{"id":1324,"date":"2023-07-26T21:19:13","date_gmt":"2023-07-26T21:19:13","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%ad%a3%e5%bc%a6%e6%b3%a2%e7%bb%9f%e8%ae%a1\/"},"modified":"2023-07-26T21:19:13","modified_gmt":"2023-07-26T21:19:13","slug":"%e6%ad%a3%e5%bc%a6%e6%b3%a2%e7%bb%9f%e8%ae%a1","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%ad%a3%e5%bc%a6%e6%b3%a2%e7%bb%9f%e8%ae%a1\/","title":{"rendered":"\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u6982\u7387\u8d28\u91cf\u51fd\u6570 (pmf)\uff1f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u6982\u7387\u8d28\u91cf\u51fd\u6570<\/strong>\uff08\u901a\u5e38\u7f29\u5199\u4e3a<strong>PMF<\/strong> \uff09\u544a\u8bc9\u6211\u4eec<a href=\"https:\/\/statorials.org\/cn\/\u968f\u673a\u53d8\u91cf-1\/\" target=\"_blank\" rel=\"noopener\">\u79bb\u6563\u968f\u673a\u53d8\u91cf<\/a>\u53d6\u7279\u5b9a\u503c\u7684\u6982\u7387\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u63b7\u4e00\u6b21\u9ab0\u5b50\u3002\u5982\u679c\u6211\u4eec\u8ba9x\u8868\u793a\u9ab0\u5b50\u843d\u5728\u7684\u6570\u5b57\uff0c\u90a3\u4e48<em>x<\/em>\u7b49\u4e8e\u4e0d\u540c\u503c\u7684\u6982\u7387\u53ef\u4ee5\u63cf\u8ff0\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(X=1)\uff1a1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X=2)\uff1a1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X=3)\uff1a1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X=4)\uff1a1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X=5)\uff1a1\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X=6)\uff1a1\/6<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u9ab0\u5b50\u843d\u5728 1 \u5230 6 \u4e4b\u95f4\u7684\u4efb\u4f55\u6570\u5b57\u4e0a\u7684\u673a\u4f1a\u5747\u7b49\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u6211\u4eec\u5982\u4f55\u5c06\u8fd9\u4e9b\u6982\u7387\u5199\u6210\u6982\u7387\u8d28\u91cf\u51fd\u6570\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12928 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pmf1-1.png\" alt=\"\u6982\u7387\u8d28\u91cf\u51fd\u6570\u793a\u4f8b\" width=\"227\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u56fe\u7684\u5de6\u4fa7\u663e\u793a\u4e86\u4e0e\u53f3\u4fa7\u7ed3\u679c\u76f8\u5173\u7684\u6982\u7387\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12929 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pmf2.png\" alt=\"\u7edf\u8ba1\u5b66\u4e2d\u7684\u6982\u7387\u8d28\u91cf\u51fd\u6570\" width=\"246\" height=\"232\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6982\u7387\u8d28\u91cf\u51fd\u6570\u7684\u4e00\u4e2a\u7279\u5f81\u662f\u6240\u6709\u6982\u7387\u4e4b\u548c\u5fc5\u987b\u4e3a 1\u3002\u60a8\u4f1a\u6ce8\u610f\u5230\u6b64 PMF \u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6982\u7387\u4e4b\u548c = 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6 = 1\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u5bf9\u6982\u7387\u8d28\u91cf\u51fd\u6570\u7684<strong>\u652f\u6301<\/strong>\u662f\u6307\u79bb\u6563\u968f\u673a\u53d8\u91cf\u53ef\u4ee5\u53d6\u7684\u503c\u7684\u96c6\u5408\u3002\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u652f\u6301\u5ea6\u4e3a {1, 2, 3, 4, 5, 6}\uff0c\u56e0\u4e3a\u9ab0\u5b50\u7684\u503c\u53ef\u4ee5\u91c7\u7528\u8fd9\u4e9b\u503c\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u3002<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u5728\u652f\u6491\u4e4b\u5916\uff0cPMF \u503c\u4e3a\u96f6\u3002\u4f8b\u5982\uff0c\u9ab0\u5b50\u843d\u5728\u201c0\u201d\u6216\u201c7\u201d\u6216\u201c8\u201d\u4e0a\u7684\u6982\u7387\u4e3a\u96f6\uff0c\u56e0\u4e3a\u8fd9\u4e9b\u6570\u5b57\u90fd\u4e0d\u5305\u542b\u5728\u62ec\u53f7\u4e2d\u3002<\/span><\/span><\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5b9e\u8df5\u4e2d\u7684\u6982\u7387\u8d28\u91cf\u51fd\u6570<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5b9e\u8df5\u4e2d\u6982\u7387\u8d28\u91cf\u51fd\u6570\u7684\u4e24\u4e2a\u6700\u5e38\u89c1\u7684\u4f8b\u5b50\u6d89\u53ca<a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\" target=\"_blank\" rel=\"noopener\">\u4e8c\u9879\u5f0f\u5206\u5e03<\/a>\u548c<a href=\"https:\/\/statorials.org\/cn\/\u9c7c\u7c7b\u5206\u5e03\/\" target=\"_blank\" rel=\"noopener\">\u6cca\u677e\u5206\u5e03<\/a>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u4e8c\u9879\u5206\u5e03<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u968f\u673a\u53d8\u91cf<em>X<\/em>\u670d\u4ece\u4e8c\u9879\u5f0f\u5206\u5e03\uff0c\u5219<em>X<\/em> = <em>k<\/em>\u6210\u529f\u7684\u6982\u7387\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u6c42\u51fa\uff1a<\/span><\/p>\n<p> <strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n\uff1a<\/strong>\u8bd5\u9a8c\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u6210\u529f\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p\uff1a<\/strong>\u7ed9\u5b9a\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><sub>n<\/sub> C <sub>k<\/sub> \uff1a<\/strong>\u5728<em>n<\/em>\u6b21\u8bd5\u9a8c\u4e2d\u83b7\u5f97<em>k\u6b21<\/em>\u6210\u529f\u7684\u65b9\u6cd5\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u629b\u786c\u5e01 3 \u6b21\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u786e\u5b9a\u8fd9 3 \u6b21\u629b\u63b7\u4e2d\u83b7\u5f97 0\u30011\u30012 \u548c 3 \u6b21\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = <sub>3<\/sub> C <sub>0<\/sub> * 0.5 <sup>0<\/sup> * (1-0.5) <sup>3-0<\/sup> = 1 * 1 * (0.5) <sup>3<\/sup> = <strong>0.125<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = <sub>3<\/sub> C <sub>1<\/sub> * 0.5 <sup>1<\/sup> * (1-0.5) <sup>3-1<\/sup> = 1 * 1 * (0.5) <sup>2<\/sup> = <strong>0.375<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = <sub>3<\/sub> C <sub>2<\/sub> * 0.5 <sup>2<\/sup> * (1-0.5) <sup>3-2<\/sup> = 1 * 1 * (0.5) <sup>1<\/sup> = <strong>0.375<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(X=3)<\/strong> = <sub>3<\/sub> C <sub>3<\/sub> * 0.5 <sup>3<\/sup> * (1-0.5) <sup>3-3<\/sup> = 1 * 1 * (0.5) <sup>0<\/sup> = <strong>0.125<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>\u9c7c\u7c7b\u5206\u5e03<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u968f\u673a\u53d8\u91cf<em>X<\/em>\u670d\u4ece\u6cca\u677e\u5206\u5e03\uff0c\u5219<em>X<\/em> = <em>k<\/em>\u6210\u529f\u7684\u6982\u7387\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\u6c42\u51fa\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = \u03bb <sup>k<\/sup> * e <sup>\u2013 \u03bb<\/sup> \/ k!<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03bb\uff1a<\/strong>\u7279\u5b9a\u65f6\u95f4\u95f4\u9694\u5185\u53d1\u751f\u7684\u5e73\u5747\u6210\u529f\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u6210\u529f\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><b>e\uff1a<\/b>\u7ea6\u7b49\u4e8e 2.71828 \u7684\u5e38\u6570<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u67d0\u5bb6\u533b\u9662\u5e73\u5747\u6bcf\u5c0f\u65f6\u5206\u5a29 2 \u540d\u5a74\u513f\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u786e\u5b9a\u7ecf\u53860\u30011\u30012\u30013\u6b21\u51fa\u751f\u7b49\u7684\u6982\u7387\u3002\u5728\u7ed9\u5b9a\u7684\u65f6\u95f4\u5185\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = 2 <sup>0<\/sup> * e <sup>\u2013 2<\/sup> \/ 0\uff01 = <strong>0.1353<\/strong><\/span><\/li>\n<li> <strong style=\"color: #000000;\">P(X=1)<\/strong> <span style=\"color: #000000;\">= 2<\/span> <sup style=\"color: #000000;\">1<\/sup> <span style=\"color: #000000;\">* e<\/span> <sup style=\"color: #000000;\">\u2013 2<\/sup> <span style=\"color: #000000;\">\/ 1\uff01 =<\/span> <strong style=\"color: #000000;\">0.2707<\/strong><\/li>\n<li> <strong style=\"color: #000000;\">P(X=2)<\/strong> <span style=\"color: #000000;\">= 2<\/span> <sup style=\"color: #000000;\">2<\/sup> <span style=\"color: #000000;\">* e<\/span> <sup style=\"color: #000000;\">\u2013 2<\/sup> <span style=\"color: #000000;\">\/ 2\uff01 =<\/span> <strong style=\"color: #000000;\">0.2707<\/strong><\/li>\n<li> <strong style=\"color: #000000;\">P(X=3)<\/strong> <span style=\"color: #000000;\">= 2<\/span> <sup style=\"color: #000000;\">3<\/sup> <span style=\"color: #000000;\">* e<\/span> <sup style=\"color: #000000;\">\u2013 2<\/sup> <span style=\"color: #000000;\">\/ 3\uff01 =<\/span> <strong style=\"color: #000000;\">0.1805<\/strong><\/li>\n<\/ul>\n<h3><strong>\u67e5\u770b PMF<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u7ecf\u5e38\u7528\u6761\u5f62\u56fe\u6765\u53ef\u89c6\u5316\u6982\u7387\u8d28\u91cf\u51fd\u6570\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u4ee5\u4e0b\u6761\u5f62\u56fe\u663e\u793a\u4e86\u4e0e\u4e0a\u4f8b\u4e2d\u63cf\u8ff0\u7684\u6cca\u677e\u5206\u5e03\u7684\u6bcf\u5c0f\u65f6\u51fa\u751f\u6570\u76f8\u5173\u7684\u6982\u7387\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8131 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poissondist1.png\" alt=\"\u5982\u4f55\u53ef\u89c6\u5316\u6982\u7387\u8d28\u91cf\u51fd\u6570\" width=\"490\" height=\"360\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8bf7\u6ce8\u610f\uff0c\u51fa\u751f\u6b21\u6570\u53ef\u4ee5\u5ef6\u4f38\u81f3\u65e0\u7a77\u5927\uff0c\u4f46\u5728 10 \u6b21\u4e4b\u540e\u6982\u7387\u4f1a\u53d8\u5f97\u975e\u5e38\u5c0f\uff0c\u4ee5\u81f3\u4e8e\u60a8\u751a\u81f3\u65e0\u6cd5\u5728\u6761\u5f62\u56fe\u4e0a\u770b\u5230\u5b83\u4eec\u3002<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>PMF \u7684\u5c5e\u6027<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6982\u7387\u8d28\u91cf\u51fd\u6570\u5177\u6709\u4ee5\u4e0b\u5c5e\u6027\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u6240\u6709\u7684\u6982\u7387\u90fd\u662f\u6b63\u652f\u6301\u7684\u3002<\/strong>\u4f8b\u5982\uff0c\u9ab0\u5b50\u843d\u5728 1 \u548c 6 \u4e4b\u95f4\u7684\u6982\u7387\u4e3a\u6b63\uff0c\u800c\u6240\u6709\u5176\u4ed6\u7ed3\u679c\u7684\u6982\u7387\u4e3a\u96f6\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u6240\u6709\u7ed3\u679c\u7684\u6982\u7387\u90fd\u5728 0 \u5230 1 \u4e4b\u95f4\u3002<\/strong>\u4f8b\u5982\uff0c\u9ab0\u5b50\u843d\u5728 1 \u5230 6 \u4e4b\u95f4\u7684\u6982\u7387\u662f 1\/6\uff0c\u5373\u6bcf\u4e2a\u7ed3\u679c\u4e3a 0.1666666\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u6240\u6709\u6982\u7387\u4e4b\u548c\u5fc5\u987b\u7b49\u4e8e1\u3002<\/strong>\u4f8b\u5982\uff0c\u9ab0\u5b50\u843d\u5728\u67d0\u4e2a\u6570\u5b57\u4e0a\u7684\u6982\u7387\u4e4b\u548c\u4e3a1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\u3002 \/6 = 1\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u968f\u673a\u53d8\u91cf-1\/\" target=\"_blank\" rel=\"noopener\">\u4ec0\u4e48\u662f\u968f\u673a\u53d8\u91cf\uff1f<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener\">CDF \u6216 PDF\uff1a\u6709\u4ec0\u4e48\u533a\u522b\uff1f<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\" target=\"_blank\" rel=\"noopener\">\u4e8c\u9879\u5206\u5e03\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u9c7c\u7c7b\u5206\u5e03\/\" target=\"_blank\" rel=\"noopener\">\u6cca\u677e\u5206\u5e03\u7b80\u4ecb<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6982\u7387\u8d28\u91cf\u51fd\u6570\uff08\u901a\u5e38\u7f29\u5199\u4e3aPMF \uff09\u544a\u8bc9\u6211\u4eec\u79bb\u6563\u968f\u673a\u53d8\u91cf\u53d6\u7279\u5b9a\u503c\u7684\u6982\u7387\u3002 \u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u63b7\u4e00\u6b21\u9ab0\u5b50\u3002\u5982\u679c\u6211\u4eec\u8ba9x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1324","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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