{"id":26754,"date":"2021-05-12T13:00:54","date_gmt":"2021-05-12T13:00:54","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26754"},"modified":"2024-05-22T00:47:24","modified_gmt":"2024-05-22T00:47:24","slug":"%e4%bc%af%e5%8a%aa%e5%88%a9%e8%af%95%e9%aa%8c%e4%b8%8e%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e4%bc%af%e5%8a%aa%e5%88%a9%e8%af%95%e9%aa%8c%e4%b8%8e%e4%ba%8c%e9%a1%b9%e5%88%86%e5%b8%83\/","title":{"rendered":"\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5206\u5e03"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5206\u5e03<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u6982\u5ff5\u53ca\u5176\u5728\u6982\u7387\u8bba\u4e2d\u7684\u5e94\u7528\u3002\u6211\u4eec\u9996\u5148\u8be6\u7ec6\u5b9a\u4e49\u4f2f\u52aa\u5229\u8bd5\u9a8c\uff0c\u7136\u540e\u8ba8\u8bba\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u6982\u5ff5\u3002\u6f84\u6e05\u8fd9\u4e9b\u6982\u5ff5\u540e\uff0c\u6211\u4eec\u5e94\u7528\u4e8c\u9879\u5b9a\u7406\u6765\u7406\u89e3\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u91cd\u590d\u5982\u4f55\u4ea7\u751f\u4e8c\u9879\u5206\u5e03\u7684\u7ed3\u679c\u3002\u6700\u540e\uff0c\u63d0\u51fa\u4e00\u4e9b\u5b9e\u9645\u7ec3\u4e60\u6765\u5e94\u7528\u548c\u5de9\u56fa\u8fd9\u4e9b\u6982\u5ff5\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5b8c\u6210\u672c\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u8bc6\u522b<\/strong>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u4e3b\u8981\u7279\u5f81\uff0c\u5305\u62ec\u5c1d\u8bd5\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u3002<\/li>\n<li><strong>\u6b63\u786e\u5e94\u7528<\/strong>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u884d\u751f\u7684\u4e8c\u9879\u4e8b\u4ef6\u7684\u7b26\u53f7\u3002<\/li>\n<li><strong>\u533a\u5206<\/strong>\u4e0d\u540c\u5f62\u5f0f\u7684\u72ec\u7acb\u6027\uff082-\u72ec\u7acb\u6027\u30013-\u72ec\u7acb\u6027\u3001n-\u72ec\u7acb\u6027\uff09\u5e76\u7406\u89e3\u5176\u5728\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7684\u5173\u7cfb\u548c\u5e94\u7528\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5b9a\u7406\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u4ee5\u53ca\u5982\u4f55\u5229\u7528\u8fd9\u79cd\u5173\u7cfb\u8ba1\u7b97\u4e00\u7cfb\u5217\u6210\u529f\u548c\u5931\u8d25\u7684\u6982\u7387\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u4e8c\u9879\u5206\u5e03\uff08\u6216\u4f2f\u52aa\u5229\u5206\u5e03\uff09\u6765\u8ba1\u7b97\u4e00\u7cfb\u5217\u5c1d\u8bd5\u4e2d\u67d0\u4e2a\u6210\u529f\u6b21\u6570\u7684\u6982\u7387\u3002<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u5185\u5bb9\u76ee\u5f55\uff1a<\/u><\/strong><br \/>\n<a href=\"#1\">\u4f2f\u52aa\u5229\u8bd5\u9a8c<\/a><br \/>\n<a href=\"#2\">\u4e0d\u540c\u5f62\u5f0f\u7684\u72ec\u7acb\u6027<\/a><br \/>\n<a href=\"#3\">\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5b9a\u7406<\/a><br \/>\n<a href=\"#4\">\u4e8c\u9879\u5206\u5e03\uff08\u6216\u4f2f\u52aa\u5229\u5206\u5e03\uff09\u4e0e\u6982\u7387\u5206\u5e03<\/a><br \/>\n<a href=\"#5\">\u7ec3\u4e60\uff1a<\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/uyljDy0bcvU\" 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>\u4f2f\u52aa\u5229\u8bd5\u9a8c<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=103s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4f2f\u52aa\u5229\u8bd5\u9a8c\u662f\u4e00\u4e2a\u968f\u673a\u5b9e\u9a8c<\/span><\/strong><\/a>\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u6210\u529f\u6982\u7387 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p.<\/span><\/span> \u5982\u679c\u4e00\u4e2a\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4ee5\u76f8\u540c\u548c\u72ec\u7acb\u7684\u65b9\u5f0f\u91cd\u590d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\uff0c\u5219\u4f1a\u5f97\u5230 <strong>\u4f2f\u52aa\u5229\u4e8b\u4ef6\uff1a<\/strong> \u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u5c1d\u8bd5\u4e2d\u67d0\u4e2a\u6570\u91cf <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u7684\u6210\u529f\u3002\u8fd9\u4e9b\u4e5f\u79f0\u4e3a <strong>\u4e8c\u9879\u4e8b\u4ef6<\/strong>\uff0c\u6211\u4eec\u901a\u8fc7\u4ee5\u4e0b\u7b26\u53f7\u8868\u793a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle Bi(n;k;p)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u53e6\u4e00\u4e2a\u91cd\u8981\u7279\u5f81\u662f\u6240\u6709\u5c1d\u8bd5\u90fd\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u4f8b\u5b50\uff1a<\/span> \u591a\u6b21\u63b7\u4e00\u4e2a6\u9762\u7684\u9ab0\u5b50\u3002\u8fd9\u4e2a\u5b9e\u9a8c\u4e2d\u7684\u4f2f\u52aa\u5229\u7c7b\u578b\u4e8b\u4ef6\u7684\u4f8b\u5b50\u5305\u62ec\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u57285\u6b21\u5c1d\u8bd5\u4e2d\u83b7\u5f973\u4e2aA\u9762\uff1a<\/strong> \u8868\u793a\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(5;3;1\/6)<\/span><\/span><\/li>\n<li><strong>\u572812\u6b21\u5c1d\u8bd5\u4e2d\u83b7\u5f977\u4e2a\u5076\u6570\uff1a<\/strong> \u8868\u793a\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(12;7;1\/3)<\/span><\/span><\/li>\n<\/ul>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h3>\u4e0d\u540c\u5f62\u5f0f\u7684\u72ec\u7acb\u6027<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=283s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7684\u5c1d\u8bd5\u72ec\u7acb\u6027<\/span><\/strong><\/a> \u5e76\u4e0d\u5b8c\u5168\u662f\u6211\u4eec\u5df2\u7ecf\u590d\u4e60\u8fc7\u7684\u72ec\u7acb\u6027\u6982\u5ff5\uff0c\u8fd9\u662f\u4e00\u4e2a\u66f4\u52a0\u4e25\u683c\u7684\u7248\u672c\u3002\u4e3a\u4e86\u89e3\u91ca\u8fd9\u79cd\u5dee\u5f02\uff0c\u8ba9\u6211\u4eec\u6765\u68c0\u67e5\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u7c7b\u578b\u3002<\/p>\n<h4>2-\u72ec\u7acb\u6027<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/toposuranos.com\/probabilidad-condicional-e-independencia-entre-eventos\/\" rel=\"noopener\" target=\"_blank\">\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u7684\u72ec\u7acb\u6027<\/a> \u662f\u5728\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u3002\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c2-\u72ec\u7acb\u6027\u201d\u3002\u5728\u8fd9\u4e9b\u672f\u8bed\u4e2d\uff0c\u6211\u4eec\u8bf4\u4e8b\u4ef6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u662f2-\u72ec\u7acb\u7684\uff0c\u5982\u679c<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B) = P(A)P(B)<\/span><\/span><\/p>\n<h4>3-\u72ec\u7acb\u6027<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u540c\u6837\u5730\uff0c\u4e09\u4e8b\u4ef6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> \u4e4b\u95f4\u76843-\u72ec\u7acb\u6027\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5b9a\u4e49<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B\\cap C) = P(A)P(B)P(C)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u91cd\u8981\u7684\u662f\u8981\u5f3a\u8c03\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> \u4e4b\u95f4\u76842-\u72ec\u7acb\u6027\u5e76\u4e0d\u4e00\u5b9a\u610f\u5473\u77403-\u72ec\u7acb\u6027\uff0c\u4f46\u5728\u76f8\u53cd\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u79cd\u63a8\u7406\u662f\u6210\u7acb\u7684\u3002<\/p>\n<h4>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7684n-\u72ec\u7acb\u6027<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u7c7b\u4f3c\u4e8e\u524d\u9762\u7684\u5b9a\u4e49\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_1, \\cdots, A_n<\/span><\/span> \u4e8b\u4ef6\u96c6\u5408\u7684n-\u72ec\u7acb\u6027\u901a\u8fc7\u4ee5\u4e0b\u5173\u7cfb\u5b9a\u4e49<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle P\\left(\\bigcap_{i=1}^n A_i\\right) = \\prod_{i=1}^n P(A_i) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-\u72ec\u7acb\u6027\u4e0d\u4e00\u5b9a\u610f\u5473\u7740<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u72ec\u7acb\u6027<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u72ec\u7acb\u6027<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-\u72ec\u7acb\u6027<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7684 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u91cd\u590d\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u72ec\u7acb\u7684\u3002<\/p>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h2>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5b9a\u7406<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=478s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8003\u8651\u4e00\u4e2a\u6210\u529f\u4e0e\u5931\u8d25\u7684\u5b9e\u9a8c<\/span><\/strong><\/a> \u6210\u529f\u6982\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span>\uff1b\u5728\u6bcf\u6b21\u5c1d\u8bd5\u4e2d\uff0c\u5931\u8d25\u7684\u6982\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1-p<\/span><\/span>\u3002\u663e\u7136\uff0c\u6bcf\u6b21\u5c1d\u8bd5\u6210\u529f\u6216\u5931\u8d25\u7684\u6982\u7387\u4e3a1\uff1b\u7531\u4e8e\u6240\u6709\u5c1d\u8bd5\u90fd\u662f\u72ec\u7acb\u7684\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u5c1d\u8bd5\u4e2d\u6210\u529f\u6216\u5931\u8d25\u7684\u6982\u7387\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^n.<\/span><\/span> \u4ece\u800c\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle 1 = 1^n = [p + (1-p)]^n = \\sum_{k=0}^n {{n}\\choose{k}} p^k(1-p)^{n-k} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5728\u6700\u540e\u4e00\u4e2a\u7b49\u5f0f\u4e2d\uff0c\u5e94\u7528\u4e86 <a href=\"https:\/\/toposuranos.com\/ejercicios-de-induccion-matematica-teorema-del-binomio-de-newton\/\" rel=\"noopener\" target=\"_blank\">\u725b\u987f\u4e8c\u9879\u5b9a\u7406\uff0c<\/a> \u5e76\u4e14\u548c\u4e2d\u7684\u5404\u9879\u53ef\u4ee5\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{k}}<\/span><\/span>\uff1a\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u5c1d\u8bd5\u4e2d\uff0c\u53d1\u751f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u6b21\u6210\u529f\u7684\u65b9\u5f0f\u6570<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p^k<\/span><\/span>\uff1a\u53d1\u751f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u6b21\u72ec\u7acb\u6210\u529f\u7684\u6982\u7387<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1-p)^{n-k}<\/span><\/span>\uff1a\u53d1\u751f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> \u6b21\u72ec\u7acb\u5931\u8d25\u7684\u6982\u7387<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u5c06\u8fd9\u4e9b\u5143\u7d20\u6309\u7167\u548c\u4e2d\u7684\u65b9\u5f0f\u7ec4\u5408\u8d77\u6765\uff0c\u6211\u4eec\u5f97\u5230\uff1a\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u5c1d\u8bd5\u4e2d\u83b7\u5f97 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u6b21\u6210\u529f\u7684\u6982\u7387\uff1b\u6216\u7b49\u6548\u5730\uff0c\u5728 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u5c1d\u8bd5\u4e2d\u83b7\u5f97 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> \u6b21\u5931\u8d25\u7684\u6982\u7387\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u5c06\u548c\u4e2d\u7684\u6bcf\u4e00\u9879\u5206\u79bb\u51fa\u6765\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u6982\u7387\uff1a<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{0}} p^0(1-p)^{n-0} = (1-p)^n<\/span><\/span><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d0\u6b21\u6210\u529f<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{1}} p^1(1-p)^{n-1} = n p(1-p)^{n-1}<\/span><\/span><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d1\u6b21\u6210\u529f<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{2}} p^2(1-p)^{n-2}<\/span><\/span><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d2\u6b21\u6210\u529f<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\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><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u6b21\u6210\u529f<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n-1}} p^{n-1}(1-p)^{n-(n-1)} = n p^{n-1}(1-p)<\/span><\/span><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-1<\/span><\/span> \u6b21\u6210\u529f<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n}} p^{n}(1-p)^{0} = p^{n}<\/span><\/span><\/td>\n<td>n \u6b21\u5c1d\u8bd5\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u6b21\u6210\u529f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u6211\u4eec\u5df2\u7ecf\u770b\u5230\uff0c\u8fd9\u4e9b\u6982\u7387\u7684\u548c\u4e3a \u00ab1\u00bb\u3002\u8fd9\u8868\u660e\u6240\u6709\u53ef\u80fd\u6027\u90fd\u5df2\u6db5\u76d6\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u4ece\u4e2d\u53ef\u4ee5\u5b9a\u4e49 <strong>\u4f2f\u52aa\u5229\u4e8b\u4ef6\u7684\u6982\u7387\uff1a<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\Large \\color{blue}{P(Bi(n;k;p)) = {{n}\\choose{k}}p^k(1-p)^{n-k}}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6211\u4eec\u4e5f\u53ef\u4ee5\u8bf4 <strong>\u6210\u529f\u6b21\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u670d\u4ece\u4e8c\u9879\u5206\u5e03\uff1a<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{\\Large \\displaystyle X\\sim Bi(n;p) \\longmapsto P(X=x) = {{n}\\choose{x}}p^x(1-p)^{n-x}}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u4e8c\u9879\u5206\u5e03\uff08\u6216\u4f2f\u52aa\u5229\u5206\u5e03\uff09\u4e0e\u6982\u7387\u5206\u5e03<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=779s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u901a\u8fc7\u4e8c\u9879\u5206\u5e03<\/span><\/strong><\/a> \u6211\u4eec\u5f00\u59cb\u4e86\u89e3\u6982\u7387\u5206\u5e03\u548c\u968f\u673a\u53d8\u91cf\u7684\u6982\u5ff5\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u968f\u673a\u53d8\u91cf\uff08\u79bb\u6563\u578b\uff09\u4e0e\u6210\u529f\u6b21\u6570\u76f8\u5173\uff0c\u5176\u6982\u7387\u5206\u5e03\u7531\u4e8c\u9879\u5b9a\u7406\u7684\u5404\u9879\u7ed9\u51fa<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\Large \\displaystyle P(X=x) = {{n}\\choose{x}}p^x(1-p)^{n-x}}<\/span><\/span><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/36s4rcfQn7M\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h2>\u7ec3\u4e60\uff1a<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u5747\u5300\u76846\u9762\u9ab0\u5b50\u63b75\u6b21\u3002\u8ba1\u7b97\u5f97\u52303\u6b21\u5076\u6570\u7684\u6982\u7387\u3002<\/li>\n<li>\u629b\u63b7\u786c\u5e0110\u6b21\u3002\u8ba1\u7b97\u4ece0\u523010\u6b21\u6b63\u9762\u7684\u6982\u7387\uff0c\u5e76\u7ed8\u5236\u663e\u793a\u6bcf\u4e2a\u7ed3\u679c\u6982\u7387\u7684\u56fe\u8868\u3002\u5982\u679c\u589e\u52a0\u63b7\u786c\u5e01\u7684\u6b21\u6570\uff0c\u5e76\u68c0\u67e5\u4ece0\u5230\u8be5\u6b21\u6570\u7684\u6b63\u9762\u6570\u91cf\u7684\u6982\u7387\uff0c\u56fe\u8868\u4f1a\u662f\u4ec0\u4e48\u6837\u5b50\uff1f\u8fd9\u91cc\u53ef\u4ee5\u4f7f\u7528Excel\u8868\u683c\u3002<\/li>\n<li>\u4e00\u4e2a\u6709 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s<\/span><\/span> \u4e2a\u5c0f\u7403\u7684\u62bd\u5956\u7bb1\uff0c\u5176\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u4e2a\u662f\u91d1\u8272\u7684\uff0c\u5176\u4f59\u662f\u767d\u8272\u7684\u3002\u5c06\u6240\u6709\u5c0f\u7403\u6df7\u5408\u540e\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\uff0c\u5f53\u62bd\u5230\u91d1\u8272\u7684\u5c0f\u7403\u65f6\u83b7\u80dc\u3002\u5982\u679c\u8fd9\u4e2a\u5b9e\u9a8c\u4ee5\u76f8\u540c\u65b9\u5f0f\u91cd\u590d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">20<\/span><\/span> \u6b21\uff0c\u4f30\u8ba1\u5728\u6bcf\u4e2a\u53ef\u80fd\u7684 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\leq r\\leq s<\/span><\/span> \u503c\u60c5\u51b5\u4e0b\u6700\u53ef\u80fd\u7684\u83b7\u80dc\u6b21\u6570\u3002\u8fd9\u91cc\u4e5f\u53ef\u4ee5\u4f7f\u7528Excel\u8868\u683c\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e0e\u4e8c\u9879\u5206\u5e03 \u6458\u8981\u5728\u8fd9\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u7814\u7a76\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u6982\u5ff5\u53ca\u5176\u5728\u6982\u7387\u8bba\u4e2d\u7684\u5e94\u7528\u3002\u6211\u4eec\u9996\u5148\u8be6\u7ec6\u5b9a\u4e49\u4f2f\u52aa\u5229\u8bd5\u9a8c\uff0c\u7136\u540e\u8ba8\u8bba\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u6982\u5ff5\u3002\u6f84\u6e05\u8fd9\u4e9b\u6982\u5ff5\u540e\uff0c\u6211\u4eec\u5e94\u7528\u4e8c\u9879\u5b9a\u7406\u6765\u7406\u89e3\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u91cd\u590d\u5982\u4f55\u4ea7\u751f\u4e8c\u9879\u5206\u5e03\u7684\u7ed3\u679c\u3002\u6700\u540e\uff0c\u63d0\u51fa\u4e00\u4e9b\u5b9e\u9645\u7ec3\u4e60\u6765\u5e94\u7528\u548c\u5de9\u56fa\u8fd9\u4e9b\u6982\u5ff5\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5b8c\u6210\u672c\u8282\u8bfe\u540e\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a \u8bc6\u522b\u4f2f\u52aa\u5229\u8bd5\u9a8c\u7684\u4e3b\u8981\u7279\u5f81\uff0c\u5305\u62ec\u5c1d\u8bd5\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u3002 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