{"id":57712,"date":"2023-12-23T19:29:50","date_gmt":"2023-12-23T17:29:50","guid":{"rendered":"https:\/\/omathimatikos.gr\/?p=57712"},"modified":"2023-12-22T09:32:09","modified_gmt":"2023-12-22T07:32:09","slug":"%ce%b7-%ce%b5%cf%86%ce%b1%cf%81%ce%bc%ce%bf%ce%b3%ce%ae-%cf%84%ce%b7%cf%82-%ce%b8%ce%b5%cf%89%cf%81%ce%af%ce%b1%cf%82-%cf%84%ce%bf%cf%85-jacob-bernoulli-%cf%83%cf%84%ce%b1-%cf%84%cf%85%cf%87%ce%b5","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=57712","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"},"content":{"rendered":"

<\/p>\n

\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 \u03c4\u03c9\u03bd \u03b3\u03bf\u03bd\u03ad\u03c9\u03bd \u03c4\u03bf\u03c5 \u03c3\u03c0\u03bf\u03cd\u03b4\u03b1\u03c3\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03b1\u03c3\u03c4\u03c1\u03bf\u03bd\u03bf\u03bc\u03af\u03b1.<\/p><\/blockquote>\n

\u03a4\u03b1\u03be\u03af\u03b4\u03b5\u03c8\u03b5 \u03c3\u03c4\u03b7\u03bd \u0395\u03c5\u03c1\u03ce\u03c0\u03b7 \u03b1\u03c0\u03cc \u03c4\u03bf 1676 \u03bc\u03ad\u03c7\u03c1\u03b9 \u03c4\u03bf 1682, \u03b5\u03bd\u03b7\u03bc\u03b5\u03c1\u03c9\u03bd\u03cc\u03bc\u03b5\u03bd\u03bf\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b5\u03c2 \u03b1\u03bd\u03b1\u03ba\u03b1\u03bb\u03cd\u03c8\u03b5\u03b9\u03c2 \u03c3\u03c4\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03c4\u03b9\u03c2 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b5\u03c2, \u03cc\u03c0\u03c9\u03c2 \u03c4\u03b1 \u03ad\u03c1\u03b3\u03b1 \u03c4\u03bf\u03c5 \u03a1\u03cc\u03bc\u03c0\u03b5\u03c1\u03c4 \u039c\u03c0\u03cc\u03b9\u03bb \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5 \u03a1\u03cc\u03bc\u03c0\u03b5\u03c1\u03c4 \u03a7\u03bf\u03c5\u03ba.<\/p>\n

\n
\"\"<\/figure>\n<\/div>\n

\u0395\u03be\u03bf\u03b9\u03ba\u03b5\u03b9\u03ce\u03b8\u03b7\u03ba\u03b5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bb\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc \u03bc\u03ad\u03c3\u03c9 \u03c4\u03b7\u03c2 \u03b1\u03bb\u03bb\u03b7\u03bb\u03bf\u03b3\u03c1\u03b1\u03c6\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u0393\u03ba\u03cc\u03c4\u03c6\u03c1\u03b9\u03bd\u03c4 \u039b\u03ac\u03b9\u03bc\u03c0\u03bd\u03b9\u03c4\u03c2, \u03ba\u03b1\u03b9 \u03bc\u03b5\u03c4\u03ac \u03c3\u03c5\u03bd\u03b5\u03c1\u03b3\u03ac\u03c3\u03c4\u03b7\u03ba\u03b5 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03b1\u03b4\u03b5\u03c1\u03c6\u03cc \u03c4\u03bf\u03c5, \u0393\u03b9\u03cc\u03c7\u03b1\u03bd, \u03c3\u03b5 \u03b4\u03b9\u03ac\u03c6\u03bf\u03c1\u03b5\u03c2 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2, \u03bc\u03b5 \u03c0\u03b9\u03bf \u03c3\u03b7\u03bc\u03b1\u03bd\u03c4\u03b9\u03ba\u03ad\u03c2 \u03c4\u03b7\u03bd \u03b4\u03b7\u03bc\u03bf\u03c3\u03af\u03b5\u03c5\u03c3\u03b7 \u03b4\u03b9\u03b1\u03c4\u03c1\u03b9\u03b2\u03ce\u03bd \u03c3\u03c4\u03b9\u03c2 \u03c5\u03c0\u03b5\u03c1\u03b2\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2 \u03ba\u03b1\u03bc\u03c0\u03cd\u03bb\u03b5\u03c2 (1696) \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b9\u03c3\u03bf\u03c0\u03b5\u03c1\u03b9\u03bc\u03b5\u03c4\u03c1\u03b9\u03ba\u03ae \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 (1700, 1701). \u03a4\u03bf 1690, \u03bf \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u03ad\u03b3\u03b9\u03bd\u03b5 \u03bf \u03c0\u03c1\u03ce\u03c4\u03bf\u03c2 \u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03b1\u03bd\u03ad\u03c0\u03c4\u03c5\u03be\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b5\u03c7\u03bd\u03b9\u03ba\u03ae \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b5\u03c0\u03af\u03bb\u03c5\u03c3\u03b7 \u03b4\u03b9\u03b1\u03c7\u03c9\u03c1\u03af\u03c3\u03b9\u03bc\u03c9\u03bd \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ce\u03bd \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03c9\u03bd.<\/p>\n

\u038c\u03c4\u03b1\u03bd \u03b3\u03cd\u03c1\u03b9\u03c3\u03b5 \u03c3\u03c4\u03b7 \u0392\u03b1\u03c3\u03b9\u03bb\u03b5\u03af\u03b1 \u03c4\u03bf 1682 \u03af\u03b4\u03c1\u03c5\u03c3\u03b5 \u03c3\u03c7\u03bf\u03bb\u03ae \u03b3\u03b9\u03b1 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03ba\u03b1\u03b9 \u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b5\u03c2. \u0394\u03b9\u03bf\u03c1\u03af\u03c3\u03c4\u03b7\u03ba\u03b5 \u03ba\u03b1\u03b8\u03b7\u03b3\u03b7\u03c4\u03ae\u03c2 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c3\u03c4\u03bf \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b9\u03bf \u03c4\u03b7\u03c2 \u0392\u03b1\u03c3\u03b9\u03bb\u03b5\u03af\u03b1\u03c2 \u03c4\u03bf 1687, \u03c0\u03b1\u03c1\u03b1\u03bc\u03ad\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03b8\u03ad\u03c3\u03b7 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03c5\u03c0\u03cc\u03bb\u03bf\u03b9\u03c0\u03b7 \u03b6\u03c9\u03ae \u03c4\u03bf\u03c5.<\/p>\n

\n
\"\"<\/figure>\n<\/div>\n

\u03a4\u03bf \u03c0\u03b9\u03bf \u03b3\u03bd\u03c9\u03c3\u03c4\u03cc \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u0393\u03b9\u03b1\u03ba\u03cc\u03bc\u03c0 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf\u00a0Ars Conjectandi (\u0397 \u03c4\u03ad\u03c7\u03bd\u03b7 \u03c4\u03bf\u03c5 \u03b5\u03b9\u03ba\u03ac\u03b6\u03b5\u03b9\u03bd)<\/em><\/strong>, \u03c4\u03bf \u03bf\u03c0\u03bf\u03af\u03bf \u03b4\u03b7\u03bc\u03bf\u03c3\u03b9\u03b5\u03cd\u03b8\u03b7\u03ba\u03b5 \u03bf\u03ba\u03c4\u03ce \u03c7\u03c1\u03cc\u03bd\u03b9\u03b1 \u03bc\u03b5\u03c4\u03ac \u03c4\u03bf\u03bd \u03b8\u03ac\u03bd\u03b1\u03c4\u03cc \u03c4\u03bf\u03c5, \u03c4\u03bf 1713 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03b1\u03bd\u03b7\u03c8\u03b9\u03cc \u03c4\u03bf\u03c5, \u039d\u03af\u03ba\u03bf\u03bb\u03b1\u03c2. \u03a3\u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03b1\u03c5\u03c4\u03cc \u03c0\u03b5\u03c1\u03b9\u03ad\u03b3\u03c1\u03b1\u03c8\u03b5 \u03c4\u03b1 \u03b3\u03bd\u03c9\u03c3\u03c4\u03ac \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03ad\u03c3\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c4\u03b7\u03c2 \u03b1\u03c0\u03b1\u03c1\u03af\u03b8\u03bc\u03b7\u03c3\u03b7\u03c2, \u03c3\u03c5\u03c7\u03bd\u03ac \u03c0\u03b1\u03c1\u03ad\u03c7\u03bf\u03bd\u03c4\u03b1\u03c2 \u03b5\u03bd\u03b1\u03bb\u03bb\u03b1\u03ba\u03c4\u03b9\u03ba\u03ad\u03c2 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03b9\u03c2. \u03a4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c0\u03b5\u03c1\u03b9\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9 \u03b5\u03c0\u03af\u03c3\u03b7\u03c2 \u03c4\u03b7\u03bd \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ae \u03c4\u03b7\u03c2 \u03b8\u03b5\u03c9\u03c1\u03af\u03b1\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c3\u03b5 \u03c4\u03c5\u03c7\u03b5\u03c1\u03ac \u03c0\u03b1\u03b9\u03c7\u03bd\u03af\u03b4\u03b9\u03b1 \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b5\u03b9\u03c3\u03ae\u03b3\u03b7\u03c3\u03b7 \u03b5\u03bd\u03cc\u03c2 \u03b8\u03b5\u03c9\u03c1\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u03b3\u03bd\u03c9\u03c3\u03c4\u03bf\u03cd \u03c9\u03c2\u00a0\u03bf \u03bd\u03cc\u03bc\u03bf\u03c2 \u03c4\u03c9\u03bd \u03bc\u03b5\u03b3\u03ac\u03bb\u03c9\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03ce\u03bd<\/strong>. \u039f\u03b9 \u03cc\u03c1\u03bf\u03b9 \u03b4\u03bf\u03ba\u03b9\u03bc\u03ad\u03c2 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03ba\u03b1\u03b9 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03c0\u03c1\u03bf\u03ad\u03c1\u03c7\u03bf\u03bd\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03b1\u03c5\u03c4\u03cc. \u039f \u03c3\u03b5\u03bb\u03b7\u03bd\u03b9\u03b1\u03ba\u03cc\u03c2 \u03ba\u03c1\u03b1\u03c4\u03ae\u03c1\u03b1\u03c2 \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03b9 \u03ad\u03c7\u03b5\u03b9 \u03bf\u03bd\u03bf\u03bc\u03b1\u03c3\u03c4\u03b5\u03af \u03c0\u03c1\u03bf\u03c2 \u03c4\u03b9\u03bc\u03ae\u03bd \u03c4\u03bf\u03c5 \u03b9\u03b4\u03af\u03bf\u03c5 \u03ba\u03b1\u03b9 \u03c4\u03bf\u03c5 \u03b1\u03b4\u03b5\u03c1\u03c6\u03bf\u03cd \u03c4\u03bf\u03c5, \u0393\u03b9\u03cc\u03c7\u03b1\u03bd.<\/p>\n

\u03a3\u03c4\u03b7\u03bd \u0395\u03c5\u03c1\u03ce\u03c0\u03b7, \u03c4\u03bf \u03b8\u03ad\u03bc\u03b1 \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03b1\u03bd\u03b1\u03c0\u03c4\u03cd\u03c7\u03b8\u03b7\u03ba\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03bc\u03b1 \u03c0\u03c1\u03ce\u03c4\u03b7 \u03c6\u03bf\u03c1\u03ac \u03c4\u03bf\u03bd \u03b4\u03ad\u03ba\u03b1\u03c4\u03bf \u03ad\u03ba\u03c4\u03bf \u03b1\u03b9\u03ce\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf \u03ad\u03c1\u03b3\u03bf \u03c4\u03bf\u03c5 \u039a\u03b1\u03c1\u03bd\u03c4\u03ac\u03bd\u03bf, \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03c4\u03bf \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03bf\u03bd \u03b3\u03b9\u03b1 \u03c4\u03b9\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03c0\u03ae\u03b3\u03b1\u03b6\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03b1\u03b3\u03ac\u03c0\u03b7 \u03c4\u03bf\u03c5 \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03c4\u03b6\u03cc\u03b3\u03bf.<\/p>\n

\n
\"\"<\/figure>\n<\/div>\n

\u0388\u03b8\u03b5\u03c3\u03b5 \u03b5\u03c0\u03af\u03c3\u03b7\u03bc\u03b1 \u03b1\u03c5\u03c4\u03cc \u03c0\u03bf\u03c5 \u03c3\u03ae\u03bc\u03b5\u03c1\u03b1 \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

\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

\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

\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

\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.
\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
\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

\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

\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

\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

\u0397\u00a0\u03ba\u03b1\u03c4\u03b1\u03bd\u03bf\u03bc\u03ae \u039c\u03c0\u03b5\u03c1\u03bd\u03bf\u03cd\u03bb\u03bb\u03b9<\/strong>\u00a0\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 \u2013 \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

\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

P(X=1)=p
\nP(X=0)=q=1-p<\/p>\n

\n\n\n\n\n
\u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2<\/strong><\/th>\n\u03c0\u03b1\u03c1\u03ac\u03bc\u03b5\u03c4\u03c1\u03bf\u03b9<\/strong><\/th>\n\u03bc\u03ad\u03c3\u03b7 \u03c4\u03b9\u03bc\u03ae<\/strong><\/th>\n\u03b4\u03b9\u03b1\u03ba\u03cd\u03bc\u03b1\u03bd\u03c3\u03b7<\/strong><\/th>\n<\/tr>\n
p(1-p)<\/td>\n\"{\\displaystyle<\/td>\np<\/td>\np(1-p)}<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

\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 + \u2026 + pn = 1.<\/p>\n

\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

\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<a.<\/p>\n

\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

\n
\"\"<\/figure>\n<\/div>\n

\u03a4\u03bf \u03c4\u03ad\u03bb\u03bf\u03c2<\/h2>\n

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