{"id":26783,"date":"2021-05-27T13:00:19","date_gmt":"2021-05-27T13:00:19","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26783"},"modified":"2024-05-22T02:09:35","modified_gmt":"2024-05-22T02:09:35","slug":"%d0%bf%d1%80%d0%be%d1%86%d0%b5%d1%81%d1%81-%d0%bf%d1%83%d0%b0%d1%81%d1%81%d0%be%d0%bd%d0%b0-%d0%b0%d0%bf%d0%bf%d1%80%d0%be%d0%ba%d1%81%d0%b8%d0%bc%d0%b0%d1%86%d0%b8%d1%8f-%d0%b1%d0%b8%d0%bd%d0%be","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%bf%d1%80%d0%be%d1%86%d0%b5%d1%81%d1%81-%d0%bf%d1%83%d0%b0%d1%81%d1%81%d0%be%d0%bd%d0%b0-%d0%b0%d0%bf%d0%bf%d1%80%d0%be%d0%ba%d1%81%d0%b8%d0%bc%d0%b0%d1%86%d0%b8%d1%8f-%d0%b1%d0%b8%d0%bd%d0%be\/","title":{"rendered":"\u041f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430: \u0410\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u041f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430: \u0410\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0420\u0435\u0437\u044e\u043c\u0435<\/strong><br \/><em>\u042d\u0442\u043e\u0442 \u0443\u0440\u043e\u043a \u0444\u043e\u043a\u0443\u0441\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u043a\u0430\u043a \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0432\u044b\u0442\u0435\u043a\u0430\u0435\u0442 \u0438\u0437 \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0441 \u0431\u043e\u043b\u044c\u0448\u0438\u043c \u0447\u0438\u0441\u043b\u043e\u043c \u043f\u043e\u043f\u044b\u0442\u043e\u043a \u0438 \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u0439 \u0438\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u044c\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e. \u0426\u0435\u043d\u0442\u0440\u0430\u043b\u044c\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u043e\u0445\u0432\u0430\u0442\u044b\u0432\u0430\u0435\u0442 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u044b \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, \u043a\u0430\u043a \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0435, \u0442\u0430\u043a \u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u0447\u0430\u0441\u0442\u0438\u0446 \u0432 \u0436\u0438\u0434\u043a\u043e\u0441\u0442\u0438 \u0438 \u0438\u0441\u043f\u0443\u0441\u043a\u0430\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u0438\u0446 \u0440\u0430\u0434\u0438\u043e\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u043c \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u043e\u043c \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0437\u0430\u0432\u0435\u0440\u0448\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0430\u0445, \u0442\u0430\u043a\u0438\u0445 \u043a\u0430\u043a \u043e\u0431\u0441\u043b\u0443\u0436\u0438\u0432\u0430\u043d\u0438\u0435 \u043a\u043b\u0438\u0435\u043d\u0442\u043e\u0432 \u0432 \u0441\u0443\u043f\u0435\u0440\u043c\u0430\u0440\u043a\u0435\u0442\u0435 \u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0441\u0435\u043b\u0435\u043d\u0438\u044f \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043c\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u0438.<\/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 \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0441\u043c\u043e\u0436\u0435\u0442:\n<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430.<\/li>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u043a\u0430\u043a \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u044e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430.<\/li>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u0443\u044e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0432 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430.<\/li>\n<li><strong>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c<\/strong> \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u041e\u0413\u041b\u0410\u0412\u041b\u0415\u041d\u0418\u0415<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/a><br \/>\n<a href=\"#2\">\u041f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u044b \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/a><br \/>\n<a href=\"#3\">\u041f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/a><br \/>\n<a href=\"#4\">\u0412\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/a><br \/>\n<a href=\"#5\">\u0412\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439<\/a><br \/>\n<a href=\"#6\">\u041f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/a><br \/>\n<\/center><br \/>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/mQ0j3FE8p2U\" 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><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=154s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u044e<\/span><\/strong><\/a> \u0434\u043b\u044f <a href=\"https:\/\/toposuranos.com\/el-ensayo-de-bernoulli-para-n-intentos-independientes\/\" rel=\"noopener\" target=\"_blank\">\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<\/a>, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0431\u043e\u043b\u044c\u0448\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043f\u043e\u043f\u044b\u0442\u043e\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0438 \u0432\u0441\u0435 \u0441 \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u043e\u0439 \u0438\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u044c\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span>. \u041a\u043e\u0433\u0434\u0430 \u043c\u044b \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u043c, \u043c\u044b \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u043c \u043e\u0442 \u0442\u0438\u043f\u0438\u0447\u043d\u043e\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u043a \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0443 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430. \u0427\u0442\u043e\u0431\u044b \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u043e, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0432\u0438\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{Bi(n;k;p_n)\\}_n,<\/span><\/span> \u0433\u0434\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p_n<\/span><\/span> \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u0435\u0442 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">np_n=\\lambda \\gt 0<\/span><\/span>. \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{n\\to\\infty}P\\left(Bi(n;k;P_n) \\right) = \\frac{\\lambda^k}{k!}e^{-\\lambda}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u043e \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043d\u0435 \u0441\u043b\u043e\u0436\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0435\u0441\u043b\u0438 \u0432\u0437\u044f\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(n;k;p_n)<\/span><\/span> \u0438 \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0438 \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n^k<\/span><\/span>, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0432\u044b\u0432\u043e\u0434:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td width=\"80px\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B(n;k;p_n))<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle={{n}\\choose{k}}p^k(1-p)^{n-k}<\/span><span style=\"color: #f00000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\cdot \\displaystyle \\frac{n^k}{n^k}<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"80px\"><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle=\\frac{n!}{(n-k)!k!}p^k(1-p)^{n-k} \\cdot \\frac{n^k}{n^k}<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"80px\"><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle=\\frac{n(n-1)\\cdots[n-(k-1)]}{n^k} \\cdot \\frac{(np_n)^k}{k!} (1-p_n)^{-k}(1-p_n)^n<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0441\u043b\u0438 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043f\u0440\u0435\u0434\u0435\u043b, \u043a\u043e\u0433\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span>, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}\n\n\\displaystyle \\lim_{n\\to\\infty} {{n}\\choose{k}}p_n^k(1-p_n)^{n-k} &amp;= \\lim_{n\\to\\infty} \\underbrace{\\frac{n(n-1)\\cdots[n-(k-1)]}{n^k}}_{\\to 1} \\cdot \\frac{\\overbrace{(np_n)^k}^{\\to\\lambda^k}}{k!} \\overbrace{(1-p_n)^{-k}}^{\\to 1} {(1-p_n)^n} \\\\ \\\\\n\n&amp;\\displaystyle = \\frac{\\lambda^k}{k!} \\lim_{n\\to\\infty}\\left(1 - \\frac{\\lambda}{n} \\right)^n \\\\ \\\\\n\n&amp; \\displaystyle = \\frac{\\lambda^k}{k!}e^{-\\lambda}\n\n\\end{array}\n\n<\/span>\n<\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442\u0441\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u044b \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Po(k;\\lambda)<\/span><\/span>, \u0447\u0435\u0440\u0435\u0437<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\displaystyle Po(k;\\lambda) := \\lim_{n\\to\\infty} {{n}\\choose{k}}p^k(1-p_n)^{n-k} = \\frac{\\lambda^k}{k!}e^{-\\lambda} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\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> \u0438\u043c\u0435\u0435\u0442 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Po(k,\\lambda),<\/span><\/span>, \u0435\u0441\u043b\u0438 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> P(X=k) = Po(k;\\lambda) <\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h2>\u041f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u044b \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/h2>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u041f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=665s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u0441 \u043e\u0431\u044a\u0435\u043c\u043e\u043c<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span>, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0436\u0438\u0434\u043a\u043e\u0441\u0442\u044c \u0441 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u043c\u0438 \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u043c\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u0430\u043c\u0438. \u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u043c, \u0447\u0442\u043e \u0436\u0438\u0434\u043a\u043e\u0441\u0442\u044c \u0445\u043e\u0440\u043e\u0448\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u0448\u0430\u043d\u0430 \u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u043d\u0435 \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0443\u044e\u0442 \u0434\u0440\u0443\u0433 \u0441 \u0434\u0440\u0443\u0433\u043e\u043c, \u043d\u0435 \u043f\u0440\u0438\u0442\u044f\u0433\u0438\u0432\u0430\u044e\u0442\u0441\u044f \u0438 \u043d\u0435 \u043e\u0442\u0442\u0430\u043b\u043a\u0438\u0432\u0430\u044e\u0442\u0441\u044f. \u042d\u0442\u0438 \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u0444\u043e\u0440\u043c\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u0442\u044c \u0447\u0435\u0440\u0435\u0437 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u0438\u044f:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u0413\u0438\u043f\u043e\u0442\u0435\u0437\u0430 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0441\u0442\u0438:<\/strong> \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0439\u0442\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u0436\u0438\u0434\u043a\u043e\u0441\u0442\u0438 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u043e\u0431\u044a\u0435\u043c\u0430 \u044d\u0442\u043e\u0439 \u043e\u0431\u043b\u0430\u0441\u0442\u0438.<\/li>\n<li><strong>\u041e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f:<\/strong> \u0421\u043e\u0431\u044b\u0442\u0438\u044f \u00abj-\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 D\u00bb, \u043f\u0440\u0438 j=1,2,&#8230;,n \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438.<\/li>\n<li><strong>\u041d\u0435\u0441\u043e\u0432\u043f\u0430\u0434\u0435\u043d\u0438\u0435:<\/strong> \u0414\u0432\u0435 \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u043d\u0435 \u043c\u043e\u0433\u0443\u0442 \u0437\u0430\u043d\u0438\u043c\u0430\u0442\u044c \u043e\u0434\u043d\u043e \u0438 \u0442\u043e \u0436\u0435 \u043c\u0435\u0441\u0442\u043e \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435.<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043e\u0431\u043b\u0430\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u0441 \u043e\u0431\u044a\u0435\u043c\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u00ab\u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span> \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u0447\u0430\u0441\u0442\u0438\u0446\u00bb \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>; \u043d\u0430\u0437\u043e\u0432\u0435\u043c \u044d\u0442\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span>. \u041f\u0443\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(v)<\/span><\/span> \u0431\u0443\u0434\u0435\u0442 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0447\u0430\u0441\u0442\u0438\u0446\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432\u043d\u0443\u0442\u0440\u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u0431\u044a\u0435\u043c\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v.<\/span><\/span> \u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span> &#8211; \u0434\u0432\u0435 \u043d\u0435\u0441\u043c\u0435\u0436\u043d\u044b\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043e\u0431\u044a\u0435\u043c\u043e\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_1<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_2<\/span><\/span> \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0442\u043e \u0435\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D=D_1\\cup D_2,<\/span><\/span> \u0438\u043c\u0435\u0435\u0442 \u043e\u0431\u044a\u0435\u043c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v,<\/span><\/span>, \u0442\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v=v_1+v_2.<\/span><\/span> \u0418 \u0442\u0430\u043a \u043a\u0430\u043a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span> \u043d\u0435\u0441\u043c\u0435\u0436\u043d\u044b\u0435 (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1\\cap D_2 = \\emptyset <\/span><\/span>), \u0442\u043e \u0431\u0443\u0434\u0435\u0442:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> h(v) = h(v_1) + h(v_2) <\/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\">V<\/span><\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0431\u044a\u0435\u043c\u043e\u043c \u0432\u0441\u0435\u0439 \u0436\u0438\u0434\u043a\u043e\u0441\u0442\u0438, \u0442\u043e \u0431\u0443\u0434\u0435\u0442:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> h(V) = 1 <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418, \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\"> h(v) =\\displaystyle \\frac{v}{V} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span> \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u0435\u043c \u0442\u0438\u043f\u0430 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0441 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p=v\/V<\/span><\/span> \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> g_k(v) =B(n;k;p=v\/V) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041e\u0434\u043d\u0430\u043a\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u043d\u0441\u0442\u0432\u043e \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u0439 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0432\u043a\u043b\u044e\u0447\u0430\u0435\u0442 \u0431\u043e\u043b\u044c\u0448\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0447\u0430\u0441\u0442\u0438\u0446 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0438 \u043e\u0431\u043b\u0430\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u044e\u0442\u0441\u044f, \u043a\u0430\u043a \u043f\u0440\u0430\u0432\u0438\u043b\u043e, \u043c\u0430\u043b\u044b \u043f\u043e \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u044b, \u0442\u0430\u043a \u0447\u0442\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(g_k(v)) = \\lim_{\\begin{matrix}n\\to\\infty\\\\ v\/V=c \\end{matrix}}P(B(n;k;p=v\/V)) =\\displaystyle \\frac{(cv)^k}{k!}e^{-cv}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0412\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=944s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u043c\u044b \u0444\u0438\u043a\u0441\u0438\u0440\u0443\u0435\u043c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e<\/span><\/strong><\/a> \u0447\u0430\u0441\u0442\u0438\u0446, \u0438\u0441\u043f\u0443\u0441\u043a\u0430\u0435\u043c\u044b\u0445 \u0440\u0430\u0434\u0438\u043e\u0430\u043a\u0442\u0438\u0432\u043d\u044b\u043c \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u043e\u043c \u0441 \u043c\u043e\u043c\u0435\u043d\u0442\u0430 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 t=0, \u0438 \u0434\u0430\u043b\u0435\u0435 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0432 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 [0,t[ \u0431\u0443\u0434\u0435\u0442 \u0438\u0441\u043f\u0443\u0449\u0435\u043d\u043e \u0440\u043e\u0432\u043d\u043e k \u0447\u0430\u0441\u0442\u0438\u0446 \u043f\u0440\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f\u0445:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u041d\u0435\u043f\u043e\u0441\u0442\u043e\u044f\u043d\u0441\u0442\u0432\u043e:<\/strong> \u0423\u0441\u043b\u043e\u0432\u0438\u044f \u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430 \u043d\u0435 \u0438\u0437\u043c\u0435\u043d\u044f\u044e\u0442\u0441\u044f \u0432\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u0438.<\/li>\n<li><strong>\u0411\u0435\u0437 \u043f\u0430\u043c\u044f\u0442\u0438:<\/strong> \u0422\u043e, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e \u0432 [0,t[, \u043d\u0435 \u0432\u043b\u0438\u044f\u0435\u0442 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0432 [t,t'[.<\/li>\n<li><strong>\u0418\u0437\u043e\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0441\u043e\u0431\u044b\u0442\u0438\u044f:<\/strong> \u0427\u0430\u0441\u0442\u0438\u0446\u044b \u0438\u0441\u043f\u0443\u0441\u043a\u0430\u044e\u0442\u0441\u044f \u043f\u043e \u043e\u0434\u043d\u043e\u0439 \u0437\u0430 \u0440\u0430\u0437.<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438 \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u0441 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u043c, \u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u0447\u0442\u043e \u043e\u043d\u0438 \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u044b. \u041a\u0430\u043a \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0439\u0442\u0438 \u0447\u0430\u0441\u0442\u0438\u0446\u0443 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043c\u0435\u0441\u0442\u0430, \u0433\u0434\u0435 \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442\u0441\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u044c, \u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u0435\u0435 \u0440\u0430\u0437\u043c\u0435\u0440\u0430, \u0442\u0430\u043a \u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u0438\u0441\u043f\u0443\u0441\u043a\u0430\u043d\u0438\u044f \u0447\u0430\u0441\u0442\u0438\u0446\u044b \u043d\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043c\u043e\u043c\u0435\u043d\u0442\u0430 \u0432\u0440\u0435\u043c\u0435\u043d\u0438, \u043a\u043e\u0433\u0434\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u0435, \u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0442 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0430 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f. \u041e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u0435 \u043f\u0430\u043c\u044f\u0442\u0438 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043e\u0442\u0441\u0443\u0442\u0441\u0442\u0432\u0438\u044e \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430\u0445: \u0442\u043e, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e \u0432 \u043e\u0434\u043d\u043e \u0432\u0440\u0435\u043c\u044f, \u043d\u0435 \u0432\u043b\u0438\u044f\u0435\u0442 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u0432 \u0434\u0440\u0443\u0433\u043e\u0435 \u0432\u0440\u0435\u043c\u044f. \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0437\u043e\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442, \u0447\u0442\u043e \u0432 \u043b\u044e\u0431\u043e\u0439 \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0438\u0441\u043f\u0443\u0449\u0435\u043d\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u043d\u0430 \u0447\u0430\u0441\u0442\u0438\u0446\u0430, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0442\u043e\u043c\u0443, \u043a\u0430\u043a \u043e\u0434\u043d\u043e \u043c\u0435\u0441\u0442\u043e \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0437\u0430\u043d\u044f\u0442\u043e \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u0434\u043d\u0438\u043c \u0442\u0435\u043b\u043e\u043c \u0432 \u043e\u0434\u0438\u043d \u043c\u043e\u043c\u0435\u043d\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u0438.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0442\u0430\u043a, \u0435\u0441\u043b\u0438 \u043c\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u0441\u043e\u0431\u044b\u0442\u0438\u0435 \u00abk \u0447\u0430\u0441\u0442\u0438\u0446 \u0438\u0441\u043f\u0443\u0441\u043a\u0430\u044e\u0442\u0441\u044f \u0432 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t<\/span><\/span>\u00ab, \u0435\u0433\u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0431\u0443\u0434\u0435\u0442 \u0441\u043e\u0431\u044b\u0442\u0438\u0435\u043c \u0432\u0438\u0434\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(t)<\/span><\/span>, \u0442\u043e \u0435\u0441\u0442\u044c:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(g_k(t)) =\\displaystyle \\frac{(ct)^k}{k!} e^{-ct}<\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h3>\u0412\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=mQ0j3FE8p2U&amp;t=1102s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041e\u0431\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430, \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u0444\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u044b.<\/span><\/strong><\/a> \u041e\u043d\u0438 \u0440\u0430\u0437\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u0443 \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0446\u0435\u043b\u0435\u0439. \u0411\u044b\u0441\u0442\u0440\u044b\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u044d\u0442\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0435 \u0431\u043e\u043b\u0435\u0435 \u044f\u0441\u043d\u044b\u043c &#8211; \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0442\u044c \u0440\u043e\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0438\u0433\u0440\u0430\u0435\u0442 \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u0430\u044f \u00abc\u00bb \u0432 \u043e\u0431\u043e\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445. \u0427\u0442\u043e\u0431\u044b \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0431\u044b\u043b\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0430, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e, \u0447\u0442\u043e\u0431\u044b \u0435\u0435 \u0430\u0440\u0433\u0443\u043c\u0435\u043d\u0442 \u0431\u044b\u043b \u0431\u0435\u0437\u0440\u0430\u0437\u043c\u0435\u0440\u043d\u044b\u043c; \u043e\u0434\u043d\u0430\u043a\u043e \u043e\u043d\u0430 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u0435\u0434\u0438\u043d\u0438\u0446\u044b \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u0438\u043b\u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u043e\u0433\u043e, \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u043c \u043b\u0438 \u043c\u044b \u0441 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0438\u043b\u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c\u0438 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430\u043c\u0438. \u042d\u0442\u0430 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430 \u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044f \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u043e\u0441\u0442\u043e\u044f\u043d\u043d\u043e\u0439 c. \u041c\u044b \u0438\u043c\u0435\u0435\u043c:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Po(k;\\lambda)=\\displaystyle \\frac{\\lambda^k}{k!}e^{-\\lambda}=\\left\\{\\begin{matrix} {\u041f\u0440\u0438 \\lambda = \\rho v } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\rho v)^k}{k!}e^{-\\rho v} &amp; {\u041f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441} \\\\ {\u041f\u0440\u0438 \\lambda = \\nu t } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\nu t)^k}{k!}e^{-\\nu t} &amp; {\u0412\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441} \\end{matrix} \\right.<\/span><\/span><\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>\u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\rho<\/span><\/span>, \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c (\u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043e\u0431\u044a\u0435\u043a\u0442\u043e\u0432 \u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0443 \u043f\u043b\u043e\u0449\u0430\u0434\u0438), \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430.<\/li>\n<li>\u0415\u0441\u043b\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\\u043d\u0443<\/span><\/span>, \u044d\u0442\u043e \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c (\u0438\u043b\u0438 \u0447\u0430\u0441\u0442\u043e\u0442\u0430, \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u043d\u0430 \u0435\u0434\u0438\u043d\u0438\u0446\u0443 \u0432\u0440\u0435\u043c\u0435\u043d\u0438), \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430.<\/li>\n<\/ul>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/8qvHRoEckSc\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"6\"><\/a><\/br><\/br><\/p>\n<h2>\u041f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u041a\u0430\u0441\u0441\u0438\u0440 \u0432 \u0441\u0443\u043f\u0435\u0440\u043c\u0430\u0440\u043a\u0435\u0442\u0435 \u043e\u0431\u0441\u043b\u0443\u0436\u0438\u0432\u0430\u0435\u0442 \u0432 \u0441\u0440\u0435\u0434\u043d\u0435\u043c 2 \u043a\u043b\u0438\u0435\u043d\u0442\u0430 \u043a\u0430\u0436\u0434\u044b\u0435 9 \u043c\u0438\u043d\u0443\u0442. \u0421\u043e\u0441\u0442\u0430\u0432\u044c\u0442\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u0443, \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0449\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043e\u0431\u0441\u043b\u0443\u0436\u0438\u0432\u0430\u043d\u0438\u044f 1, 2, 3 \u0438 \u0442\u0430\u043a \u0434\u0430\u043b\u0435\u0435 \u0434\u043e 5 \u0447\u0435\u043b\u043e\u0432\u0435\u043a \u0437\u0430 5 \u043c\u0438\u043d\u0443\u0442.<\/li>\n<li>\u0412\u0435\u0442\u0435\u0440\u0438\u043d\u0430\u0440\u043d\u0430\u044f \u043a\u043b\u0438\u043d\u0438\u043a\u0430 \u043c\u043e\u0436\u0435\u0442 \u043f\u0440\u0438\u043d\u044f\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c 12 \u043a\u043b\u0438\u0435\u043d\u0442\u043e\u0432 \u0432 \u0434\u0435\u043d\u044c. \u0415\u0441\u043b\u0438 \u0432 \u0441\u0440\u0435\u0434\u043d\u0435\u043c \u043e\u043d\u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442 9 \u043a\u043b\u0438\u0435\u043d\u0442\u043e\u0432 \u0432 \u0434\u0435\u043d\u044c, \u043a\u0430\u043a\u043e\u0432\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0432 \u043b\u044e\u0431\u043e\u0439 \u0434\u0435\u043d\u044c \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u0435\u0432\u044b\u0448\u0435\u043d\u0430 \u0435\u043c\u043a\u043e\u0441\u0442\u044c \u043a\u043b\u0438\u043d\u0438\u043a\u0438?<\/li>\n<li>\u0412 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043c\u0435\u0441\u0442\u0435 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0430\u0441\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 10 \u0447\u0435\u043b\u043e\u0432\u0435\u043a \u043d\u0430 1000 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u0435\u0442\u0440\u043e\u0432. \u041a\u0430\u043a\u043e\u0432\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043d\u0430 \u0443\u0447\u0430\u0441\u0442\u043a\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c\u044e 60 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u043c\u0435\u0442\u0440\u043e\u0432 \u0431\u0443\u0434\u0435\u0442 \u043c\u0435\u043d\u0435\u0435 15 \u0447\u0435\u043b\u043e\u0432\u0435\u043a?<\/li>\n<li>\u041a\u0443\u0440\u0438\u0446\u0430 \u0445\u043e\u0447\u0435\u0442 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u0434\u043e\u0440\u043e\u0433\u0443. \u0418\u0434\u044f \u043f\u043e \u043f\u0440\u044f\u043c\u043e\u0439, \u0435\u0439 \u043f\u043e\u0442\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044f 58 \u0441\u0435\u043a\u0443\u043d\u0434. \u0415\u0441\u043b\u0438 \u0434\u043e\u0440\u043e\u0433\u0430 \u0438\u043c\u0435\u0435\u0442 \u0442\u0440\u0430\u043d\u0441\u043f\u043e\u0440\u0442\u043d\u043e\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435 3 \u0430\u0432\u0442\u043e\u043c\u043e\u0431\u0438\u043b\u044f \u0432 \u043c\u0438\u043d\u0443\u0442\u0443, \u0438 \u0435\u0441\u043b\u0438 \u0430\u0432\u0442\u043e\u043c\u043e\u0431\u0438\u043b\u044c \u043f\u0440\u043e\u0435\u0434\u0435\u0442, \u043f\u043e\u043a\u0430 \u043a\u0443\u0440\u0438\u0446\u0430 \u043f\u044b\u0442\u0430\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0435\u0439\u0442\u0438, \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043d\u0435\u0438\u0437\u0431\u0435\u0436\u043d\u043e \u0441\u0431\u0438\u0442\u0430 \u043d\u0430\u0441\u043c\u0435\u0440\u0442\u044c. \u041a\u0430\u043a\u043e\u0432\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043a\u0443\u0440\u0438\u0446\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u0442 \u0434\u043e\u0440\u043e\u0433\u0443 \u0436\u0438\u0432\u043e\u0439?<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u041f\u0440\u043e\u0446\u0435\u0441\u0441 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430: \u0410\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u0420\u0435\u0437\u044e\u043c\u0435\u042d\u0442\u043e\u0442 \u0443\u0440\u043e\u043a \u0444\u043e\u043a\u0443\u0441\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u043d\u0430 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0435 \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430 \u043a\u0430\u043a \u0430\u043f\u043f\u0440\u043e\u043a\u0441\u0438\u043c\u0430\u0446\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430, \u043d\u0430\u0447\u0438\u043d\u0430\u044f \u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u041f\u0443\u0430\u0441\u0441\u043e\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 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