{"id":213,"date":"2023-08-04T02:39:23","date_gmt":"2023-08-04T02:39:23","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d0%b1%d0%b5%d1%82%d0%b0-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5\/"},"modified":"2023-08-04T02:39:23","modified_gmt":"2023-08-04T02:39:23","slug":"%d0%b1%d0%b5%d1%82%d0%b0-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d0%b1%d0%b5%d1%82%d0%b0-%d1%80%d0%b0%d1%81%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d0%b5%d0%bd%d0%b8%d0%b5\/","title":{"rendered":"\u0411\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435"},"content":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0435\u0442\u0430-\u0434\u0438\u0441\u0442\u0440\u0438\u0431\u0443\u0442\u0438\u0432 \u0438 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u043e\u043d \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-beta\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0411\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (0,1) \u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0434\u0432\u0443\u043c\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438: \u03b1 \u0438 \u03b2. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u043e\u0442 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u03b1 \u0438 \u03b2.<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u0442\u043e\u043c, \u0447\u0442\u043e \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u043e\u0439 \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u0430\u0432\u043b\u044f\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u03b1 \u0438 \u03b2. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0445 \u0432\u0435\u043b\u0438\u0447\u0438\u043d, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043c\u0435\u0436\u0434\u0443 0 \u0438 1.<\/p>\n<p> \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439, \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0449\u0438\u0445 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u0430\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c. \u041d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u043c\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ee1d0d8a1624a017b8ef9ce8a67c694e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex]X\\sim Beta(\\alpha,\\beta)\\\\[2ex]X\\sim \\beta_{\\alpha,\\beta}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"121\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0412 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0435 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438\u043c\u0435\u0435\u0442 \u043e\u0447\u0435\u043d\u044c \u0440\u0430\u0437\u043d\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u043d\u044b\u0445 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0439 \u0432 \u0440\u0430\u0437\u043d\u044b\u0445 \u0432\u044b\u0431\u043e\u0440\u043a\u0430\u0445. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0432 \u0443\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0430\u043c\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u041f\u0435\u0440\u0442\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-beta\"><\/span> \u0413\u0440\u0430\u0444\u0438\u043a \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423\u0447\u0438\u0442\u044b\u0432\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u043d\u0438\u0436\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/p>\n<p> \u041d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0433\u0440\u0430\u0444\u0438\u043a \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u03b1 \u0438 \u03b2. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-graphique-beta.png\" alt=\"\u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0430 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f\" class=\"wp-image-4315\" width=\"621\" height=\"372\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u043d\u0438\u0436\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043a\u0443\u043c\u0443\u043b\u044f\u0442\u0438\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u03b1 \u0438 \u03b2. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-beta-cumulative.png\" alt=\"\u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0430 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0439 \u0431\u0435\u0442\u0430-\u0432\u0435\u0440\u0441\u0438\u0438\" class=\"wp-image-4316\" width=\"621\" height=\"373\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-beta\"><\/span> \u0425\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a\u043e\u0432\u044b \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0432\u0430\u0436\u043d\u044b\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f.<\/p>\n<ul>\n<li> \u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u03b1 \u0438 \u03b2 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u0438 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-442bebaba847543d6db71cdf0127a4b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\alpha >0\\\\[2ex] \\beta >0\\end{array}&#187; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;54&#8243; width=&#187;44&#8243; style=&#187;vertical-align: 0px;&#187;><\/p>\n<\/p>\n<ul>\n<li> \u041e\u0431\u043b\u0430\u0441\u0442\u044c \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u0434\u0438\u0430\u043f\u0430\u0437\u043e\u043d\u0435 \u043e\u0442 0 \u0434\u043e 1, \u0434\u0432\u0430 \u043a\u0440\u0430\u0439\u043d\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043d\u0435 \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u044e\u0442\u0441\u044f.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-60f8667881e2c5a08eae2db3c3e04708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0421\u0440\u0435\u0434\u043d\u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u043e \u0430\u043b\u044c\u0444\u0430, \u0434\u0435\u043b\u0435\u043d\u043d\u043e\u043c\u0443 \u043d\u0430 \u0441\u0443\u043c\u043c\u0443 \u0430\u043b\u044c\u0444\u0430 \u043f\u043b\u044e\u0441 \u0431\u0435\u0442\u0430.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4530a8b72211111e8bec79b6388e00a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] E[X]=\\cfrac{\\alpha}{\\alpha+\\beta}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"81\" width=\"111\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0414\u0438\u0441\u043f\u0435\u0440\u0441\u0438\u044e \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-71c6ef40db833722e63c56cd763d6601_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim B(\\alpha,\\beta)\\\\[2ex] Var(X)=\\cfrac{\\alpha\\cdot \\beta}{(\\alpha+\\beta+1)\\cdot (\\alpha+\\beta)^2}\\end{array} \" title=\"Rendered by QuickLaTeX.com\" height=\"82\" width=\"255\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0414\u043b\u044f \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0430\u043b\u044c\u0444\u0430 \u0438 \u0431\u0435\u0442\u0430 \u0431\u043e\u043b\u044c\u0448\u0435 1 \u0440\u0435\u0436\u0438\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0431\u0435\u0442\u0430 \u043c\u043e\u0436\u043d\u043e \u043b\u0435\u0433\u043a\u043e \u043d\u0430\u0439\u0442\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-472cafc0cf9d1cf782206ddc7c9475d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Mo=\\cfrac{\\alpha-1}{\\alpha+\\beta-2}\\qquad \\alpha,\\beta>1&#8243; title=&#187;Rendered by QuickLaTeX.com&#187; height=&#187;42&#8243; width=&#187;225&#8243; style=&#187;vertical-align: -16px;&#187;><\/p>\n<\/p>\n<ul>\n<li> \u041f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-48f1f2a13df23d7c779bc37da4b49368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{x^{\\alpha-1}(1-x)^{\\beta-1}}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"218\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0413\u0434\u0435 B(\u03b1,\u03b2) \u2014 \u0431\u0435\u0442\u0430-\u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4eb1d2659d9993f9d05a35cce63fc14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(\\alpha,\\beta)=\\int_0^1x^{\\alpha-1}(1-x)^{\\beta-1}dx\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"248\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041a\u0443\u043c\u0443\u043b\u044f\u0442\u0438\u0432\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-031b21ea3e2964d3ac4e6f222356d55b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{B(x;\\alpha,\\beta)}{B(\\alpha,\\beta)}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"176\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> \u0413\u0434\u0435 B(x;\u03b1,\u03b2) \u2014 \u043d\u0435\u043f\u043e\u043b\u043d\u0430\u044f \u0431\u0435\u0442\u0430-\u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c\u0430\u044f \u043a\u0430\u043a:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c64764f48f86e8f97df5ed1e8d7fbe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B(x;\\,a,b) = \\int_0^x t^{a-1}\\,(1-t)^{b-1}\\,dt\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"255\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 X \u2014 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c\u0430\u044f \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c, \u0442\u043e 1-X \u2014 \u044d\u0442\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u043c\u0430\u044f \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c, \u0430\u043b\u044c\u0444\u0430- \u0438 \u0431\u0435\u0442\u0430-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0431\u0435\u0442\u0430- \u0438 \u0430\u043b\u044c\u0444\u0430-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c65dd399bb92ffe982784a6c1b6e5b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(\\alpha,\\beta) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ 1-X\\sim B(\\beta,\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"361\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u0430\u043b\u044c\u0444\u0430- \u0438 \u0431\u0435\u0442\u0430-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u044b \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0432\u043d\u044b 1, \u0442\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u043c\u0443 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 0 \u0438 1.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-10010ad6c6959b44a8ae0fe4361b4034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim B(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ X\\sim U(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"321\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0435\u0442\u0430-\u0434\u0438\u0441\u0442\u0440\u0438\u0431\u0443\u0442\u0438\u0432 \u0438 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u043e\u043d \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435? \u0411\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u2014 \u044d\u0442\u043e \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435 \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 (0,1) \u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0437\u043e\u0432\u0430\u043d\u043d\u043e\u0435 \u0434\u0432\u0443\u043c\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438: \u03b1 \u0438 \u03b2. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0431\u0435\u0442\u0430-\u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0437\u0430\u0432\u0438\u0441\u044f\u0442 \u043e\u0442 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u03b1 \u0438 \u03b2. 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