{"id":26774,"date":"2021-05-27T13:00:52","date_gmt":"2021-05-27T13:00:52","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26774"},"modified":"2024-05-22T01:46:06","modified_gmt":"2024-05-22T01:46:06","slug":"%e6%b3%8a%e6%9d%be%e8%bf%87%e7%a8%8b%ef%bc%9a%e4%ba%8c%e9%a1%b9%e8%bf%87%e7%a8%8b%e7%9a%84%e8%bf%91%e4%bc%bc","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e6%b3%8a%e6%9d%be%e8%bf%87%e7%a8%8b%ef%bc%9a%e4%ba%8c%e9%a1%b9%e8%bf%87%e7%a8%8b%e7%9a%84%e8%bf%91%e4%bc%bc\/","title":{"rendered":"\u6cca\u677e\u8fc7\u7a0b\uff1a\u4e8c\u9879\u8fc7\u7a0b\u7684\u8fd1\u4f3c"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6cca\u677e\u8fc7\u7a0b\uff1a\u4e8c\u9879\u8fc7\u7a0b\u7684\u8fd1\u4f3c<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u8fd9\u8282\u8bfe\u91cd\u70b9\u4ecb\u7ecd\u6cca\u677e\u8fc7\u7a0b\u4f5c\u4e3a\u4e8c\u9879\u8fc7\u7a0b\u7684\u8fd1\u4f3c\uff0c\u9996\u5148\u5b9a\u4e49\u6cca\u677e\u5206\u5e03\u7684\u7cfb\u6570\uff0c\u8be5\u5206\u5e03\u662f\u7531\u5927\u91cf\u5c1d\u8bd5\u548c\u975e\u5e38\u5c0f\u7684\u4e2a\u4f53\u6982\u7387\u7684\u4f2f\u52aa\u5229\u4e8b\u4ef6\u5f97\u51fa\u7684\u3002\u8bfe\u7a0b\u7684\u6838\u5fc3\u5185\u5bb9\u662f\u8ba8\u8bba\u6cca\u677e\u8fc7\u7a0b\u7684\u8fd1\u4f3c\uff0c\u5305\u62ec\u7a7a\u95f4\u548c\u65f6\u95f4\u8fc7\u7a0b\uff0c\u5206\u522b\u4ee5\u6db2\u4f53\u4e2d\u7684\u5fae\u5c0f\u9897\u7c92\u548c\u653e\u5c04\u6027\u7269\u8d28\u7684\u7c92\u5b50\u53d1\u5c04\u4e3a\u4f8b\u3002\u6700\u540e\uff0c\u901a\u8fc7\u5728\u4e0d\u540c\u60c5\u5883\u4e0b\u5e94\u7528\u6cca\u677e\u5206\u5e03\u7684\u5b9e\u9645\u4f8b\u5b50\u8fdb\u884c\u603b\u7ed3\uff0c\u5982\u8d85\u5e02\u4e2d\u7684\u5ba2\u6237\u670d\u52a1\u548c\u67d0\u5730\u7684\u4eba\u53e3\u5bc6\u5ea6\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>\u7406\u89e3<\/strong>\u6cca\u677e\u5206\u5e03\u7684\u5b9a\u4e49\u548c\u7cfb\u6570\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u6cca\u677e\u8fc7\u7a0b\u4f5c\u4e3a\u4e8c\u9879\u8fc7\u7a0b\u7684\u8fd1\u4f3c\u3002<\/li>\n<li><strong>\u7406\u89e3<\/strong>\u7a7a\u95f4\u548c\u65f6\u95f4\u6cca\u677e\u8fc7\u7a0b\u7684\u5f62\u5f0f\u7b49\u4ef7\u6027\u3002<\/li>\n<li><strong>\u4f7f\u7528<\/strong>\u6cca\u677e\u5206\u5e03\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u3002<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u5185\u5bb9\u76ee\u5f55<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u6cca\u677e\u5206\u5e03\u7684\u7cfb\u6570\u548c\u5b9a\u4e49<\/a><br \/>\n<a href=\"#2\">\u6cca\u677e\u8fc7\u7a0b\u7684\u8fd1\u4f3c<\/a><br \/>\n<a href=\"#3\">\u7a7a\u95f4\u6cca\u677e\u8fc7\u7a0b<\/a><br \/>\n<a href=\"#4\">\u65f6\u95f4\u6cca\u677e\u8fc7\u7a0b<\/a><br \/>\n<a href=\"#5\">\u65f6\u95f4\u548c\u7a7a\u95f4<\/a><br \/>\n<a href=\"#6\">\u6cca\u677e\u5206\u5e03\u7684\u5b9e\u9645\u5e94\u7528\u793a\u4f8b<\/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>\u6cca\u677e\u5206\u5e03\u7684\u7cfb\u6570\u548c\u5b9a\u4e49<\/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;\">\u73b0\u5728\u6211\u4eec\u8003\u8651\u4e00\u4e2a\u8fd1\u4f3c<\/span><\/strong><\/a>\u4e8e<a href=\"https:\/\/toposuranos.com\/el-ensayo-de-bernoulli-para-n-intentos-independientes\/\" rel=\"noopener\" target=\"_blank\">\u4e8c\u9879\u5206\u5e03<\/a>\uff0c\u5176\u4e2d\u8003\u8651\u5927\u91cf\u7684\u5c1d\u8bd5<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>\uff0c\u6bcf\u6b21\u5c1d\u8bd5\u7684\u6982\u7387\u975e\u5e38\u5c0f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span>\u3002\u5f53\u6211\u4eec\u8fd9\u6837\u505a\u65f6\uff0c\u6211\u4eec\u4ece\u5178\u578b\u7684\u4e8c\u9879\u8fc7\u7a0b\u8f6c\u53d8\u4e3a\u6cca\u677e\u8fc7\u7a0b\u3002\u4e3a\u4e86\u5f62\u8c61\u5316\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u5047\u8bbe\u4e00\u4e2a\u5f62\u5f0f\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{Bi(n;k;p_n)\\}_n,<\/span><\/span>\u7684\u5e8f\u5217\uff0c\u5176\u4e2d<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span>\u4e14<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p_n<\/span><\/span>\u6ee1\u8db3\u5173\u7cfb<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">np_n=\\lambda \\gt 0<\/span><\/span>\u3002\u7531\u6b64\u6211\u4eec\u5c06\u770b\u5230<\/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;\">\u8fd9\u5b9e\u9645\u4e0a\u5e76\u4e0d\u96be\u8bc1\u660e\uff0c\u5982\u679c\u6211\u4eec\u5c06\u4f2f\u52aa\u5229\u4e8b\u4ef6\u7684\u6982\u7387<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(n;k;p_n)<\/span><\/span>\u4e58\u4ee5\u5e76\u9664\u4ee5<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n^k<\/span><\/span>\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u63a8\u7406\uff1a<\/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;\">\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u8ba1\u7b97\u5f53<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n\\to\\infty<\/span><\/span>\u65f6\u7684\u6781\u9650\uff0c\u5c06\u4f1a\u5f97\u5230\uff1a<\/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;\">\u7531\u6b64\uff0c\u6cca\u677e\u7cfb\u6570<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Po(k;\\lambda)<\/span><\/span>\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u5b9a\u4e49\uff1a<\/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;\">\u5e76\u4e14\u8bf4\u4e00\u4e2a\u968f\u673a\u53d8\u91cf<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span>\u5177\u6709\u6cca\u677e\u5206\u5e03\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X\\sim Po(k,\\lambda),<\/span><\/span>\u5982\u679c\u6ee1\u8db3\uff1a<\/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>\u6cca\u677e\u8fc7\u7a0b\u7684\u8fd1\u4f3c<\/h2>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h3>\u7a7a\u95f4\u6cca\u677e\u8fc7\u7a0b<\/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;\">\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u4f53\u79ef\u4e3a<\/span><\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span>\u7684\u5bb9\u5668\uff0c\u5176\u4e2d\u6709\u5747\u5300\u6df7\u5408\u7684<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>\u4e2a\u5fae\u5c0f\u9897\u7c92\u3002\u8fd9\u91cc\u6211\u4eec\u5047\u8bbe\u6db2\u4f53\u88ab\u5145\u5206\u6405\u62cc\uff0c\u9897\u7c92\u4e4b\u95f4\u6ca1\u6709\u76f8\u4e92\u4f5c\u7528\uff0c\u4e0d\u76f8\u4e92\u5438\u5f15\u4e5f\u4e0d\u6392\u65a5\u3002\u8fd9\u4e9b\u5047\u8bbe\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u58f0\u660e\u5f62\u5f0f\u5316\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u7a7a\u95f4\u5747\u5300\u6027\u5047\u8bbe\uff1a<\/strong>\u5728\u6db2\u4f53\u7684\u67d0\u4e00\u533a\u57df<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span>\u4e2d\u627e\u5230\u4e00\u4e2a\u9897\u7c92\u7684\u6982\u7387\u4ec5\u53d6\u51b3\u4e8e\u8be5\u533a\u57df\u7684\u4f53\u79ef\u3002<\/li>\n<li><strong>\u65e0\u76f8\u4e92\u4f5c\u7528\uff1a<\/strong>\u00ab\u7b2cj\u4e2a\u9897\u7c92\u5728\u533a\u57dfD\u5185\u00bb\u7684\u4e8b\u4ef6\uff0c\u5bf9\u4e8ej=1,2,&#8230;,n\uff0c\u90fd\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002<\/li>\n<li><strong>\u65e0\u91cd\u53e0\uff1a<\/strong>\u4e24\u4e2a\u9897\u7c92\u4e0d\u80fd\u5360\u636e\u7a7a\u95f4\u7684\u540c\u4e00\u4f4d\u7f6e\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u7ed9\u5b9a\u4e00\u4e2a\u4f53\u79ef\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>\u7684\u533a\u57df<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span>\uff0c\u5728<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D<\/span><\/span>\u4e2d\u6709<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span>\u4e2a\u9897\u7c92\u7684\u4e8b\u4ef6\u7684\u6982\u7387\u4ec5\u53d6\u51b3\u4e8e<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>\uff1b\u6211\u4eec\u79f0\u6b64\u4e8b\u4ef6\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span>\u3002\u8bbe<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(v)<\/span><\/span>\u4e3a\u9897\u7c92\u5728\u4f53\u79ef\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v<\/span><\/span>\u7684\u533a\u57df\u5185\u7684\u6982\u7387\u3002\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span>\u662f\u4e24\u4e2a\u4e0d\u76f8\u4ea4\u7684\u533a\u57df\uff0c\u4f53\u79ef\u5206\u522b\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_1<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_2<\/span><\/span>\uff0c\u90a3\u4e48\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D=D_1\\cup D_2,<\/span><\/span>\u5176\u4f53\u79ef\u4e3a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v,<\/span><\/span>\u5219<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v=v_1+v_2.<\/span><\/span>\u7531\u4e8e<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1<\/span><\/span>\u548c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_2<\/span><\/span>\u662f\u4e0d\u76f8\u4ea4\u7684(<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">D_1\\cap D_2 = \\emptyset <\/span><\/span>)\uff0c\u56e0\u6b64\u6709<\/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;\">\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V<\/span><\/span>\u662f\u6574\u4e2a\u6db2\u4f53\u7684\u4f53\u79ef\uff0c\u5219\u6709<\/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;\">\u56e0\u6b64\uff1a<\/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;\">\u7531\u6b64\u6211\u4eec\u5f97\u51fa\u4e8b\u4ef6<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(v)<\/span><\/span>\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u8d1d\u52aa\u5229\u7c7b\u578b\u7684\u4e8b\u4ef6\uff0c\u5176\u4e2d<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p=v\/V<\/span><\/span>\uff0c\u8868\u793a\u4e3a\uff1a<\/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;\">\u7136\u800c\uff0c\u5927\u591a\u6570\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6d89\u53ca\u5927\u91cf\u7684\u9897\u7c92<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>\uff0c\u8003\u8651\u7684\u533a\u57df\u76f8\u5bf9\u4e8e\u7cfb\u7edf\u7684\u5927\u5c0f\u6765\u8bf4\u5f80\u5f80\u662f\u5f88\u5c0f\u7684\uff0c\u56e0\u6b64\u6ee1\u8db3\u5e94\u7528\u6cca\u677e\u8fd1\u4f3c\u7684\u6761\u4ef6\uff0c\u5f97\u5230\uff1a<\/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>\u65f6\u95f4\u6cca\u677e\u8fc7\u7a0b<\/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;\">\u5047\u8bbe\u6211\u4eec\u6b63\u5728\u8bb0\u5f55<\/span><\/strong><\/a>\u653e\u5c04\u6027\u7269\u8d28\u4ece\u65f6\u523bt=0\u5f00\u59cb\u53d1\u5c04\u7684\u7c92\u5b50\u6570\u91cf\uff0c\u5e76\u636e\u6b64\u8ba1\u7b97\u5728\u533a\u95f4[0,t[\u5185\u6b63\u597d\u53d1\u5c04k\u4e2a\u7c92\u5b50\u7684\u6982\u7387\uff0c\u57fa\u4e8e\u4ee5\u4e0b\u5047\u8bbe\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u4e0d\u53d8\u6027\uff1a<\/strong>\u5b9e\u9a8c\u6761\u4ef6\u5728\u65f6\u95f4\u4e0a\u4e0d\u53d8\u3002<\/li>\n<li><strong>\u65e0\u8bb0\u5fc6\u6027\uff1a<\/strong>[0,t[\u5185\u53d1\u751f\u7684\u4e8b\u60c5\u4e0d\u5f71\u54cd[t,t'[\u5185\u53d1\u751f\u7684\u4e8b\u60c5\u3002<\/li>\n<li><strong>\u5b64\u7acb\u4e8b\u4ef6\uff1a<\/strong>\u7c92\u5b50\u4e00\u6b21\u53ea\u53d1\u5c04\u4e00\u4e2a\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u6211\u4eec\u6bd4\u8f83\u65f6\u95f4\u8fc7\u7a0b\u7684\u5047\u8bbe\u4e0e\u7a7a\u95f4\u8fc7\u7a0b\u7684\u5047\u8bbe\uff0c\u4f1a\u53d1\u73b0\u5b83\u4eec\u5f62\u5f0f\u4e0a\u662f\u7b49\u4ef7\u7684\u3002\u6b63\u5982\u627e\u5230\u67d0\u4e00\u533a\u57df\u5185\u4e00\u4e2a\u9897\u7c92\u7684\u6982\u7387\u4e0d\u4f9d\u8d56\u4e8e\u9009\u62e9\u533a\u57df\u7684\u4f4d\u7f6e\uff0c\u800c\u4ec5\u4f9d\u8d56\u4e8e\u533a\u57df\u7684\u5927\u5c0f\uff0c\u89c2\u5bdf\u5230\u7c92\u5b50\u7684\u53d1\u5c04\u6982\u7387\u4e0d\u4f9d\u8d56\u4e8e\u6d4b\u91cf\u7684\u65f6\u523b\uff0c\u800c\u4ec5\u4f9d\u8d56\u4e8e\u89c2\u5bdf\u7684\u65f6\u95f4\u95f4\u9694\u3002\u65e0\u8bb0\u5fc6\u6027\u7c7b\u4f3c\u4e8e\u7a7a\u95f4\u8fc7\u7a0b\u7684\u65e0\u76f8\u4e92\u4f5c\u7528\uff1a\u5728\u53e6\u4e00\u4e2a\u65f6\u523b\u53d1\u751f\u7684\u4e8b\u60c5\u4e0d\u4f1a\u5f71\u54cd\u5176\u4ed6\u65f6\u523b\u7684\u53d1\u751f\u60c5\u51b5\u3002\u6700\u540e\uff0c\u5b64\u7acb\u4e8b\u4ef6\u610f\u5473\u7740\u5728\u67d0\u4e00\u65f6\u523b\u53ea\u4f1a\u53d1\u5c04\u4e00\u4e2a\u7c92\u5b50\uff0c\u8fd9\u7c7b\u4f3c\u4e8e\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u4f4d\u7f6e\u53ea\u80fd\u88ab\u4e00\u4e2a\u7269\u4f53\u5360\u636e\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5b9a\u4e49\u4e8b\u4ef6\u00bb\u5728\u65f6\u95f4\u533a\u95f4<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">t<\/span><\/span>\u5185\u53d1\u5c04\u4e86k\u4e2a\u7c92\u5b50\u00bb\uff0c\u5176\u53d1\u751f\u7684\u6982\u7387\u5c06\u662f<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g_k(t)<\/span><\/span>\u5f62\u5f0f\u7684\u4e8b\u4ef6\uff0c\u5373\uff1a<\/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>\u65f6\u95f4\u548c\u7a7a\u95f4<\/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;\">\u4e24\u4e2a\u8fc7\u7a0b\uff0c\u7a7a\u95f4\u548c\u65f6\u95f4\uff0c\u5728\u5f62\u5f0f\u4e0a\u662f\u7b49\u4ef7\u7684\u3002<\/span><\/strong><\/a> \u4ec5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u6709\u4e0d\u540c\u7684\u89e3\u91ca\u3002\u5feb\u901f\u6f84\u6e05\u8fd9\u4e00\u533a\u522b\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u89c2\u5bdf\u5728\u4e24\u79cd\u60c5\u51b5\u4e0b\u90fd\u51fa\u73b0\u7684\u5e38\u6570\u00bbc\u00bb\u7684\u4f5c\u7528\u3002\u4e3a\u4e86\u4f7f\u6307\u6570\u51fd\u6570\u5b9a\u4e49\u826f\u597d\uff0c\u5fc5\u987b\u4f7f\u5176\u53c2\u6570\u65e0\u91cf\u7eb2\uff1b\u7136\u800c\uff0c\u8fd9\u5305\u542b\u65f6\u95f4\u6216\u7a7a\u95f4\u5355\u4f4d\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u6211\u4eec\u5904\u7406\u7684\u662f\u65f6\u95f4\u8fc7\u7a0b\u8fd8\u662f\u7a7a\u95f4\u8fc7\u7a0b\u3002\u8fd9\u4e2a\u95ee\u9898\u6b63\u662f\u7531\u5e38\u6570c\u6765\u89e3\u51b3\u7684\u3002\u6211\u4eec\u6709\uff1a<\/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} {\u53d6\\,\\lambda = \\rho v } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\rho v)^k}{k!}e^{-\\rho v} &amp; {\u7a7a\u95f4\u8fc7\u7a0b} \\\\ {\u53d6\\,\\lambda = \\nu t } &amp; \\longmapsto &amp;\\displaystyle \\frac{(\\nu t)^k}{k!}e^{-\\nu t} &amp; {\u65f6\u95f4\u8fc7\u7a0b} \\end{matrix} \\right.<\/span><\/span><\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\rho<\/span><\/span>\uff0c\u5219\u4e3a\u7a7a\u95f4\u5bc6\u5ea6\uff08\u5355\u4f4d\u7a7a\u95f4\u5185\u7684\u7269\u4f53\u6570\u91cf\uff09\uff0c\u56e0\u6b64\u5b9a\u4e49\u4e00\u4e2a\u7a7a\u95f4\u6cca\u677e\u8fc7\u7a0b\u3002<\/li>\n<li>\u5982\u679c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c=\\nu<\/span><\/span>\uff0c\u5219\u4e3a\u65f6\u95f4\u5bc6\u5ea6\uff08\u6216\u9891\u7387\uff0c\u6bcf\u5355\u4f4d\u65f6\u95f4\u7684\u53d1\u751f\u6b21\u6570\uff09\uff0c\u56e0\u6b64\u5b9a\u4e49\u4e00\u4e2a\u65f6\u95f4\u6cca\u677e\u8fc7\u7a0b\u3002<\/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>\u6cca\u677e\u5206\u5e03\u7684\u5b9e\u9645\u5e94\u7528\u793a\u4f8b<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u8d85\u5e02\u6536\u94f6\u53f0\u5e73\u5747\u6bcf9\u5206\u949f\u63a5\u5f852\u4f4d\u987e\u5ba2\u3002\u8bf7\u5236\u4f5c\u4e00\u4e2a\u8868\u683c\uff0c\u663e\u793a\u57285\u5206\u949f\u5185\u63a5\u5f851\u30012\u30013\u53ca\u81f35\u4f4d\u987e\u5ba2\u7684\u6982\u7387\u3002<\/li>\n<li>\u4e00\u5bb6\u517d\u533b\u8bca\u6240\u6bcf\u5929\u6700\u591a\u53ef\u63a5\u5f8512\u4f4d\u987e\u5ba2\u3002\u5982\u679c\u4ed6\u4eec\u5e73\u5747\u6bcf\u5929\u63a5\u5f859\u4f4d\u987e\u5ba2\uff0c\u95ee\u5728\u4efb\u4f55\u4e00\u5929\u8d85\u51fa\u8bca\u6240\u63a5\u5f85\u80fd\u529b\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<li>\u67d0\u5730\u6bcf1000\u5e73\u65b9\u7c73\u670910\u4eba\u3002\u95ee\u572860\u5e73\u65b9\u7c73\u7684\u533a\u57df\u5185\u627e\u5230\u5c11\u4e8e15\u4eba\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<li>\u4e00\u53ea\u9e21\u60f3\u8981\u8fc7\u9a6c\u8def\u3002\u76f4\u7ebf\u884c\u8d70\u9700\u898158\u79d2\u3002\u5982\u679c\u9a6c\u8def\u4e0a\u6bcf\u5206\u949f\u67093\u8f86\u8f66\u7ecf\u8fc7\uff0c\u5982\u679c\u9e21\u5728\u8bd5\u56fe\u8fc7\u9a6c\u8def\u65f6\u6709\u8f66\u7ecf\u8fc7\uff0c\u5b83\u80af\u5b9a\u4f1a\u88ab\u649e\u6b7b\u3002\u95ee\u8fd9\u53ea\u9e21\u5b89\u5168\u8fc7\u9a6c\u8def\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6cca\u677e\u8fc7\u7a0b\uff1a\u4e8c\u9879\u8fc7\u7a0b\u7684\u8fd1\u4f3c 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