{"id":169,"date":"2018-05-08T20:51:53","date_gmt":"2018-05-08T17:51:53","guid":{"rendered":"http:\/\/siteblog.tuc.gr\/athomadakis\/?p=169"},"modified":"2018-05-08T20:54:34","modified_gmt":"2018-05-08T17:54:34","slug":"%ce%b8%ce%b5%cf%89%cf%81%ce%af%ce%b1-%cf%80%ce%b9%ce%b8%ce%b1%ce%bd%ce%bf%cf%84%ce%ae%cf%84%cf%89%ce%bd","status":"publish","type":"post","link":"https:\/\/siteblog.tuc.gr\/athomadakis\/2018\/05\/08\/%ce%b8%ce%b5%cf%89%cf%81%ce%af%ce%b1-%cf%80%ce%b9%ce%b8%ce%b1%ce%bd%ce%bf%cf%84%ce%ae%cf%84%cf%89%ce%bd\/","title":{"rendered":"\u0398\u03b5\u03c9\u03c1\u03af\u03b1 \u03a0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd"},"content":{"rendered":"<p>\u0397\u00a0<b>\u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd<\/b>\u00a0(\u03b1\u03b3\u03b3\u03bb\u03b9\u03ba\u03ac:\u00a0<i>Probability Theory<\/i>) \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03b1\u03be\u03b9\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae 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\u03c4\u03b1 \u03b5\u03c5\u03c1\u03ae\u03bc\u03b1\u03c4\u03b1 \u03c4\u03b7\u03c2\u00a0\u03ba\u03b2\u03b1\u03bd\u03c4\u03bf\u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae\u03c2.<\/p>\n<p>&nbsp;<\/p>\n<h3><span id=\"\u039a\u03bb\u03b1\u03c3\u03b9\u03ba\u03ae_\u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\" class=\"mw-headline\">\u039a\u03bb\u03b1\u03c3\u03b9\u03ba\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1<\/span><\/h3>\n<p>\u0397 \u03ad\u03bd\u03bd\u03bf\u03b9\u03b1 \u03c4\u03b7\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03bf\u03c1\u03af\u03c3\u03c4\u03b7\u03ba\u03b5 \u03b1\u03c1\u03c7\u03b9\u03ba\u03ce\u03c2, \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c8\u03b5\u03b9 \u03c4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03bd\u03cc\u03c2\u00a0\u03c0\u03b5\u03b9\u03c1\u03ac\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03cd\u03c7\u03b7\u03c2, \u03cc\u03c0\u03c9\u03c2 \u03c0.\u03c7. \u03b7 \u03c1\u03af\u03c8\u03b7 \u03b5\u03bd\u03cc\u03c2 \u03b6\u03b1\u03c1\u03b9\u03bf\u03cd \u03ae \u03bd\u03bf\u03bc\u03af\u03c3\u03bc\u03b1\u03c4\u03bf\u03c2. \u039f\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9\u00a0\u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03af\u00a0\u03bf\u03b9 \u03bf\u03c0\u03bf\u03af\u03bf\u03b9 \u03b1\u03bd\u03b1\u03c4\u03af\u03b8\u03b5\u03bd\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03c3\u03c5\u03bc\u03b2\u03bf\u03cd\u03bd \u03ae \u03cc\u03c7\u03b9 \u03bc\u03b5 \u03ba\u03ac\u03c0\u03bf\u03b9\u03bf\u03bd \u03c4\u03c5\u03c7\u03b1\u03af\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf. \u039c\u03b5 \u03c4\u03bf\u03bd \u03c3\u03c5\u03bd\u03ae\u03b8\u03b7 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03b9\u03c3\u03bc\u03cc, \u03bf\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2\u00a0<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\">{\\displaystyle P(E)}<\/span><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/687fe7f4688af755503fd00e7538f285e2a9954b\" alt=\"P(E)\" \/><\/span>\u00a0\u03b1\u03bd\u03b1\u03c4\u03af\u03b8\u03b5\u03bd\u03c4\u03b1\u03b9 \u03c3\u03c4\u03b1 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03b1\u00a0. \u039f\u03b9 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9\u00a0\u03ba\u03b1\u03bd\u03bf\u03bd\u03b9\u03ba\u03bf\u03c0\u03bf\u03b9\u03b7\u03bc\u03ad\u03bd\u03b5\u03c2\u00a0\u03ba\u03b1\u03b9 \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bd\u00a0\u03c0\u03c1\u03b1\u03b3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ad\u03c2\u00a0\u03c4\u03b9\u03bc\u03ad\u03c2 \u03c3\u03c4\u03bf \u03b4\u03b9\u03ac\u03c3\u03c4\u03b7\u03bc\u03b1 \u03b1\u03c0\u03cc 0 \u03bc\u03ad\u03c7\u03c1\u03b9 1.<\/p>\n<p>\u0399\u03c3\u03c7\u03cd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03ba\u03ac\u03c4\u03c9\u03b8\u03b9 \u03bf\u03c1\u03b9\u03c3\u03bc\u03bf\u03af:<\/p>\n<ul>\n<li><b>\u0391\u03c0\u03bb\u03cc \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf<\/b>\u00a0\u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03b4\u03c5\u03bd\u03b1\u03c4\u03cc \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03bd\u03cc\u03c2 \u03c0\u03b5\u03b9\u03c1\u03ac\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03cd\u03c7\u03b7\u03c2 \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bd\u03ae\u03b8\u03c9\u03c2 \u03c3\u03c5\u03bc\u03b2\u03bf\u03bb\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03bc\u03b5\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8e38c617b7caec849872ad02749d764d84b86766\" alt=\"\\,\\omega \" \/><\/span>.<\/li>\n<li><b>\u0394\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03c7\u03ce\u03c1\u03bf\u03c2<\/b>\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/771ad27abf999ca4ae152aeb523d93eca2447b7e\" alt=\"\\Omega \\,\" \/><\/span>\u00a0\u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf\u00a0\u03c3\u03cd\u03bd\u03bf\u03bb\u03bf\u00a0\u03cc\u03bb\u03c9\u03bd \u03c4\u03c9\u03bd \u03b1\u03c0\u03bb\u03ce\u03bd \u03b5\u03bd\u03b4\u03b5\u03c7\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd. \u0393\u03b9\u03b1 \u03ad\u03bd\u03b1 \u03b1\u03c0\u03bb\u03cc \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8e38c617b7caec849872ad02749d764d84b86766\" alt=\"\\,\\omega \" \/><\/span>\u00a0\u03b9\u03c3\u03c7\u03cd\u03b5\u03b9\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f12ad53d93495367ebae484dfe30d3e2cf6e3171\" alt=\"\\,\\omega \\in \\Omega \" \/><\/span>.<\/li>\n<li><b>\u0393\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2<\/b>\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c6aaf5ce10d6add44b973e28fb3d95f37abf3721\" alt=\"A\\,\" \/><\/span>\u00a0\u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03bd\u03bf\u03bb\u03bf \u03b4\u03c5\u03bd\u03b1\u03c4\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd. \u0388\u03bd\u03b1 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03ad\u03c7\u03b5\u03b9 \u03c9\u03c2 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u03b1\u03c0\u03bb\u03ac \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03b1 \u03ba\u03b1\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9\u00a0\u03c5\u03c0\u03bf\u03c3\u03cd\u03bd\u03bf\u03bb\u03bf\u00a0\u03c4\u03bf\u03c5\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b0e18d8b3feb06ce5dd005da29b284bee5453753\" alt=\"\\Omega ,\\,\" \/><\/span><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/cfa06b132710e21846718b7259c87b564a22adcb\" alt=\"A\\subset \\Omega \\,\" \/><\/span>. To\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/771ad27abf999ca4ae152aeb523d93eca2447b7e\" alt=\"\\Omega \\,\" \/><\/span>\u00a0\u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf \u03af\u03b4\u03b9\u03bf \u03ad\u03bd\u03b1 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03bd\u03bf\u03bc\u03b1\u03b6\u03b5\u03c4\u03b1\u03b9\u00a0<i>\u03b2\u03ad\u03b2\u03b1\u03b9\u03bf \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2<\/i>.<\/li>\n<\/ul>\n<h4><span id=\".CE.A0.CE.B1.CF.81.CE.AC.CE.B4.CE.B5.CE.B9.CE.B3.CE.BC.CE.B1.CF.84.CE.B1\"><\/span><span id=\"\u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03b1\" class=\"mw-headline\">\u03a0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03b1<\/span><\/h4>\n<dl>\n<dt>\u03a1\u03af\u03c8\u03b7 \u03b6\u03b1\u03c1\u03b9\u03bf\u03cd<\/dt>\n<\/dl>\n<p>\u0398\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03c9\u03c2 \u03c0\u03b5\u03af\u03c1\u03b1\u03bc\u03b1 \u03c4\u03cd\u03c7\u03b7\u03c2 \u03c4\u03b7\u03bd \u03c1\u03af\u03c8\u03b7 \u03b5\u03bd\u03cc\u03c2 \u03b6\u03b1\u03c1\u03b9\u03bf\u03cd. \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 \u03ad\u03be\u03b9 \u03b1\u03c0\u03bb\u03ac \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03b1. \u0388\u03c3\u03c4\u03c9\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/5d4eca248bd42dcafcd998790cc7f2a7182e5d52\" alt=\"\\,\\omega _{1}\" \/><\/span>\u00a0\u03c4\u03bf \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03bd\u03b1 \u03c6\u03ad\u03c1\u03bf\u03c5\u03bc\u03b5 1 \u03ba\u03b1\u03b9 \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03bf\u03af\u03c7\u03c9\u03c2 \u03c4\u03b1\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/b1ac8d6e3f8b3c95977b19f7a741ec15f7523f84\" alt=\"\\,\\omega _{i},i=2,\\dots ,6\" \/><\/span>. \u039f \u03b4\u03b5\u03b9\u03b3\u03bc\u03b1\u03c4\u03bf\u03c7\u03ce\u03c1\u03bf\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03bf<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e7727909f89243a7cb0ab83a272a2718ca15183a\" alt=\"\\,\\Omega =\\{\\omega _{1},\\omega _{2},\\omega _{3},\\omega _{4},\\omega _{5},\\omega _{6}\\}\" \/><\/span>\u00a0\u03ae \u03b3\u03b9\u03b1 \u03bb\u03cc\u03b3\u03bf\u03c5\u03c2 \u03b1\u03c0\u03bb\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/1e6891646cc8e807f8be26f7e3d52c90ef1ef740\" alt=\"\\,\\Omega =\\{1,2,3,4,5,6\\}\" \/><\/span>. \u03a4\u03bf \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c6aaf5ce10d6add44b973e28fb3d95f37abf3721\" alt=\"A\\,\" \/><\/span>\u00a0\u03bd\u03b1 \u03c6\u03ad\u03c1\u03bf\u03c5\u03bc\u03b5 \u03b6\u03c5\u03b3\u03cc \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 <span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e0a49173037d056ce99a14605e4c0f71c8c088d7\" alt=\"\\,A=\\{2,4,6\\}\" \/><\/span>. \u03a4\u03bf \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c2\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d8a72cbbfdbb8b9d0dad053538c330994b308bae\" alt=\"B\\,\" \/><\/span>\u00a0\u03bd\u03b1 \u03c6\u03ad\u03c1\u03bf\u03c5\u03bc\u03b5 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc \u03bc\u03b9\u03ba\u03c1\u03cc\u03c4\u03b5\u03c1\u03bf \u03ae \u03af\u03c3\u03bf \u03c4\u03bf\u03c5 2 \u03b5\u03af\u03bd\u03b1\u03b9\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/77f45ba790fa7c587696b73f5232efd1131038bf\" alt=\"\\,B=\\{1,2\\}\" \/><\/span>.<\/p>\n<p>\u0397 \u03ba\u03bb\u03b1\u03c3\u03b9\u03ba\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c3\u03b5 \u03c0\u03b5\u03b9\u03c1\u03ac\u03bc\u03b1\u03c4\u03b1 \u03c4\u03cd\u03c7\u03b7\u03c2, \u03cc\u03c0\u03bf\u03c5 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b1\u03c0\u03bb\u03ce\u03bd \u03b5\u03bd\u03b4\u03b5\u03c7\u03bf\u03bc\u03ad\u03bd\u03c9\u03bd \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b5\u03c0\u03b5\u03c1\u03b1\u03c3\u03bc\u03ad\u03bd\u03bf \u03ba\u03b1\u03b9 \u03cc\u03bb\u03b1 \u03c4\u03b1 \u03b1\u03c0\u03bb\u03ac \u03b5\u03bd\u03b4\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b9\u03c3\u03bf\u03c0\u03af\u03b8\u03b1\u03bd\u03b1. \u03a3\u03b5 \u03b1\u03c5\u03c4\u03ae \u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b5\u03bd\u03cc\u03c2 \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03bf\u03c2 \u0391 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c4\u03bf \u03c0\u03b7\u03bb\u03af\u03ba\u03bf \u03c4\u03bf\u03c5 \u03c0\u03bb\u03ae\u03b8\u03bf\u03c5\u03c2 \u03c4\u03c9\u03bd \u03b5\u03c5\u03bd\u03bf\u03ca\u03ba\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd \u03c9\u03c2 \u03c0\u03c1\u03bf\u03c2 \u03c4\u03bf \u03c0\u03bb\u03ae\u03b8\u03bf\u03c2 \u03c4\u03c9\u03bd \u03b4\u03c5\u03bd\u03b1\u03c4\u03ce\u03bd \u03b1\u03c0\u03bf\u03c4\u03b5\u03bb\u03b5\u03c3\u03bc\u03ac\u03c4\u03c9\u03bd.<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/70bb5ef1afd93a1c73aa3f69a803187d5a656626\" alt=\"P(A)={\\frac {\\#A}{\\#\\Omega }}\" \/><\/span><\/dd>\n<\/dl>\n<p>\u03a3\u03c5\u03bd\u03b5\u03c7\u03af\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03bf \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d2f4b9ef7bc4af167969e87cee3302c28d420701\" alt=\"P(A)={\\frac {\\#A}{\\#\\Omega }}={\\frac {\\#\\{2,4,6\\}}{\\#\\{1,2,3,4,5,6\\}}}={\\frac 36}=0,5\" \/><\/span><\/dd>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/ca526568e3c0a34d6cb61b377226394409739670\" alt=\"P(B)={\\frac {\\#B}{\\#\\Omega }}={\\frac {\\#\\{1,2\\}}{\\#\\{1,2,3,4,5,6\\}}}={\\frac 26}=0,333\" \/><\/span><\/dd>\n<\/dl>\n<dl>\n<dt>\u03a0\u03b1\u03c1\u03ac\u03b4\u03bf\u03be\u03bf \u03c4\u03c9\u03bd \u03b3\u03b5\u03bd\u03b5\u03b8\u03bb\u03af\u03c9\u03bd<\/dt>\n<\/dl>\n<p>\u03a4\u03bf\u00a0\u03c0\u03b1\u03c1\u03ac\u03b4\u03bf\u03be\u03bf \u03c4\u03c9\u03bd \u03b3\u03b5\u03bd\u03b5\u03b8\u03bb\u03af\u03c9\u03bd\u00a0\u03b1\u03c3\u03c7\u03bf\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1: \u03a3\u03b5 \u03bc\u03af\u03b1 \u03bf\u03bc\u03ac\u03b4\u03b1 23 \u03b1\u03c4\u03cc\u03bc\u03c9\u03bd \u03c0\u03bf\u03b9\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b4\u03cd\u03bf \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03ac \u03c4\u03b1 \u03ac\u03c4\u03bf\u03bc\u03b1 \u03bd\u03b1 \u03ad\u03c7\u03bf\u03c5\u03bd \u03c4\u03b7\u03bd \u03af\u03b4\u03b9\u03b1 \u03b7\u03bc\u03ad\u03c1\u03b1 \u03b3\u03b5\u03bd\u03ad\u03b8\u03bb\u03b9\u03b1; \u0395\u03bd\u03ce \u03b4\u03b9\u03b1\u03b9\u03c3\u03b8\u03b7\u03c4\u03b9\u03ba\u03ac \u03b8\u03b1 \u03c0\u03b5\u03c1\u03b9\u03bc\u03ad\u03bd\u03b1\u03bc\u03b5 \u03bc\u03b9\u03b1 \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03ac \u03bc\u03b9\u03ba\u03c1\u03ae \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1, \u03b1\u03c5\u03c4\u03ae \u03b1\u03c0\u03bf\u03b4\u03b5\u03b9\u03ba\u03bd\u03cd\u03b5\u03c4\u03b1\u03b9 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 50%.<\/p>\n<h3><span id=\".CE.9C.CE.AD.CF.84.CF.81.CE.BF_.CF.80.CE.B9.CE.B8.CE.B1.CE.BD.CF.8C.CF.84.CE.B7.CF.84.CE.B1.CF.82\"><\/span><span id=\"\u039c\u03ad\u03c4\u03c1\u03bf_\u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2\" class=\"mw-headline\">\u039c\u03ad\u03c4\u03c1\u03bf \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2<\/span><\/h3>\n<p>\u0397 \u03b1\u03be\u03b9\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b8\u03b5\u03bc\u03b5\u03bb\u03af\u03c9\u03c3\u03b7 \u03c4\u03c9\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd \u03c0\u03c1\u03bf\u03ae\u03bb\u03b8\u03b5 \u03b1\u03c0\u03cc \u03c4\u03bf\u03bd \u03a1\u03ce\u03c3\u03bf \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u00a0\u0391\u03bd\u03c4\u03c1\u03ad\u03b9 \u039a\u03bf\u03bb\u03bc\u03bf\u03b3\u03ba\u03cc\u03c1\u03bf\u03b2\u00a0(<i>Andrey Kolmogorov<\/i>).<\/p>\n<p>\u0388\u03c3\u03c4\u03c9 \u03ad\u03bd\u03b1 \u03c3\u03cd\u03bd\u03bf\u03bb\u03bf\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f\" alt=\"\\Omega \" \/><\/span>\u00a0\u03ba\u03b1\u03b9 \u03bc\u03af\u03b1\u00a0\u03c3-\u03ac\u03bb\u03b3\u03b5\u03b2\u03c1\u03ac\u00a0\u03c4\u03bf\u03c5\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676\" alt=\"{\\mathcal {F}}\" \/><\/span>. \u03a0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f60e07ebc2aadee94e4cbbccef71fd9bcf44f5f9\" alt=\"P\\,\" \/><\/span>\u00a0\u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7d18e36d6128d3b878c2418f3d6d869b8a145b48\" alt=\"P:{\\mathcal {F}}\\to \\mathbb{R} \" \/><\/span>\u00a0\u03c0\u03bf\u03c5 \u03b9\u03ba\u03b1\u03bd\u03bf\u03c0\u03bf\u03b9\u03b5\u03af:<\/p>\n<ol>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/cd2ac7448538a454258adf82162921b65f0abf71\" alt=\"P(A)\\geq 0,\\;\\forall A\\in {\\mathcal {F}}\" \/><\/span><\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9459a887f1d91afd5027ea283820e0131cd3c065\" alt=\"P(\\Omega )=1\\,\" \/><\/span><\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2d58b16ba1a75cde5abfe14c977fc0d44778d9de\" alt=\"P(\\cup _{{i\\in I}}A_{i})=\\sum _{{i\\in I}}P(A_{i})\\quad \\forall \\{A_{i}\\}_{{i\\in I}}\\subset {\\mathcal {F}},I\\subset \\mathbb{N} :A_{i}\\cap A_{j}=\\emptyset \\;\\forall i\\neq j\" \/><\/span><\/li>\n<\/ol>\n<p>\u0397 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ad\u03bd\u03b1\u00a0\u03bc\u03ad\u03c4\u03c1\u03bf\u00a0\u03c3\u03c4\u03bf\u03bd\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4af05190f6fb10d1eec88b5f66f940dc88b5ec87\" alt=\"(\\Omega ,{\\mathcal {F}})\" \/><\/span>\u00a0\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u00a0<span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/9459a887f1d91afd5027ea283820e0131cd3c065\" alt=\"P(\\Omega )=1\\,\" \/><\/span>.<\/p>\n<p>\u0391\u03bd \u03c3\u03c4\u03b7\u03bd \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 <span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f60e07ebc2aadee94e4cbbccef71fd9bcf44f5f9\" alt=\"P\\,\" \/><\/span>\u00a0\u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af \u03bc\u03af\u03b1\u00a0\u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03c0\u03c5\u03ba\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2\u00a0f, \u03c4\u03cc\u03c4\u03b5 \u03b7 \u03c0\u03b9\u03b8\u03b1\u03bd\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u0391 \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03c9\u03c2:<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/75f557dedc3b4dad1ad0775f4348a3b237cbaf51\" alt=\"P(A)=\\int _{A}f(x)dx\\;\" \/><\/span><\/dd>\n<\/dl>\n<p>\u0399\u03c3\u03c7\u03cd\u03bf\u03c5\u03bd \u03bf\u03b9 \u03ba\u03ac\u03c4\u03c9\u03b8\u03b9 \u03b9\u03b4\u03b9\u03cc\u03c4\u03b7\u03c4\u03b5\u03c2:<\/p>\n<ul>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2ccb877e4d70a99c1ff22598b79343e9204d9029\" alt=\"P(\\Omega \\backslash A)=1-P(A)\" \/><\/span><\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2f93aaf626de15ab2b78f569b48cf3b7d33244e4\" alt=\"P(\\emptyset )=0\" \/><\/span><\/li>\n<li><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0c8de5b03034abcef68b1d393382856497e295a0\" alt=\"P(A\\cup B)=P(A)+P(B)-P(A\\cap B)\" \/><\/span>.<\/li>\n<\/ul>\n<h3><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>\u0397\u00a0\u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03c0\u03b9\u03b8\u03b1\u03bd\u03bf\u03c4\u03ae\u03c4\u03c9\u03bd\u00a0(\u03b1\u03b3\u03b3\u03bb\u03b9\u03ba\u03ac:\u00a0Probability Theory) \u03b5\u03af\u03bd\u03b1\u03b9 \u03bc\u03b9\u03b1 \u03b1\u03be\u03b9\u03c9\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae \u03b8\u03b5\u03c9\u03c1\u03af\u03b1 \u03bc\u03ad\u03c4\u03c1\u03bf\u03c5. \u03a0\u03c1\u03cc\u03ba\u03b5\u03b9\u03c4\u03b1\u03b9 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae \u03b3\u03b9\u03b1 \u03c4\u03bf\u03bd \u03ba\u03bb\u03ac\u03b4\u03bf \u03c4\u03c9\u03bd\u00a0\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd\u00a0\u03bf \u03bf\u03c0\u03bf\u03af\u03bf\u03c2 \u03b1\u03c3\u03c7\u03bf\u03bb\u03b5\u03af\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 <span class=\"ellipsis\">&hellip;<\/span> <span class=\"more-link-wrap\"><a href=\"https:\/\/siteblog.tuc.gr\/athomadakis\/2018\/05\/08\/%ce%b8%ce%b5%cf%89%cf%81%ce%af%ce%b1-%cf%80%ce%b9%ce%b8%ce%b1%ce%bd%ce%bf%cf%84%ce%ae%cf%84%cf%89%ce%bd\/\" class=\"more-link\"><span>Read More &rarr;<\/span><\/a><\/span><\/p>\n","protected":false},"author":254,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-169","post","type-post","status-publish","format-standard","hentry","category-11"],"_links":{"self":[{"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/posts\/169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/users\/254"}],"replies":[{"embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/comments?post=169"}],"version-history":[{"count":1,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/posts\/169\/revisions"}],"predecessor-version":[{"id":170,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/posts\/169\/revisions\/170"}],"wp:attachment":[{"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/media?parent=169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/categories?post=169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/siteblog.tuc.gr\/athomadakis\/wp-json\/wp\/v2\/tags?post=169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}