0397 \u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1 \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03ba\u03b1\u03b9 \u03a6\u03b5\u03c1\u03bc\u03ac \u03c0\u03c1\u03bf\u03ba\u03ac\u03bb\u03b5\u03c3\u03b5 \u03c4\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03ac\u03bb\u03bb\u03c9\u03bd \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, \u03cc\u03c0\u03c9\u03c2 \u03bf \u039a\u03c1\u03af\u03c3\u03c4\u03b9\u03b1\u03bd \u03a7\u03cc\u03c5\u03c7\u03b5\u03bd\u03c2, \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03c4\u03bf 1657 \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b5 \u03c4\u03bf De ratiociniis in aleae ludo (\u03a5\u03c0\u03bf\u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03bf\u03af \u03c3\u03c4\u03b1 \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03c4\u03cd\u03c7\u03b7\u03c2).\u039a\u03b1\u03c4\u03ac \u03c4\u03b7\u03bd \u03b4\u03b9\u03ac\u03c1\u03ba\u03b5\u03b9\u03b1 \u03b1\u03c5\u03c4\u03ae\u03c2 \u03c4\u03b7\u03c2 \u03c0\u03b5\u03c1\u03b9\u03cc\u03b4\u03bf\u03c5 \u03bf \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03ac \u03c4\u03bf\u03c5 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03c4\u03bf \u03c4\u03c1\u03af\u03b3\u03c9\u03bd\u03bf \u03c4\u03bf\u03c5 \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb. \u0391\u03bd\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd\u03c4\u03b1\u03bd \u03c3\u03c4\u03bf \u03c4\u03c1\u03af\u03b3\u03c9\u03bd\u03bf, \u03c3\u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 Trait\u00e9 du triangle arithm\u00e9tique (\u03a7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03ac \u03c4\u03bf\u03c5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03bf\u03cd \u03c4\u03c1\u03b9\u03b3\u03ce\u03bd\u03bf\u03c5), \u03c9\u03c2 \u03c4\u03bf \u00ab\u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03cc \u03c4\u03c1\u03af\u03b3\u03c9\u03bd\u03bf\u00bb.<\/p>\n<p>\u0391\u03c1\u03b3\u03cc\u03c4\u03b5\u03c1\u03b1 \u03bf \u0393\u03b9\u03b1\u03bd \u03bd\u03c4\u03b5 \u0392\u03b9\u03c4 \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b5 \u03c0\u03b1\u03c1\u03cc\u03bc\u03bf\u03b9\u03bf \u03c5\u03bb\u03b9\u03ba\u03cc \u03c3\u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 Waerdye van Lyf-Renten, \u03c3\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b5 \u03c3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b5\u03c2 \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03af\u03c3\u03b5\u03b9 \u03c4\u03bf \u03c0\u03c1\u03bf\u03c3\u03b4\u03cc\u03ba\u03b9\u03bc\u03bf \u03b6\u03c9\u03ae\u03c2.<\/p>\n<p>\u039f \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03b5\u03af\u03c7\u03b5 \u03bc\u03b5\u03b3\u03ac\u03bb\u03b7 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd \u03ad\u03c1\u03b3\u03bf\u03c5 \u03bc\u03b5\u03c4\u03b1\u03be\u03cd 1684 \u03ba\u03b1\u03b9 1689 \u03c3\u03c4\u03b7\u03bd \u03bf\u03c0\u03bf\u03af\u03b1 \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9 \u03ba\u03b1\u03b9 \u03c4\u03bf Ars Conjectandi.<br \/>\n\u038c\u03c4\u03b1\u03bd \u03be\u03b5\u03ba\u03af\u03bd\u03b7\u03c3\u03b5 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u03c4\u03bf 1684 \u03c3\u03b5 \u03b7\u03bb\u03b9\u03ba\u03af\u03b1 30 \u03b5\u03c4\u03ce\u03bd, \u03b4\u03b5\u03bd \u03b5\u03af\u03c7\u03b5 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03b4\u03b9\u03b1\u03b2\u03ac\u03c3\u03b5\u03b9 \u03c4\u03bf<br \/>\n\u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03b3\u03b9\u03b1 \u03c4\u03bf \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03cc \u03c4\u03c1\u03af\u03b3\u03c9\u03bd\u03bf \u03bf\u03cd\u03c4\u03b5 \u03c4\u03bf\u03c5 \u03bd\u03c4\u03b5 \u0392\u03b9\u03c4 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c3\u03c4\u03b1\u03c4\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1. \u0395\u03af\u03c7\u03b5 \u03b6\u03b7\u03c4\u03ae\u03c3\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03b1\u03bd\u03c4\u03af\u03b3\u03c1\u03b1\u03c6\u03bf \u03c4\u03bf\u03c5 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03bf\u03c5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03c4\u03bf\u03c5, \u0393\u03ba\u03cc\u03c4\u03c6\u03c1\u03b9\u03bd\u03c4 \u0392\u03af\u03bb\u03c7\u03b5\u03bb\u03bc \u039b\u03ac\u03b9\u03bc\u03c0\u03bd\u03b9\u03c4\u03c2, \u03b1\u03bb\u03bb\u03ac \u03bf \u039b\u03ac\u03b9\u03bc\u03c0\u03bd\u03b9\u03c4\u03c2 \u03b4\u03b5\u03bd \u03ba\u03b1\u03c4\u03ac\u03c6\u03b5\u03c1\u03b5 \u03bd\u03b1 \u03c4\u03bf\u03c5 \u03c4\u03bf \u03c3\u03c4\u03b5\u03af\u03bb\u03b5\u03b9. \u03a4\u03bf\u03c5 \u03ad\u03c3\u03c4\u03b5\u03b9\u03bb\u03b5 \u03c9\u03c3\u03c4\u03cc\u03c3\u03bf \u03c4\u03b1 \u03ad\u03c1\u03b3\u03b1 \u03c4\u03bf\u03c5 \u03a0\u03b1\u03c3\u03ba\u03ac\u03bb \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5 \u03a7\u03cc\u03c5\u03c7\u03b5\u03bd\u03c2, \u03c3\u03c4\u03b1 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b2\u03b1\u03c3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf Ars Conjectandi.<\/p>\n<p>\u039f \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03bf\u03bd\u03cc\u03bc\u03b1\u03c3\u03b5 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf Ars Conjectandi \u03b5\u03c0\u03b5\u03b9\u03b4\u03ae \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03c4\u03bf \u03c3\u03c5\u03bd\u03b4\u03ad\u03c3\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 ars inveniendi \u03c4\u03bf\u03c5 \u03c3\u03c7\u03bf\u03bb\u03b1\u03c3\u03c4\u03b9\u03ba\u03b9\u03c3\u03bc\u03bf\u03cd, \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c3\u03b5\u03b9\u03c1\u03ac \u03c4\u03bf\u03c5 \u03c5\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03b9 \u03cc\u03c4\u03b9 \u03c4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03ac \u03c4\u03bf\u03c5 \u03b8\u03b1 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b1\u03bd \u03bd\u03b1 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03c3\u03c4\u03bf\u03cd\u03bd \u03c3\u03b5 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03c0\u03c4\u03c5\u03c7\u03ad\u03c2 \u03c4\u03b7\u03c2 \u03b6\u03c9\u03ae\u03c2 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03ba\u03bf\u03b9\u03bd\u03c9\u03bd\u03af\u03b1\u03c2.<\/p>\n<p>\u03a4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9, \u03b1\u03c1\u03c7\u03b9\u03ba\u03ac \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03c5\u03bc\u03ad\u03bd\u03bf \u03c3\u03c4\u03b1 \u03bb\u03b1\u03c4\u03b9\u03bd\u03b9\u03ba\u03ac, \u03b4\u03b9\u03b1\u03b9\u03c1\u03b5\u03af\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c4\u03ad\u03c3\u03c3\u03b5\u03c1\u03b1 \u03bc\u03ad\u03c1\u03b7.<\/p>\n<p>\u03a4o \u03c0\u03c1\u03ce\u03c4\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03c9\u03c2 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9.<\/p>\n<p>\u0397\u00a0<b>\u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03bb\u03b9<\/b> \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03b4\u03b9\u03b1\u03ba\u03c1\u03b9\u03c4\u03ae \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae\u03c2 \u03c4\u03c5\u03c7\u03b1\u03af\u03b1\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae\u03c2. \u03a0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03ad\u03bd\u03b1 \u03c4\u03c5\u03c7\u03b1\u03af\u03bf \u03c0\u03b5\u03af\u03c1\u03b1\u03bc\u03b1 \u03bc\u03b5 \u03b4\u03cd\u03bf \u03c0\u03b9\u03b8\u03b1\u03bd\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 (\u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 &#8211; \u03b1\u03c0\u03bf\u03c4\u03c5\u03c7\u03af\u03b1) \u03ba\u03b1\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1\u03c2 p.<\/p>\n<p>\u0398\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b7\u03bd \u03c4\u03c5\u03c7\u03b1\u03af\u03b1 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae \u03a7 \u03c0\u03bf\u03c5 \u03c0\u03b1\u03af\u03c1\u03bd\u03b5\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2 0 \u03ae 1. \u0393\u03b9\u03b1 \u03a7=1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1 \u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03a7=0 \u03b1\u03c0\u03bf\u03c4\u03c5\u03c7\u03af\u03b1. \u0397 \u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03bb\u03b9 \u03c0\u03b1\u03af\u03c1\u03bd\u03b5\u03b9 \u03c4\u03b9\u03c2 \u03b5\u03be\u03ae\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2:<\/p>\n<dl>\n<dd>P(X=1)=p<br \/>\nP(X=0)=q=1-p<\/dd>\n<\/dl>\n<p>&nbsp;<\/p>\n<table class=\"wikitable\">\n<tbody>\n<tr>\n<th><b>\u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2<\/b><\/th>\n<th><b>\u03c0\u03b1\u03c1\u03ac\u03bc\u03b5\u03c4\u03c1\u03bf\u03b9<\/b><\/th>\n<th><b>\u03bc\u03ad\u03c3\u03b7 \u03c4\u03b9\u03bc\u03ae<\/b><\/th>\n<th><b>\u03b4\u03b9\u03b1\u03ba\u03cd\u03bc\u03b1\u03bd\u03c3\u03b7<\/b><\/th>\n<\/tr>\n<tr>\n<td><span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">p(1-p)<\/span><\/span><\/td>\n<td><span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">,<img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4449572ac985c35af802cf3a3f8e28594be10554\" alt=\"{\\displaystyle \\,p\\in [0,1]}\" aria-hidden=\"true\" \/><br \/>\n<\/span><\/span><\/td>\n<td><span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">p<\/span><\/span><\/td>\n<td><span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">p(1-p)}<br \/>\n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>\u03a3\u03c4\u03bf \u03c0\u03c1\u03ce\u03c4\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03bf \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03c4\u03b7\u03bd \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03a7\u03cc\u03c5\u03c7\u03b5\u03bd\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u03c4\u03b9\u03bc\u03ae, \u03ae \u03bf \u03b6\u03c5\u03b3\u03b9\u03c3\u03bc\u03ad\u03bd\u03bf\u03c2 \u03bc\u03ad\u03c3\u03bf\u03c2 \u03cc\u03bb\u03c9\u03bd \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03ce\u03bd \u03b5\u03bd\u03b4\u03b5\u03c7\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03b5\u03bd\u03cc\u03c2 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03bf\u03c2. \u039f \u03a7\u03cc\u03c5\u03c7\u03b5\u03bd\u03c2 \u03b5\u03af\u03c7\u03b5 \u03b1\u03bd\u03b1\u03c0\u03c4\u03cd\u03be\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b1\u03ba\u03cc\u03bb\u03bf\u03c5\u03b8\u03b7 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7: E = p0a0+p1a1+p2a2+\u00b7\u00b7\u00b7+pnan p0+p1+\u00b7\u00b7\u00b7+pn . \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7, \u03c4\u03bf E \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b1\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u03c4\u03b9\u03bc\u03ae, \u03c4\u03bf pi \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03bd\u03b1 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03c9\u03b8\u03b5\u03af \u03ba\u03ac\u03b8\u03b5 \u03c4\u03b9\u03bc\u03ae, \u03ba\u03b1\u03b9 \u03c4\u03bf ai \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c4\u03b9\u03bc\u03ad\u03c2. \u039f \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03ba\u03b1\u03bd\u03bf\u03bd\u03b9\u03ba\u03bf\u03c0\u03bf\u03af\u03b7\u03c3\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u03c4\u03b9\u03bc\u03ae \u03c5\u03c0\u03bf\u03b8\u03ad\u03c4\u03bf\u03bd\u03c4\u03b1\u03c2 \u03cc\u03c4\u03b9 pi \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03cc\u03bb\u03c9\u03bd \u03c4\u03c9\u03bd \u03be\u03ad\u03bd\u03c9\u03bd \u03b5\u03bd\u03b4\u03b5\u03c7\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd, \u03bf\u03b4\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03bf\u03c2 \u03ad\u03c4\u03c3\u03b9 \u03c3\u03c4\u03bf \u03c3\u03c5\u03bc\u03c0\u03ad\u03c1\u03b1\u03c3\u03bc\u03b1 \u03cc\u03c4\u03b9 p0 + p1 + &#8230; + pn = 1.<\/p>\n<p>\u039c\u03af\u03b1 \u03b1\u03ba\u03cc\u03bc\u03b1 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03bd\u03b1\u03c0\u03c4\u03cd\u03c7\u03b8\u03b7\u03ba\u03b5 \u03c3\u03b5 \u03b1\u03c5\u03c4\u03cc \u03c4\u03bf \u03c4\u03bc\u03ae\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bd\u03b1 \u03b5\u03c0\u03b9\u03c4\u03b5\u03c5\u03c7\u03b8\u03b5\u03af \u03c4\u03bf\u03c5\u03bb\u03ac\u03c7\u03b9\u03c3\u03c4\u03bf\u03bd \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03b9\u03ce\u03bd \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03c0\u03b5\u03b9\u03c1\u03b1\u03bc\u03ac\u03c4\u03c9\u03bd, \u03c0\u03bf\u03c5 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ad\u03c2 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9, \u03bc\u03b5 \u03b4\u03b9\u03ac\u03c6\u03bf\u03c1\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03b4\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03cc\u03bc\u03c9\u03c2 \u03cc\u03c4\u03b9 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03b9\u03c4\u03c5\u03c7\u03af\u03b1\u03c2 \u03c3\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03c0\u03b5\u03af\u03c1\u03b1\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03af\u03b4\u03b9\u03b1.<\/p>\n<p>\u03a3\u03c4\u03bf \u03c4\u03c1\u03af\u03c4\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2, \u03bf \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03b5\u03c6\u03ac\u03c1\u03bc\u03bf\u03c3\u03b5 \u03c4\u03b9\u03c2 \u03c4\u03b5\u03c7\u03bd\u03b9\u03ba\u03ad\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2, \u03c0\u03bf\u03c5 \u03bc\u03b5\u03bb\u03ad\u03c4\u03b7\u03c3\u03b5 \u03c3\u03c4\u03b1 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b1 \u03bc\u03ad\u03c1\u03b7, \u03c3\u03b5 \u03ba\u03bf\u03b9\u03bd\u03ac \u03c4\u03c5\u03c7\u03b5\u03c1\u03ac \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03b5\u03c0\u03bf\u03c7\u03ae\u03c2 \u03bc\u03b5 \u03c4\u03c1\u03ac\u03c0\u03bf\u03c5\u03bb\u03b1 \u03ae \u03b6\u03ac\u03c1\u03b9\u03b1. \u03a0\u03b1\u03c1\u03bf\u03c5\u03c3\u03af\u03b1\u03c3\u03b5 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b5 \u03b1\u03c5\u03c4\u03ac \u03b1\u03bb\u03bb\u03ac \u03ba\u03b1\u03b9 \u03b3\u03b5\u03bd\u03b9\u03ba\u03b5\u03cd\u03c3\u03b5\u03b9\u03c2 \u03b1\u03c5\u03c4\u03ce\u03bd \u03c7\u03c9\u03c1\u03af\u03c2 \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03b5\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2. \u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03ad\u03bd\u03b1 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b5\u03af\u03c7\u03b5 \u03bd\u03b1 \u03ba\u03ac\u03bd\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b1\u03bc\u03b5\u03bd\u03cc\u03bc\u03b5\u03bd\u03b7 \u03c4\u03b9\u03bc\u03ae \u03c6\u03b9\u03b3\u03bf\u03cd\u03c1\u03c9\u03bd \u03c0\u03bf\u03c5 \u03b8\u03b1 \u03c4\u03c1\u03b1\u03b2\u03bf\u03cd\u03c3\u03b5 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03c2 \u03b1\u03c0\u03cc \u03bc\u03b9\u03b1 \u03c4\u03c1\u03ac\u03c0\u03bf\u03c5\u03bb\u03b1 20 \u03c6\u03cd\u03bb\u03bb\u03c9\u03bd \u03bc\u03b5 10 \u03c6\u03b9\u03b3\u03bf\u03cd\u03c1\u03b5\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03c3\u03b5 \u03bd\u03b1 \u03b3\u03b5\u03bd\u03b9\u03ba\u03b5\u03c5\u03b8\u03b5\u03af \u03c3\u03b5 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03bc\u03b5 a \u03c6\u03cd\u03bb\u03bb\u03b1 \u03c0\u03bf\u03c5 \u03b5\u03af\u03c7\u03b1\u03bd b \u03c6\u03b9\u03b3\u03bf\u03cd\u03c1\u03b5\u03c2 \u03ad\u03c4\u03c3\u03b9 \u03ce\u03c3\u03c4\u03b5 b&lt;a.<\/p>\n<p>\u03a4\u03bf \u03c4\u03ad\u03c4\u03b1\u03c1\u03c4\u03bf \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b5\u03cd\u03b5\u03c4\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c3\u03b5 \u03c0\u03c1\u03bf\u03c3\u03c9\u03c0\u03b9\u03ba\u03ad\u03c2, \u03b4\u03b9\u03ba\u03b1\u03c3\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9\u03ba\u03bf\u03bd\u03bf\u03bc\u03b9\u03ba\u03ad\u03c2 \u03b1\u03c0\u03bf\u03c6\u03ac\u03c3\u03b5\u03b9\u03c2. \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03b5\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bf \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c3\u03c4\u03bf\u03bd \u03c4\u03c1\u03cc\u03c0\u03bf \u03c3\u03ba\u03ad\u03c8\u03b7\u03c2 \u03c0\u03bf\u03c5 \u03c3\u03c7\u03b5\u03c4\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2, \u03ba\u03b1\u03c4\u03ac \u03c4\u03bf\u03bd \u03bf\u03c0\u03bf\u03af\u03bf \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03b5\u03bc\u03c0\u03b5\u03b9\u03c1\u03b9\u03ba\u03cc \u03c4\u03c1\u03cc\u03c0\u03bf. \u0394\u03b9\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03bc\u03b5 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03c0\u03bf\u03c5 \u03c3\u03c7\u03b5\u03c4\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bd\u03cc\u03bc\u03bf \u03c4\u03c9\u03bd \u03bc\u03b5\u03b3\u03ac\u03bb\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd, \u03c3\u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03bf \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03c0\u03b5\u03c1\u03b9\u03ad\u03b3\u03c1\u03b1\u03c8\u03b5 \u03cc\u03c4\u03b9 \u03c0\u03c1\u03bf\u03b2\u03bb\u03ad\u03c0\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b1 \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03c0\u03b1\u03c1\u03b1\u03c4\u03ae\u03c1\u03b7\u03c3\u03b7\u03c2 \u03b8\u03b1 \u03c0\u03c1\u03bf\u03c3\u03b5\u03b3\u03b3\u03af\u03b6\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03b8\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03ba\u03b1\u03b8\u03ce\u03c2 \u03b3\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ad\u03c2, \u03b5\u03bd\u03ce \u03ba\u03b1\u03c4\u03ac \u03c4\u03b7\u03bd \u03c3\u03c7\u03bf\u03bb\u03ae \u03c4\u03b7\u03c2 \u03c3\u03c5\u03c7\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2, \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03bd\u03c4\u03af\u03c3\u03c4\u03c1\u03bf\u03c6\u03b1. \u039f \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03ae\u03c4\u03b1\u03bd \u03c0\u03bf\u03bb\u03cd \u03c0\u03b5\u03c1\u03ae\u03c6\u03b1\u03bd\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03b1\u03c5\u03c4\u03cc \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1, \u03b1\u03bd\u03b1\u03c6\u03b5\u03c1\u03cc\u03bc\u03b5\u03bd\u03bf\u03c2 \u03c3\u03b5 \u03b1\u03c5\u03c4\u03cc \u03c9\u03c2 \u03c4\u03bf \u00ab\u03c7\u03c1\u03c5\u03c3\u03cc \u03b8\u03b5\u03ce\u03c1\u03b7\u03bc\u03ac\u00bb \u03c4\u03bf\u03c5,\u00a0 \u03ba\u03b1\u03b9 \u03c3\u03c7\u03bf\u03bb\u03af\u03b1\u03c3\u03b5 \u03cc\u03c4\u03b9 \u03ae\u03c4\u03b1\u03bd \u00ab\u03ad\u03bd\u03b1 \u03c0\u03c1\u03cc\u03b2\u03bb\u03b7\u03bc\u03b1 \u03bc\u03b5 \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b5\u03af\u03c7\u03b5 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b7\u03b8\u03b5\u03af \u03b3\u03b9\u03b1 \u03b5\u03af\u03ba\u03bf\u03c3\u03b9 \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1\u00bb.<\/p>\n<h2><span id=\"\u03a4\u03bf_\u03c4\u03ad\u03bb\u03bf\u03c2\" class=\"mw-headline\">\u03a4\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2<\/span><\/h2>\n<p>\u039f \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03b5\u03c0\u03ad\u03bb\u03b5\u03be\u03b5 \u03c4\u03bf \u03c3\u03c7\u03ae\u03bc\u03b1 \u03bc\u03af\u03b1\u03c2\u00a0\u03bb\u03bf\u03b3\u03b1\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ae\u03c2 \u03c3\u03c0\u03b5\u03af\u03c1\u03b1\u03c2\u00a0\u03ba\u03b1\u03b9 \u03c4\u03b7 \u03c6\u03c1\u03ac\u03c3\u03b7\u00a0<i>Eadem mutata resurgo<\/i>\u00a0(<i>\u0391\u03bb\u03bb\u03b1\u03b3\u03bc\u03ad\u03bd\u03bf\u03c2 \u03ba\u03b1\u03b9 \u03cc\u03bc\u03c9\u03c2 \u03bf \u03af\u03b4\u03b9\u03bf\u03c2, \u03b1\u03bd\u03b1\u03c3\u03c4\u03b1\u03af\u03bd\u03bf\u03bc\u03b1\u03b9<\/i>) \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c4\u03b1\u03c6\u03cc\u03c0\u03bb\u03b1\u03ba\u03ac \u03c4\u03bf\u03c5. \u0397 \u03c3\u03c0\u03b5\u03af\u03c1\u03b1 \u03c0\u03bf\u03c5 \u03ba\u03b1\u03c4\u03b1\u03c3\u03ba\u03b5\u03c5\u03ac\u03c3\u03c4\u03b7\u03ba\u03b5 \u03c9\u03c3\u03c4\u03cc\u03c3\u03bf \u03c4\u03b5\u03bb\u03b9\u03ba\u03ac \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c4\u03b5\u03c7\u03bd\u03af\u03c4\u03b5\u03c2 \u03ae\u03c4\u03b1\u03bd\u00a0\u03c3\u03c0\u03b5\u03af\u03c1\u03b1 \u03c4\u03bf\u03c5 \u0391\u03c1\u03c7\u03b9\u03bc\u03ae\u03b4\u03b7.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Lectures Bureau<\/strong><\/p>\n<p><em><strong>\u03a0\u0397\u0393\u0395\u03a3: 1. WIKIPEDIA<\/strong><\/em><br \/>\n<em><strong>\u00a0 \u00a0 2.http:\/\/portal.survey.ntua.gr\/main\/labs\/hgeod\/ddeli\/analmgeo\/Digital_library\/Wikepedia_Articles_on%20Propabilities.pdf<br \/>\n<\/strong><\/em><\/p>\n<p>&nbsp;<\/p>\n<p><em><strong><br \/>\n<\/strong>\u0395\u03b9\u03ba\u03cc\u03bd\u03b1: https:\/\/dribbble.com\/shots\/6720610-Jacob-Bernoulli<strong><br \/>\n<\/strong><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u039f \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 (Jacob Bernoulli, 6 \u0399\u03b1\u03bd\u03bf\u03c5\u03b1\u03c1\u03af\u03bf\u03c5 1655 \u2013 16 \u0391\u03c5\u03b3\u03bf\u03cd\u03c3\u03c4\u03bf\u03c5 1705) \u03ae\u03c4\u03b1\u03bd \u0395\u03bb\u03b2\u03b5\u03c4\u03cc\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03b4\u03b9\u03b1\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03bf\u03b9\u03ba\u03bf\u03b3\u03ad\u03bd\u03b5\u03b9\u03b1\u03c2 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9. \u039f \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u03b3\u03b5\u03bd\u03bd\u03ae\u03b8\u03b7\u03ba\u03b5 \u03c3\u03c4\u03b7 \u0392\u03b1\u03c3\u03b9\u03bb\u03b5\u03af\u03b1. \u0391\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03af\u03b1 \u03c4\u03bf\u03c5 \u03c0\u03b1\u03c4\u03ad\u03c1\u03b1 \u03c4\u03bf\u03c5, \u03c3\u03c0\u03bf\u03cd\u03b4\u03b1\u03c3\u03b5 \u03b8\u03b5\u03bf\u03bb\u03bf\u03b3\u03af\u03b1 \u03ba\u03b1\u03b9 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03ba\u03bb\u03b7\u03c1\u03b9\u03ba\u03cc\u03c2. \u0391\u03bd\u03c4\u03b9\u03b8\u03ad\u03c4\u03c9\u03c2 \u03cc\u03bc\u03c9\u03c2 \u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03af\u03b5\u03c2&#8230;<\/p>\n","protected":false},"author":1,"featured_media":38285,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[66],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=900%2C609&ssl=1","rttpg_featured_image_url":{"full":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=900%2C609&ssl=1",900,609,false],"landscape":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg",900,609,false],"portraits":["https:\/\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg",900,609,false],"thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=150%2C150&ssl=1",150,150,true],"medium":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=300%2C203&ssl=1",300,203,true],"large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=900%2C609&ssl=1",900,609,true],"1536x1536":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=900%2C609&ssl=1",900,609,true],"2048x2048":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=900%2C609&ssl=1",900,609,true],"portfolio-square":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=570%2C570&ssl=1",570,570,true],"portfolio-portrait":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=600%2C609&ssl=1",600,609,true],"portfolio-landscape":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=800%2C600&ssl=1",800,600,true],"menu-featured-post":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=345%2C198&ssl=1",345,198,true],"qode-carousel_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=400%2C260&ssl=1",400,260,true],"portfolio_slider":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=500%2C380&ssl=1",500,380,true],"portfolio_masonry_regular":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=500%2C500&ssl=1",500,500,true],"portfolio_masonry_wide":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=900%2C500&ssl=1",900,500,true],"portfolio_masonry_tall":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=500%2C609&ssl=1",500,609,true],"portfolio_masonry_large":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=900%2C609&ssl=1",900,609,true],"portfolio_masonry_with_space":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=700%2C474&ssl=1",700,474,true],"latest_post_boxes":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=539%2C303&ssl=1",539,303,true],"woocommerce_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=300%2C300&ssl=1",300,300,true],"woocommerce_single":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?fit=600%2C406&ssl=1",600,406,true],"woocommerce_gallery_thumbnail":["https:\/\/i0.wp.com\/www.lecturesbureau.gr\/1\/wp-content\/uploads\/2020\/11\/post-2369b.jpg?resize=100%2C100&ssl=1",100,100,true]},"rttpg_author":{"display_name":"admin","author_link":"https:\/\/www.lecturesbureau.gr\/1\/author\/admin\/"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/www.lecturesbureau.gr\/1\/category\/science\/\" rel=\"category tag\">\u0395\u03a0\u0399\u03a3\u03a4\u0397\u039c\u0397<\/a>","rttpg_excerpt":"\u039f \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 (Jacob Bernoulli, 6 \u0399\u03b1\u03bd\u03bf\u03c5\u03b1\u03c1\u03af\u03bf\u03c5 1655 \u2013 16 \u0391\u03c5\u03b3\u03bf\u03cd\u03c3\u03c4\u03bf\u03c5 1705) \u03ae\u03c4\u03b1\u03bd \u0395\u03bb\u03b2\u03b5\u03c4\u03cc\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2, \u03ad\u03bd\u03b1\u03c2 \u03b1\u03c0\u03cc \u03c4\u03bf\u03c5\u03c2 \u03c0\u03bf\u03bb\u03bb\u03bf\u03cd\u03c2 \u03b4\u03b9\u03b1\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf\u03c5\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03bf\u03cd\u03c2 \u03c4\u03b7\u03c2 \u03bf\u03b9\u03ba\u03bf\u03b3\u03ad\u03bd\u03b5\u03b9\u03b1\u03c2 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9. \u039f 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