{"id":763,"date":"2023-07-28T20:30:47","date_gmt":"2023-07-28T20:30:47","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%83\/"},"modified":"2023-07-28T20:30:47","modified_gmt":"2023-07-28T20:30:47","slug":"%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%87%a0%e4%bd%95%e5%88%86%e5%b8%83\/","title":{"rendered":"\u51e0\u4f55\u5206\u5e03\u7b80\u4ecb"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u51e0\u4f55\u5206\u5e03<\/strong>\u63cf\u8ff0\u4e86\u5728\u4e00\u7cfb\u5217\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7ecf\u5386\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u7ecf\u5386\u4e00\u5b9a\u6b21\u6570\u7684\u5931\u8d25\u7684\u6982\u7387\u3002<\/span><\/p>\n<blockquote>\n<p><span style=\"color: #000000;\"><strong>\u4f2f\u52aa\u5229\u8bd5\u9a8c<\/strong>\u662f\u4e00\u79cd\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7ed3\u679c\u7684\u5b9e\u9a8c\u2014\u2014\u201c\u6210\u529f\u201d\u6216\u201c\u5931\u8d25\u201d\u2014\u2014\u5e76\u4e14\u6bcf\u6b21\u8fdb\u884c\u5b9e\u9a8c\u7684\u6210\u529f\u6982\u7387\u90fd\u662f\u76f8\u540c\u7684\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f2f\u52aa\u5229\u6587\u7ae0\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\u629b\u786c\u5e01\u3002\u786c\u5e01\u53ea\u80fd\u843d\u5728\u4e24\u4e2a\u6b63\u9762\u4e0a\uff08\u6211\u4eec\u53ef\u4ee5\u5c06\u6b63\u9762\u79f0\u4e3a\u201c\u547d\u4e2d\u201d\uff0c\u53cd\u9762\u79f0\u4e3a\u201c\u5931\u8d25\u201d\uff09\uff0c\u5e76\u4e14\u5047\u8bbe\u786c\u5e01\u662f\u516c\u5e73\u7684\uff0c\u6bcf\u6b21\u7ffb\u8f6c\u6210\u529f\u7684\u6982\u7387\u4e3a 0.5\u3002<\/span><\/p>\n<\/blockquote>\n<p><span style=\"color: #000000;\">\u5982\u679c<a href=\"https:\/\/statorials.org\/cn\/\u968f\u673a\u53d8\u91cf-1\/\" target=\"_blank\" rel=\"noopener\">\u968f\u673a\u53d8\u91cf<\/a><em>X<\/em>\u670d\u4ece\u51e0\u4f55\u5206\u5e03\uff0c\u5219\u5728\u7ecf\u5386\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u7ecf\u5386<em>k \u6b21<\/em>\u5931\u8d25\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) = (1-p) <sup>kp<\/sup><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u7684\u5931\u8d25\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p\uff1a<\/strong>\u6bcf\u6b21\u8bd5\u9a8c\u6210\u529f\u7684\u6982\u7387<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u5fc5\u987b\u63b7\u4e00\u679a\u516c\u5e73\u7684\u786c\u5e01\u591a\u5c11\u6b21\u624d\u80fd\u51fa\u73b0\u6b63\u9762\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u786e\u5b9a\u7ecf\u5386 0\u30011\u30012\u30013 \u6b21\u6545\u969c\u7b49\u7684\u6982\u7387\u3002\u5728\u786c\u5e01\u843d\u5728\u6b63\u9762\u4e4b\u524d\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><em><strong>\u6ce8\u610f\uff1a<\/strong>\u5982\u679c\u786c\u5e01\u7b2c\u4e00\u6b21\u629b\u63b7\u65f6\u6b63\u9762\u671d\u4e0a\uff0c\u5219\u201c\u5931\u8d25\u201d\u6b21\u6570\u4e3a 0\u3002<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = (1-.5) <sup>0<\/sup> (.5) = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = (1-.5) <sup>1<\/sup> (.5) = <strong>0.25<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=2)<\/strong> = (1-.5) <sup>2<\/sup> (.5) = <strong>0.125<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=3)<\/strong> = (1-0.5) <sup>3<\/sup> (0.5) = <strong>0.0625<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u4efb\u610f\u6b21\u6570\u7684\u786c\u5e01\u629b\u63b7\u7684\u6982\u7387\uff0c\u76f4\u5230\u65e0\u7a77\u5927\u3002\u7136\u540e\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u76f4\u65b9\u56fe\u6765\u53ef\u89c6\u5316\u8be5\u6982\u7387\u5206\u5e03\uff1a<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8160 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist1.png\" alt=\"\u51e0\u4f55\u6982\u7387\u5206\u5e03\u76f4\u65b9\u56fe\" width=\"442\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3><strong>\u7d2f\u79ef\u51e0\u4f55\u6982\u7387\u7684\u8ba1\u7b97<\/strong><\/h3>\n<p>\u6211\u4eec\u7ecf\u5386 k \u6b21\u6216\u66f4\u5c11\u7684\u5931\u8d25\u76f4\u5230\u7b2c\u4e00\u6b21\u6210\u529f\u7684\u7d2f\u79ef\u6982\u7387\u53ef\u4ee5<span style=\"color: #000000;\">\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f<\/span><span style=\"color: #000000;\"><em>\u627e\u5230<\/em><strong>\uff1a<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u2264k) = 1 \u2013 (1-p) <sup>k+1<\/sup><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>k\uff1a<\/strong>\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u7684\u5931\u8d25\u6b21\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p\uff1a<\/strong>\u6bcf\u6b21\u8bd5\u9a8c\u6210\u529f\u7684\u6982\u7387<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u786c\u5e01\u6700\u7ec8\u6b63\u9762\u671d\u4e0a\u4e4b\u524d\u201c\u672a\u547d\u4e2d\u201d\u4e09\u6b21\u6216\u66f4\u5c11\u7684\u6982\u7387\u3002\u6211\u4eec\u5c06\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u8ba1\u7b97\u8be5\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22643)<\/strong> = 1 \u2013 (1-0.5) <sup>3+1<\/sup> = <strong>0.9375<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7c7b\u4f3c\u7684\u516c\u5f0f\u8ba1\u7b97\u6bcf\u4e2a\u7d2f\u79ef\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22640)<\/strong> = 1 \u2013 (1-.5) <sup>0+1<\/sup> = <strong>0.5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22641)<\/strong> = 1 \u2013 (1-0.5) <sup>1+1<\/sup> = <strong>0.75<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X\u22642)<\/strong> = 1 \u2013 (1-0.5) <sup>2+1<\/sup> = <strong>0.875<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u4efb\u610f\u6b21\u6570\u7684\u7d2f\u79ef\u6982\u7387\uff0c\u76f4\u5230\u65e0\u7a77\u5927\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u76f4\u65b9\u56fe\u6765\u53ef\u89c6\u5316\u8fd9\u4e2a\u7d2f\u79ef\u6982\u7387\u5206\u5e03\uff1a<\/span> <\/p>\n<div class=\"wp-block-image\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8162 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/geomdist2.png\" alt=\"\u51e0\u4f55\u7d2f\u79ef\u6982\u7387\u5206\u5e03\" width=\"459\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/div>\n<h3><strong>\u51e0\u4f55\u5206\u5e03\u7684\u6027\u8d28<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u51e0\u4f55\u5206\u5e03\u5177\u6709\u4ee5\u4e0b\u6027\u8d28\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5206\u5e03\u7684\u5e73\u5747\u503c\u4e3a<strong>(1-p) \/ p<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5206\u5e03\u7684\u65b9\u5dee\u4e3a<strong>(1-p) \/ p <sup>2<\/sup><\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u9884\u8ba1\u786c\u5e01\u5728\u53cd\u9762\u843d\u5730\u4e4b\u524d\u6b63\u9762\u671d\u4e0a\u7684\u5e73\u5747\u6b21\u6570\u4e3a (1-p) \/ p = (1-.5) \/ .5 = <strong>1<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u76f4\u5230\u6b63\u9762\u671d\u4e0a\u4e3a\u6b62\u7684\u629b\u63b7\u6b21\u6570\u7684\u65b9\u5dee\u4e3a (1-p)\/ <sup>p2<\/sup> =(1-.5)\/\u3002 <sup>52<\/sup> = <strong>2<\/strong> \u3002<\/span><\/p>\n<h3><strong>\u51e0\u4f55\u5206\u5e03\u7ec3\u4e60\u9898<\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u4ee5\u4e0b\u7ec3\u4e60\u9898\u6765\u6d4b\u8bd5\u60a8\u5bf9\u51e0\u4f55\u5206\u5e03\u7684\u4e86\u89e3\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><em><strong>\u6ce8\u610f\uff1a<\/strong>\u6211\u4eec\u5c06\u4f7f\u7528<a href=\"https:\/\/statorials.org\/cn\/\u51e0\u4f55\u5206\u5e03\u8ba1\u7b97\u5668\/\" target=\"_blank\" rel=\"noopener\">\u51e0\u4f55\u5206\u5e03\u8ba1\u7b97\u5668<\/a>\u6765\u8ba1\u7b97\u8fd9\u4e9b\u95ee\u9898\u7684\u7b54\u6848\u3002<\/em><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u98981<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u9898\uff1a<\/strong>\u4e00\u540d\u7814\u7a76\u4eba\u5458\u5728\u56fe\u4e66\u9986\u5916\u7b49\u5019\uff0c\u8be2\u95ee\u4eba\u4eec\u662f\u5426\u652f\u6301\u67d0\u9879\u6cd5\u5f8b\u3002\u67d0\u4e2a\u4eba\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u6982\u7387\u4e3a p = 0.2\u3002\u4e0e\u7814\u7a76\u4eba\u5458\u4ea4\u8c08\u7684\u7b2c\u56db\u4e2a\u4eba\u7b2c\u4e00\u4e2a\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u6982\u7387\u6709\u591a\u5927\uff1f<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: #000000;\"><strong>\u7b54\u6848\uff1a<\/strong>\u76f4\u5230\u7b2c\u4e00\u6b21\u6210\u529f\u4e3a\u6b62\u7684\u201c\u5931\u8d25\u201d\u6b21\u6570\uff0c\u5373\u5728\u7b2c\u4e00\u4e2a\u4eba\u652f\u6301\u8be5\u6cd5\u5f8b\u4e4b\u524d\u4e0d\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u4eba\u6570\u4e3a 3\u3002\u56e0\u6b64\uff0c\u5728\u4f7f\u7528 p = 0.2 \u548c x \u7684\u51e0\u4f55\u5206\u5e03\u8ba1\u7b97\u5668\u65f6= 3 \u6b21\u5931\u8d25\uff0c\u6211\u4eec\u53d1\u73b0 P(X=3) = <strong>0.10240<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u98982<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u9898\uff1a<\/strong>\u4e00\u540d\u7814\u7a76\u4eba\u5458\u5728\u56fe\u4e66\u9986\u5916\u7b49\u5019\uff0c\u8be2\u95ee\u4eba\u4eec\u662f\u5426\u652f\u6301\u67d0\u9879\u6cd5\u5f8b\u3002\u67d0\u4e2a\u4eba\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u6982\u7387\u4e3a p = 0.2\u3002\u7814\u7a76\u4eba\u5458\u5fc5\u987b\u4e0e\u56db\u4e2a<em>\u4ee5\u4e0a<\/em>\u7684\u4eba\u4ea4\u8c08\u624d\u80fd\u627e\u5230\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u4eba\u7684\u6982\u7387\u6709\u591a\u5927\uff1f<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: #000000;\"><strong>\u7b54\u6848\uff1a<\/strong>\u4f7f\u7528\u51e0\u4f55\u5206\u5e03\u8ba1\u7b97\u5668\uff0cp = 0.2 \u4e14 x = 4 \u6b21\u5931\u8d25\uff0c\u6211\u4eec\u53d1\u73b0 P(X&gt;4) = <strong>0.32768<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u98983<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u95ee\u9898\uff1a<\/strong>\u4e00\u540d\u7814\u7a76\u4eba\u5458\u5728\u56fe\u4e66\u9986\u5916\u7b49\u5019\uff0c\u8be2\u95ee\u4eba\u4eec\u662f\u5426\u652f\u6301\u67d0\u9879\u6cd5\u5f8b\u3002\u67d0\u4e2a\u4eba\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u6982\u7387\u4e3a p = 0.2\u3002\u5728\u627e\u5230\u652f\u6301\u8be5\u6cd5\u5f8b\u7684\u4eba\u4e4b\u524d\uff0c\u7814\u7a76\u4eba\u5458\u9700\u8981\u4e0e\u591a\u5c11\u4eba\u4ea4\u8c08\uff1f<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"><span style=\"color: #000000;\"><strong>\u7b54\u6848\uff1a<\/strong>\u56de\u60f3\u4e00\u4e0b\uff0c\u51e0\u4f55\u5206\u5e03\u7684\u5e73\u5747\u503c\u662f<strong>(1-p) \/ p<\/strong> \u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5e73\u5747\u503c\u5c06\u4e3a (1-.2) \/ .2 = <strong>4<\/strong> \u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u51e0\u4f55\u5206\u5e03\u63cf\u8ff0\u4e86\u5728\u4e00\u7cfb\u5217\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u7ecf\u5386\u7b2c\u4e00\u6b21\u6210\u529f\u4e4b\u524d\u7ecf\u5386\u4e00\u5b9a\u6b21\u6570\u7684\u5931\u8d25\u7684\u6982\u7387\u3002 \u4f2f\u52aa\u5229\u8bd5\u9a8c\u662f\u4e00\u79cd\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7ed3 [&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-763","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\/ -->\n<title>\u51e0\u4f55\u5206\u5e03\u7b80\u4ecb - Statory<\/title>\n<meta name=\"description\" content=\"\u51e0\u4f55\u5206\u5e03\u7684\u7b80\u5355\u4ecb\u7ecd\uff0c\u5305\u62ec\u51e0\u4e2a\u5206\u6b65\u793a\u4f8b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u51e0\u4f55\u5206\u5e03\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta 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