{"id":215,"date":"2023-08-04T02:51:27","date_gmt":"2023-08-04T02:51:27","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%a4%9a%e9%a1%b9%e5%88%86%e5%b8%83-1\/"},"modified":"2023-08-04T02:51:27","modified_gmt":"2023-08-04T02:51:27","slug":"%e5%a4%9a%e9%a1%b9%e5%88%86%e5%b8%83-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%a4%9a%e9%a1%b9%e5%88%86%e5%b8%83-1\/","title":{"rendered":"\u591a\u9879\u5206\u5e03"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u591a\u9879\u5206\u5e03\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u591a\u9879\u5206\u5e03\u7684\u5b9a\u4e49\u3001\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u5c5e\u6027\u662f\u4ec0\u4e48\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u4f7f\u7528\u5728\u7ebf\u8ba1\u7b97\u5668\u8ba1\u7b97\u591a\u9879\u5206\u5e03\u7684\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-distribucion-multinomial\"><\/span>\u4ec0\u4e48\u662f\u591a\u9879\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u591a\u9879\u5f0f\u5206\u5e03<\/strong>\uff08\u6216<strong>\u591a\u9879\u5f0f\u5206\u5e03<\/strong>\uff09\u662f\u4e00\u79cd\u6982\u7387\u5206\u5e03\uff0c\u63cf\u8ff0\u4e86\u7ecf\u8fc7\u591a\u6b21\u8bd5\u9a8c\u540e\uff0c\u82e5\u5e72\u4e92\u65a5\u4e8b\u4ef6\u53d1\u751f\u7ed9\u5b9a\u6b21\u6570\u7684\u6982\u7387\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u4e00\u4e2a\u968f\u673a\u5b9e\u9a8c\u53ef\u4ee5\u4ea7\u751f\u4e09\u4e2a\u6216\u66f4\u591a\u7684\u6392\u4ed6\u4e8b\u4ef6\uff0c\u5e76\u4e14\u6bcf\u4e2a\u4e8b\u4ef6\u5355\u72ec\u53d1\u751f\u7684\u6982\u7387\u5df2\u77e5\uff0c\u5219\u4f7f\u7528\u591a\u9879\u5206\u5e03\u6765\u8ba1\u7b97\u5f53\u8fdb\u884c\u591a\u4e2a\u5b9e\u9a8c\u65f6\uff0c\u4e00\u5b9a\u6570\u91cf\u7684\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002\u6bcf\u6b21\u7684\u65f6\u95f4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u591a\u9879\u5206\u5e03\u662f\u4e8c\u9879\u5206\u5e03\u7684\u63a8\u5e7f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-multinomial\"><\/span>\u591a\u9879\u5206\u5e03\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97<strong>\u591a\u9879\u5206\u5e03\u6982\u7387\uff0c<\/strong>\u5fc5\u987b\u9996\u5148\u786e\u5b9a\u6570\u636e\u603b\u6570\u7684\u9636\u4e58\u4e0e\u6bcf\u4e2a\u4e8b\u4ef6\u51fa\u73b0\u6b21\u6570\u7684\u9636\u4e58\u4e4b\u95f4\u7684\u5546\uff0c\u5e76\u5c06\u7ed3\u679c\u4e58\u4ee5\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u7684\u4e58\u79ef\u3002\u5f97\u51fa\u6240\u8ff0\u4e8b\u4ef6\u53d1\u751f\u7684\u6b21\u6570\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c<strong>\u591a\u9879\u5206\u5e03\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-multinomiale.png\" alt=\"\u591a\u9879\u5206\u5e03\" class=\"wp-image-4038\" width=\"255\" height=\"201\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fda1e51b12ba3624074fcbebad72b1fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u8ba1\u7b97\u7684\u591a\u9879\u5206\u5e03\u7684\u6982\u7387\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6267\u884c\u7684\u6d4b\u8bd5\u603b\u6570\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u4e8b\u4ef6\u53d1\u751f\u7684\u6b21\u6570<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5db80b23c0dc6e4f21c509cb298856a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002<\/li>\n<\/ul>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u53d8\u91cf\u670d\u4ece\u591a\u9879\u5206\u5e03\u7684\u6982\u7387\u3002<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-distribucion-multinomial\"><\/span>\u591a\u9879\u5206\u5e03\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u5b8c\u6210\u5bf9\u591a\u9879\u5206\u5e03\u6982\u5ff5\u7684\u7406\u89e3\uff0c\u4e0b\u9762\u60a8\u5df2\u7ecf\u89e3\u51b3\u4e86\u8ba1\u7b97\u591a\u9879\u5206\u5e03\u6982\u7387\u7684\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u4e00\u5bb6\u5546\u5e97\u51fa\u552e\u4e09\u79cd\u4e0d\u540c\u7684\u4ea7\u54c1\u3002\u5f53\u987e\u5ba2\u8d2d\u4e70\u4ea7\u54c1\u65f6\uff0c\u8d2d\u4e70\u4ea7\u54c1A\u3001\u4ea7\u54c1B\u6216\u4ea7\u54c1C\u7684\u6982\u7387\u5206\u522b\u4e3a30%\u300115%\u548c55%\u3002\u6c42\u5f53\u5546\u5e97\u552e\u51fa 8 \u4ef6\u5546\u54c1\u65f6\uff0c\u5176\u4e2d 2 \u4ef6\u662f\u4ea7\u54c1 A\u30011 \u4ef6\u662f\u4ea7\u54c1 B\u30015 \u4ef6\u662f\u4ea7\u54c1 C \u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n<p>\u5b9a\u4e49\u7684\u95ee\u9898\u53d7\u591a\u9879\u5206\u5e03\u652f\u914d\uff0c\u56e0\u6b64\u6709\u5fc5\u8981\u5e94\u7528\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684\u516c\u5f0f\uff1a<\/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-49dc5602a9a1901438dc4edcc710dc19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=\\cfrac{n!}{x_1!\\cdot x_2!\\cdot x_3!}\\cdot p_1^{x_1}\\cdot p_2^{x_2}\\cdot p_3^{x_3}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"243\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u5c06\u95ee\u9898\u4e2d\u7684\u6570\u636e\u4ee3\u5165\u516c\u5f0f\u5e76\u8fdb\u884c\u6982\u7387\u8ba1\u7b97\uff1a<\/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-5f37e4f989eec3ca56a21ffac72d5bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=\\cfrac{8!}{2!\\cdot 1!\\cdot 5!}\\cdot 0,30^{2}\\cdot 0,15^{1}\\cdot 0,55^{5}=0,114\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"339\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u95ee\u9898\u9648\u8ff0\u4e2d\u6240\u8bf4\u7684\u53d1\u751f\u7684\u6982\u7387\u662f 11.4%\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-distribucion-multinomial\"><\/span>\u591a\u9879\u5206\u5e03\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7b2c\u4e00\u4e2a\u6846\u4e2d\u5199\u4e0b\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6b21\u6570\uff0c\u5e76\u4ee5\u76f8\u540c\u7684\u987a\u5e8f\u5728\u7b2c\u4e8c\u4e2a\u6846\u4e2d\u5199\u4e0b\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002\u7136\u540e\u5728\u6700\u540e\u4e00\u4e2a\u7a7a\u683c\u4e2d\u8f93\u5165\u5c1d\u8bd5\u7684\u603b\u6b21\u6570\u3002<\/p>\n<p>\u6570\u636e\u5fc5\u987b\u7528\u7a7a\u683c\u5206\u9694\uff0c\u5e76\u4f7f\u7528\u53e5\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u8f93\u5165\u3002<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li>\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6b21\u6570\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-80cbc7a82ea5a8d49668a36a100d2f99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"28\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosx\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"2 1 5 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero de ocurrencias de cada evento aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u6bcf\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d67865a274f876a3db22d9e4fbf7dd7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(p_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<p>\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosp\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"0.30 0.15 0.55 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce la probabilidad de ocurrencia de cada evento aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u603b\u5c1d\u8bd5\u6b21\u6570\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f885e06969ad5024ff75f150976b0d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p>= <input name=\"n\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width: 60px\" placeholder=\"8\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de ensayos realizados aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\u6982\u7387\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-distribucion-multinomial\"><\/span>\u591a\u9879\u5206\u5e03\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u591a\u9879\u5f0f\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u5728\u591a\u9879\u5206\u5e03\u4e2d\uff0c\u8fd0\u884c<em>n \u6b21<\/em>\u8bd5\u9a8c\u65f6\u4e8b\u4ef6<em>i<\/em>\u53d1\u751f\u7684\u6b21\u6570\u7684\u671f\u671b\u503c\u7b49\u4e8e\u6267\u884c\u7684\u8bd5\u9a8c\u603b\u6570\u4e58\u4ee5\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002<\/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-e42371d5eeca9b3d8c2c0bed0ae46184_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[x_i]=n\\cdot p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5728\u591a\u9879\u5206\u5e03\u4e2d\uff0c\u4e8b\u4ef6<em>i<\/em>\u7684\u65b9\u5dee\u4f7f\u7528\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u8ba1\u7b97\uff1a<\/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-d66fb9e09a988e6b9e41024c9cc45d39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(x_i)=n\\cdot p_i\\cdot (1-p_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u540c\u6837\uff0c\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u7b49\u4e8e\u8bd5\u9a8c\u603b\u6570\u4e58\u4ee5\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u7684\u4e58\u79ef\u518d\u4e58\u4ee5-1\uff1a<\/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-59384e75fe14408722fcac8535c0cb43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(x_i,x_j)=-n\\cdot p_i\\cdot p_j\\qquad i\\neq j\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"264\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<ul>\n<li>\u591a\u9879\u5206\u5e03\u7684\u77e9\u751f\u6210\u51fd\u6570\u4e3a\uff1a<\/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-bac4a8ab71804d8c8b64a2823660768d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\sum_{i=1}^k p_ie^{t_i}\\right) ^n\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"94\" style=\"vertical-align: -23px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u591a\u9879\u5206\u5e03\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u591a\u9879\u5206\u5e03\u7684\u5b9a\u4e49\u3001\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u5206\u5e03\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-215","post","type-post","status-publish","format-standard","hentry","category-12"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u591a\u9879\u5206\u5e03 - \u6982\u7387\u4e0e\u7edf\u8ba1<\/title>\n<meta name=\"description\" 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