{"id":27279,"date":"2021-10-08T13:00:20","date_gmt":"2021-10-08T13:00:20","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27279"},"modified":"2024-06-20T11:43:36","modified_gmt":"2024-06-20T11:43:36","slug":"%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d1%8b%d0%b5-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%b2%d0%b5%d1%80%d0%be%d1%8f%d1%82%d0%bd%d0%be%d1%81","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d0%bd%d0%b5%d0%bf%d1%80%d0%b5%d1%80%d1%8b%d0%b2%d0%bd%d1%8b%d0%b5-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d1%8f-%d0%b2%d0%b5%d1%80%d0%be%d1%8f%d1%82%d0%bd%d0%be%d1%81\/","title":{"rendered":"\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0420\u0435\u0437\u044e\u043c\u0435<\/strong><br \/><em>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0433\u043b\u0443\u0431\u043e\u043a\u043e \u0438\u0437\u0443\u0447\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438, \u0432\u044b\u0434\u0435\u043b\u044f\u044f \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043f\u044f\u0442\u0438 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445: \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 (\u0413\u0430\u0443\u0441\u0441\u043e\u0432\u043e) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430 \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430. \u041f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0438\u0435 \u043a\u0430\u0436\u0434\u043e\u0435 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439, \u0438 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u0438\u0445 \u043f\u043e\u0441\u043b\u0435\u0434\u0441\u0442\u0432\u0438\u044f \u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u043e\u0446\u0435\u043d\u043a\u0430 \u0432\u044b\u0431\u0440\u043e\u0441\u0430 \u0447\u0430\u0441\u0442\u0438\u0446 \u0432 \u0440\u0430\u0434\u0438\u043e\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u0445 \u043e\u0431\u0440\u0430\u0437\u0446\u0430\u0445 \u0438\u043b\u0438 \u0440\u0430\u0441\u0447\u0435\u0442 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0448\u0430\u0440\u0430 \u043d\u0430 \u0440\u0435\u043b\u044c\u0441\u0435 \u0441 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f\u043c\u0438. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u043f\u0438\u0441\u0430\u043d\u043e, \u043a\u0430\u043a \u044d\u0442\u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u044b \u0438 \u0430\u0434\u0430\u043f\u0442\u0438\u0440\u043e\u0432\u0430\u043d\u044b \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0426\u0415\u041b\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f:<\/strong><br \/>\n\u041f\u043e \u043e\u043a\u043e\u043d\u0447\u0430\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0443\u0447\u0435\u043d\u0438\u043a \u0441\u043c\u043e\u0436\u0435\u0442:\n<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c<\/strong> \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438: \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435, \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435, \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435, \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 (\u0413\u0430\u0443\u0441\u0441\u043e\u0432\u043e), \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430 \u0438 \u0413\u0430\u043c\u043c\u0430.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/u>:<\/strong><br \/>\n<a href=\"#1\"><strong>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438?<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u041f\u044f\u0442\u044c \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/strong><\/a><br \/>\n<a href=\"#3\">\u042d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#4\">\u0420\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#5\">\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 (\u0413\u0430\u0443\u0441\u0441\u043e\u0432\u043e) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/a><br \/>\n<a href=\"#6\">\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430<\/a><br \/>\n<a href=\"#7\">\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430<\/a><br \/>\n<a href=\"#8\"><strong>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/strong><\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/REOTUa7K8uQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u043b\u0438 <a href=\"http:\/\/toposuranos.com\/material\/es\/conoce-el-espacio-muestral-de-la-teoria-de-las-probabilidades\/\" target=\"_blank\" rel=\"noopener\">\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u0432\u044b\u0431\u043e\u0440\u043a\u0438<\/a>, \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438, \u0447\u0442\u043e \u043e\u043d\u0438 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u0434\u0432\u0443\u0445 \u0442\u0438\u043f\u043e\u0432: \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u044b\u0435 \u0438 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435. \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438, \u0447\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 <a href=\"http:\/\/toposuranos.com\/material\/es\/distribuciones-discretas-de-probabilidad-y-ejemplos\/\" target=\"_blank\" rel=\"noopener\">\u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438.<\/a> \u0422\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u0441\u0442\u0430\u043b\u0430 \u043e\u0447\u0435\u0440\u0435\u0434\u044c \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p>&nbsp;<\/p>\n<p><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438?<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=86s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0421\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0438\u043c\u0435\u0435\u0442 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X : \\mathbb{R} \\longrightarrow \\mathbb{R}^+,<\/span><\/span> \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u043d\u0430\u0437\u043e\u0432\u0435\u043c <strong>\u041f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c\u044e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X,<\/span><\/span><\/strong> \u0442\u0430\u043a\u0430\u044f, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\forall A \\subseteq \\mathbb{R}<\/span><\/span> \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(X\\in A) = \\displaystyle \\int_A f_X(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u0435\u0441\u043b\u0438 \u0432\u0437\u044f\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=]a,b]<\/span><\/span>, \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(a\\lt X \\leq b) = \\displaystyle \\int_a^b f_X(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0438 \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=-\\infty<\/span><\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x) = P( X \\leq x) = \\displaystyle \\int_{-\\infty}^x f_X(t)dt<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0438\u0437 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 (c) <a href=\"http:\/\/toposuranos.com\/material\/es\/variables-aleatorias-y-distribuciones-de-probabilidades\/\" rel=\"noopener\" target=\"_blank\">\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/a> \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty} f_X(t)dt = 1<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u043e\u0441\u043d\u043e\u0432\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043a \u044d\u0442\u043e\u043c\u0443 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e \u0434\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x),<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0439 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,<\/span><\/span> \u0438 \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u0435\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X(x)<\/span><\/span> \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span>, \u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f_X(x)<\/span><\/span> \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430. \u0418\u0437 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_X(x)<\/span><\/span> \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 (d) (<a href=\"http:\/\/toposuranos.com\/material\/es\/variables-aleatorias-y-distribuciones-de-probabilidades\/\" rel=\"noopener\" target=\"_blank\">\u0441\u043c. \u0437\u0434\u0435\u0441\u044c<\/a>) \u0441\u043b\u0435\u0434\u0443\u0435\u0442:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x=X)=0<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u043f\u043e\u044d\u0442\u043e\u043c\u0443<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x\\leq X)= P(x\\lt X)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/span> &#8211; \u043b\u044e\u0431\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0449\u0430\u044f \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f\\geq 0<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty}f(x)dx = 1,<\/span><\/span> \u0442\u043e \u0435\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c\u044e.<\/p>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>\u041f\u044f\u0442\u044c \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/h2>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u042d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=714s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u042d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/span><\/strong><\/a> \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha \\gt 0 <\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0438\u0434\u0430:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(t) = \\left\\{\\begin{array}{lll}\n\n1 - e^{-t\/\\alpha} &amp; ; &amp; t\\geq 0 \\\\ \\\\\n\n0 &amp; ; &amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(t) = \\left\\{\\begin{array}{lll}\n\n\\frac{1}{\\alpha}e^{-t\/\\alpha} &amp; ; &amp; t\\geq 0 \\\\ \\\\\n\n0 &amp; ; &amp; t\\lt 0\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span>, \u043c\u044b \u043f\u0438\u0448\u0435\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Ex(\\alpha).<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0412 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, \u0435\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0440\u0430\u0434\u0438\u043e\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u0439 \u043e\u0431\u0440\u0430\u0437\u0435\u0446, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0437\u043b\u0443\u0447\u0430\u0435\u0442 \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0441\u043e \u0441\u0440\u0435\u0434\u043d\u0435\u0439 \u0441\u043a\u043e\u0440\u043e\u0441\u0442\u044c\u044e \u0438\u0437\u043b\u0443\u0447\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c,<\/span><\/span>, \u0442\u043e \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T<\/span><\/span>, \u043a\u043e\u0433\u0434\u0430 \u0438\u0437\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u0430\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u0430, \u0438\u043c\u0435\u0435\u0442 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1\/c.<\/span><\/span> \u0418\u043d\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T\\sim Ex(1\/c),<\/span><\/span> \u0438 \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(T\\geq t)= e^{-ct}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0420\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=930s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0420\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/span><\/strong><\/a> \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\left\\{\\begin{array}{lll}\n\n\\displaystyle\\frac{1}{b-a} &amp; ; &amp; x\\in[a,b] \\\\ \\\\\n\n0 &amp; ; &amp; E.O.C.\n\n\\end{array}\\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438 \u043c\u044b \u0431\u0440\u043e\u0441\u0438\u043c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0439 \u0448\u0430\u0440\u0438\u043a \u043d\u0430 \u0440\u0435\u043b\u044c\u0441 \u0441 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u043d\u0430 \u043a\u043e\u043d\u0446\u0430\u0445 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u0438 \u043e\u043d \u0431\u0443\u0434\u0435\u0442 \u0443\u043f\u0440\u0443\u0433\u043e \u043e\u0442\u0441\u043a\u0430\u043a\u0438\u0432\u0430\u0442\u044c \u043e\u0442 \u0433\u0440\u0430\u043d\u0438\u0446, \u0442\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span>, \u0441\u0432\u044f\u0437\u0430\u043d\u043d\u0430\u044f \u0441 \u043e\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u043e\u0439 \u0448\u0430\u0440\u0438\u043a\u0430 \u0438\u0437-\u0437\u0430 \u0442\u0440\u0435\u043d\u0438\u044f, \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0431\u0443\u0434\u0435\u0442 \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u0430 \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Un(a,b)<\/span>.<\/span><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h3>\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 (\u0413\u0430\u0443\u0441\u0441\u043e\u0432\u043e) \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1109s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0418\u0437 \u0432\u0441\u0435\u0445 \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439<\/span><\/strong><\/a> \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438, \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u0438\u043c \u0438\u0437 \u0441\u0430\u043c\u044b\u0445 \u043f\u043e\u043f\u0443\u043b\u044f\u0440\u043d\u044b\u0445 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435.<\/p>\n<h4>\u0421\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1150s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0421\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/span><\/strong><\/a> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0435\u0440\u0435\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u044e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\phi_{0,1}(x) = \\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u044f\u0441\u043d\u043e, \u0447\u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi\\gt 0.<\/span><\/span> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438, \u043f\u0440\u043e\u0441\u0442\u043e \u0443\u0431\u0435\u0434\u0438\u0432\u0448\u0438\u0441\u044c, \u0447\u0442\u043e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int_{-\\infty}^{+\\infty}\\phi_{0,1}(x)dx<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0432 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I^2<\/span><\/span>, \u043a\u043e\u0433\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I =\\int_{-\\\u0438\u043d\u043d\u043e\u0441\u0442\u044c}^{+\\\u0438\u043d\u043d\u043e\u0441\u0442\u044c}\\phi(x)dx=1.<\/span><\/span> \u0412 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438, \u044d\u0442\u043e:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\nI^2 &amp; = \\displaystyle \\int_{-\\infinity}^{+\\infinity}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2} dx \\int_{-\\infinity}^{+\\infinity}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2}dx \\\\ \\\\\n\n&amp; = \\displaystyle \\int_{-\\infinity}^{+\\infinity}\\frac{1}{\\sqrt{2\\pi}} e^{-x^2\/2} dx \\int_{-\\infinity}^{+\\infinity}\\frac{1}{\\sqrt{2\\pi}} e^{-y^2\/2} dy \\\\ \\\\\n\n&amp; = \\displaystyle \\frac{1}{{2\\pi}} \\int_{-\\infinity}^{+\\infinity} \\int_{-\\infinity}^{+\\infinity} e^{-\\frac{x^2 + y^2}{2}} dxdy \\\\ \\\\\n\n\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041d\u043e \u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u0447\u0442\u043e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle \\int_{-\\infinity}^{+\\infinity} \\int_{-\\infinity}^{+\\infinity} e^{-\\frac{x^2 + y^2}{2}} dxdy = \\int_{0}^{2\\pi} \\int_{0}^{+\\infinity} e^{-r^2\/2} rdr d\\theta = 2\\pi <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I^2 = 1,<\/span><\/span> \u043f\u043e\u044d\u0442\u043e\u043c\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I=\\int_{-\\infinity}^{+\\infinity}\\phi_{0,1}(x)dx = 1. <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0439 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(x) = \\int_{-\\\u0438\u043d\u043d\u043e\u0441\u0442\u044c}^x\\phi_{0,1}(t)dt.<\/span><\/span> \u0415\u0441\u043b\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0438\u043c\u0435\u0435\u0442 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0442\u043e \u043f\u0438\u0448\u0435\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim N(0,1).<\/span><\/span> \u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{0,1}(x)<\/span><\/span> \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u043e \u044f\u0432\u043d\u043e, \u043e\u0434\u043d\u0430\u043a\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0442\u0430\u0431\u043b\u0438\u0446\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0431\u044b\u0441\u0442\u0440\u043e \u043f\u043e\u043b\u0443\u0447\u0430\u0442\u044c \u043f\u0440\u0438\u0431\u043b\u0438\u0437\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f.<\/p>\n<h4>\u041d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma<\/span><\/span><\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=1875s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0418\u0437 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0439 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0439 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\phi_{0,1}<\/span><\/span> \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma,<\/span><\/span> \u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu\\in\\mathbb{R}<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma\\gt 0 <\/span><\/span> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0441\u0440\u0435\u0434\u043d\u0438\u043c \u0438 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u043c \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435\u043c. \u041f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441 \u044d\u0442\u0438\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\phi_{\\mu,\\sigma}(x) = \\frac{1}{\\sigma}\\phi_{0,1}\\left(\\frac{x-\\mu}{\\sigma} \\right)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\sigma,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Phi_{\\mu,\\sigma}(x)<\/span><\/span>, \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u0438\u0434:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Phi_{\\\u043c\u0443,\\\u03c3}(\u0445) = \u222b_{-\u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438}^\u0445 \\frac{1}{\\\u03c3}\\ \u03c6_{0,1}\\left(\\frac{t-\\\u03bc}{\\\u03c3}\\right)\u0434\u0442 = \\frac{1}{\\sqrt{2\u03c0\u03c3}}\u222b_{-\u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u0438}^\u0445 \u0435^{-\\frac{(\u0442-\u03bc)^2}{2\u03c3^2}}\u0434\u0442<\/span><\/span><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0415\u0441\u043b\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0438\u043c\u0435\u0435\u0442 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu, \\sigma,<\/span><\/span>, \u0442\u043e \u043c\u044b \u043f\u0438\u0448\u0435\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim N(\\mu, \\sigma).<\/span><\/span><\/\u043f><br \/>\n<a name=\"6\"><\/a><\/\u0431\u0440><\/\u0431\u0440><br \/>\n<\u04373>\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430<\/\u04373><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\"><\u0430 href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=2230s\" \u0446\u0435\u043b\u0435\u0432\u0430\u044f=\"_blank\" rel=\"noopener\"><\u0441\u0438\u043b\u044c\u043d\u044b\u0439><\u0441\u043f\u0430\u043d \u0441\u0442\u0438\u043b\u044c=\"\u0446\u0432\u0435\u0442: #ff0000;\">\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430<\/\u0441\u043f\u0430\u043d><\/\u0441\u0438\u043b\u044c\u043d\u044b\u0439><\/\u0430> \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0430\u043b\u044c\u0444\u0430,\\\u0431\u0435\u0442\u0430 \\\u0433\u0442 0[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0438\u043c\u0435\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0438\u0434\u0430:<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u0446\u0435\u043d\u0442\u0440; \u0446\u0432\u0435\u0442: #000000;\"><\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]F(t) = \\\u043b\u0435\u0432\u043e{\\\u043d\u0430\u0447\u0430\u0442\u044c{\u043c\u0430\u0441\u0441\u0438\u0432}{\u043b\u043b\u044c}<br \/>\n\\\u043b\u0435\u0432\u043e(1 &#8211; \u0435^{-\u0442\/\\\u0430\u043b\u044c\u0444\u0430} \\\u043f\u0440\u0430\u0432\u043e)^\u0431\u0435\u0442\u0430 &#038;\u0430\u043c\u043f;;&#038;\u0430\u043c\u043f; \u0442\\\u0433\u0435 0 \\\\ \\\\<br \/>\n0 &#038;\u0430\u043c\u043f;;&#038;\u0430\u043c\u043f; \u0442\\\u043b\u0442 0<br \/>\n\\\u043a\u043e\u043d\u0435\u0446{\u043c\u0430\u0441\u0441\u0438\u0432}\\\u043f\u0440\u0430\u0432\u043e.[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0415\u0441\u043b\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]X[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0438\u043c\u0435\u0435\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0430\u043b\u044c\u0444\u0430, \\\u0431\u0435\u0442\u0430[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d>, \u0442\u043e \u043c\u044b \u043f\u0438\u0448\u0435\u043c <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]X\\\u0441\u0438\u043c We(\\\u0430\u043b\u044c\u0444\u0430,\\\u0431\u0435\u0442\u0430).[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435\u043c \u0434\u043b\u044f \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]We(\\\u0430\u043b\u044c\u0444\u0430,1) = Ex(\\\u0430\u043b\u044c\u0444\u0430).[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u0430 \u0438\u043c\u044f=\"7\"><\/\u0430><\/\u0431\u0440><\/\u0431\u0440><br \/>\n<\u04373>\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430<\/\u04373><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\"><\u0430 href=\"https:\/\/www.youtube.com\/watch?v=REOTUa7K8uQ&amp;t=2311s\" \u0446\u0435\u043b\u0435\u0432\u0430\u044f=\"_blank\" rel=\"noopener\"><\u0441\u0438\u043b\u044c\u043d\u044b\u0439><\u0441\u043f\u0430\u043d \u0441\u0442\u0438\u043b\u044c=\"\u0446\u0432\u0435\u0442: #ff0000;\">\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430<\/\u0441\u043f\u0430\u043d><\/\u0441\u0438\u043b\u044c\u043d\u044b\u0439><\/\u0430> \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0431\u0435\u0442\u0430,\\\u0430\u043b\u044c\u0444\u0430[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0438\u043c\u0435\u0435\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0438\u0434\u0430:<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u0446\u0435\u043d\u0442\u0440; \u0446\u0432\u0435\u0442: #000000;\"><\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]f(t) = \\\u043b\u0435\u0432\u043e{\\\u043d\u0430\u0447\u0430\u0442\u044c{\u043c\u0430\u0441\u0441\u0438\u0432}{\u043b\u043b\u0440}<br \/>\n\\\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \\frac{1}{\\\u0430\u043b\u044c\u0444\u0430 \\\u0413\u0430\u043c\u043c\u0430(\\\u0431\u0435\u0442\u0430)}\\\u043b\u0435\u0432\u043e(\\frac{t}{\\\u0430\u043b\u044c\u0444\u0430} \\\u043f\u0440\u0430\u0432\u043e)^{\\\u0431\u0435\u0442\u0430-1}\u0435^{-\u0442\/\\\u0430\u043b\u044c\u0444\u0430} &#038;\u0430\u043c\u043f;;&#038;\u0430\u043c\u043f; \u0442\\\u0433\u0435 0 \\\\ \\\\<br \/>\n0 &#038;\u0430\u043c\u043f;;&#038;\u0430\u043c\u043f; \u0442\\\u043b\u0442 0<br \/>\n\\\u043a\u043e\u043d\u0435\u0446{\u043c\u0430\u0441\u0441\u0438\u0432}\\\u043f\u0440\u0430\u0432\u043e.[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0413\u0434\u0435 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0413\u0430\u043c\u043c\u0430(\u0441) = \\\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \\\u0438\u043d\u0442_0^{+\u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0441\u0442\u044c}\u0443^{\u0441-1}\u0435^{-\u0443}\u0434\u0443 [\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u044d\u0442\u043e \u0442\u043e, \u0447\u0442\u043e \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e \u043a\u0430\u043a \u00ab\u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0413\u0430\u043c\u043c\u0430\u00bb.<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u041e\u0434\u043d\u0438\u043c \u0438\u0437 \u0441\u0430\u043c\u044b\u0445 \u0437\u0430\u043c\u0435\u0442\u043d\u044b\u0445 \u0441\u0432\u043e\u0439\u0441\u0442\u0432 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0413\u0430\u043c\u043c\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e, \u0447\u0442\u043e \u043e\u043d\u0430 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043e\u0431\u043e\u0431\u0449\u0438\u0442\u044c \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b\u044b \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043d\u0430 \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 (\u0438 \u0434\u0430\u0436\u0435 \u043d\u0430 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0435). \u041d\u0435 \u0441\u043b\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c, \u0447\u0442\u043e <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0413\u0430\u043c\u043c\u0430(\u0441+1) = \u0441\\\u0413\u0430\u043c\u043c\u0430(\u0441)[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u043f\u043e \u0447\u0430\u0441\u0442\u044f\u043c. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0442\u0430\u043a \u043a\u0430\u043a <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0413\u0430\u043c\u043c\u0430(1)=1[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u0446\u0435\u043d\u0442\u0440; \u0446\u0432\u0435\u0442: #000000;\"><\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u043b\u0435\u0432\u043e(\\forall \u043d\\\u0432\\mathbb{N}\\\u043f\u0440\u0430\u0432\u043e)\\\u043b\u0435\u0432\u043e(\\\u0413\u0430\u043c\u043c\u0430(\u043d) = (\\\u043d-1)! \\\u043f\u0440\u0430\u0432\u043e)[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0415\u0441\u043b\u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]X[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0438\u043c\u0435\u0435\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0431\u0435\u0442\u0430, \\\u0430\u043b\u044c\u0444\u0430[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d>, \u0442\u043e \u043c\u044b \u043f\u0438\u0448\u0435\u043c <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]X\\\u0441\u0438\u043c Ga(\\\u0430\u043b\u044c\u0444\u0430,\\\u0431\u0435\u0442\u0430).[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0435\u0449\u0435 \u043e\u0434\u043d\u0438\u043c \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435\u043c \u0434\u043b\u044f \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u0447\u0442\u043e <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]Ga(\\\u0430\u043b\u044c\u0444\u0430,1) = Ex(\\\u0430\u043b\u044c\u0444\u0430).[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0412 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u0441 \u0447\u0430\u0441\u0442\u043e\u0442\u043e\u0439 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\u0441[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> (\u043a\u0430\u043a \u0432 \u0441\u043b\u0443\u0447\u0430\u0435 \u0440\u0430\u0434\u0438\u043e\u0430\u043a\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0430\u0434\u0430), \u0435\u0441\u043b\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]T[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0435\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438, \u043a\u043e\u0433\u0434\u0430 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 m-\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u044f; \u0442\u043e\u0433\u0434\u0430, \u0434\u043b\u044f <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]t\\\u0433\u0435 0[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0438 \u0447\u0438\u0441\u043b\u0430 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]N[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0441\u043e\u0431\u044b\u0442\u0438\u0439, \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u044f\u0449\u0438\u0445 \u0432 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441][0,t][\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u043c\u044b \u0438\u043c\u0435\u0435\u043c <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]t\\lt T \\leftrightarrow N\\lt \u043c[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d>, \u0438, \u0442\u0430\u043a \u043a\u0430\u043a <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]N\\\u0441\u0438\u043c Po(ct),[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d>, \u044d\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442:<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u0446\u0435\u043d\u0442\u0440; \u0446\u0432\u0435\u0442: #000000;\"><\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]1-F_T(t) = P(T\\\u0433\u0442 t) = \\\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \\\u0441\u0443\u043c_{\u043a=0}^{\u043c-1}Po(\u043a; ct)=\u0435^{-\u0446\u0442}\\\u0441\u0443\u043c_{\u043a=0}^{\u043c-1}\\frac{(\u0446\u0442)^\u043a}{\u043a!}[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0418 \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u0435\u0441\u043b\u0438 \u043c\u044b \u044d\u0442\u043e \u0432\u044b\u0432\u0435\u0434\u0435\u043c, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438<\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u0446\u0435\u043d\u0442\u0440; \u0446\u0432\u0435\u0442: #000000;\"><\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 f(t) = c\u0435^{-\u0446\u0442}\\frac{(\u0446\u0442)^{\u043c-1}}{(\u043c-1)!}[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u043f \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\">\u0418 \u043f\u043e\u044d\u0442\u043e\u043c\u0443, <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]T\\\u0441\u0438\u043c Ga(1\/\u0446, \u043c).[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d><\/\u043f><br \/>\n<\u0430 \u0438\u043c\u044f=\"8\"><\/\u0430><\/\u0431\u0440><\/\u0431\u0440><br \/>\n<\u04372>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f<\/\u04372><br \/>\n<\u043e\u043b \u0441\u0442\u0438\u043b\u044c=\"\u0442\u0435\u043a\u0441\u0442-\u0432\u044b\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u043d\u0438\u0435: \u043e\u043f\u0440\u0430\u0432\u0434\u0430\u0442\u044c; \u0446\u0432\u0435\u0442: #000000;\"><br \/>\n \t<\u043b\u0438>\u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0443\u044e <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\u0446[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 f(x) = \\frac{\u0446}{x^2+1}[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u0431\u044b\u043b\u0430 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 (\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u041a\u043e\u0448\u0438)<\/\u043b\u0438><br \/>\n \t<\u043b\u0438>\u0418\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]Un(a.b),[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0435\u0433\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/\u043b\u0438><br \/>\n \t<\u043b\u0438>\u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f <\u0441\u043f\u0430\u043d dir=\"ltr\">[\u043b\u0430\u0442\u0435\u043a\u0441]\\Phi_{\\\u043c\u0443,\\\u03c3}(\u0445)[\/\u043b\u0430\u0442\u0435\u043a\u0441]<\/\u0441\u043f\u0430\u043d> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438.<\/\u043b\u0438><br \/>\n<\/\u043e\u043b><br \/>\n<\u0446\u0435\u043d\u0442\u0440><\u0438\u0444\u0440\u0430\u043c\u0435 \u0448\u0438\u0440\u0438\u043d\u0430=\"560\" \u0432\u044b\u0441\u043e\u0442\u0430=\"315\" src=\"https:\/\/www.youtube.com\/embed\/kdxgrB1h98g\" \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u0435=\"YouTube video player\" \u0440\u0430\u043c\u043a\u0430=\"0\" \u043f\u043e\u0437\u0432\u043e\u043b\u0438\u0442\u044c=\"\u0430\u043a\u0441\u0435\u043b\u0435\u0440\u043e\u043c\u0435\u0442\u0440; \u0430\u0432\u0442\u043e\u0438\u0433\u0440\u0430; \u0431\u0443\u0444\u0435\u0440 \u043e\u0431\u043c\u0435\u043d\u0430- \u0437\u0430\u043f\u0438\u0441\u044c; \u0437\u0430\u0448\u0438\u0444\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043c\u0435\u0434\u0438\u0430; \u0433\u0438\u0440\u043e\u0441\u043a\u043e\u043f; \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0430 \u0432 \u043a\u0430\u0440\u0442\u0438\u043d\u043a\u0435\" allowfullscreen><\/iframe><\/\u0446\u0435\u043d\u0442\u0440><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0420\u0435\u0437\u044e\u043c\u0435\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0433\u043b\u0443\u0431\u043e\u043a\u043e \u0438\u0437\u0443\u0447\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 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\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435, \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0412\u0435\u0439\u0431\u0443\u043b\u043b\u0430 \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0413\u0430\u043c\u043c\u0430. \u041f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0449\u0438\u0435 \u043a\u0430\u0436\u0434\u043e\u0435 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439, \u0438 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043d\u044b \u0438\u0445 \u043f\u043e\u0441\u043b\u0435\u0434\u0441\u0442\u0432\u0438\u044f \u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 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