{"id":2820,"date":"2023-07-20T13:32:55","date_gmt":"2023-07-20T13:32:55","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%87%b3%e5%b0%91%e6%9c%89%e4%b8%a4%e4%b8%aa%e7%9a%84%e6%a6%82%e7%8e%87\/"},"modified":"2023-07-20T13:32:55","modified_gmt":"2023-07-20T13:32:55","slug":"%e8%87%b3%e5%b0%91%e6%9c%89%e4%b8%a4%e4%b8%aa%e7%9a%84%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%87%b3%e5%b0%91%e6%9c%89%e4%b8%a4%e4%b8%aa%e7%9a%84%e6%a6%82%e7%8e%87\/","title":{"rendered":"\u5982\u4f55\u627e\u5230\u201c\u81f3\u5c11\u4e24\u6b21\u201d\u6210\u529f\u7684\u6982\u7387"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u901a\u7528\u516c\u5f0f\u6765\u6c42\u51fa\u4e00\u7cfb\u5217\u8bd5\u9a8c\u4e2d<strong>\u81f3\u5c11\u4e24\u6b21\u6210\u529f\u7684\u6982\u7387<\/strong>\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 17px;\"> <strong>P(at least two successes) = 1 - P(zero successes) - P(one success)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u5728\u4e0a\u9762\u7684\u516c\u5f0f\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b<a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\" target=\"_blank\" rel=\"noopener\">\u4e8c\u9879\u5206\u5e03<\/a>\u516c\u5f0f\u8ba1\u7b97\u6bcf\u4e2a\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/span><\/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;\">\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u4f7f\u7528\u6b64\u516c\u5f0f\u6765\u67e5\u627e\u4e0d\u540c\u573a\u666f\u4e2d\u201c\u81f3\u5c11\u4e24\u6b21\u201d\u6210\u529f\u7684\u6982\u7387\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a\u7f5a\u7403\u5c1d\u8bd5<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6cf0\u7684\u7f5a\u7403\u547d\u4e2d\u7387\u4e3a 25%\u3002\u5982\u679c\u4ed6\u5c1d\u8bd5 5 \u6b21\u7f5a\u7403\uff0c\u6c42\u4ed6\u81f3\u5c11\u7f5a\u4e2d\u4e24\u6b21\u7684\u6982\u7387\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u4ed6\u6070\u597d\u7f5a\u7403 0 \u6b21\u6216\u7f5a\u7403 1 \u6b21\u7684\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = <sub>5<\/sub> C <sub>0<\/sub> * 0.25 <sup>0<\/sup> * (1-0.25) <sup>5-0<\/sup> = 1 * 1 * 0.75 <sup>5<\/sup> = <strong>0.2373<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = <sub>5<\/sub> C <sub>1<\/sub> * 0.25 <sup>1<\/sup> * (1-0.25) <sup>5-1<\/sup> = 5 * 0.25 * 0.75 <sup>4<\/sup> = <strong>0.3955<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u4ee5\u4e0b\u516c\u5f0f\uff0c\u6c42\u51fa Ty \u81f3\u5c11\u7f5a\u7403\u4e24\u6b21\u7684\u6982\u7387\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 P(X=0) \u2013 P(X=1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 0.2372 \u2013 0.3955<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = <strong>0.3673<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ty \u5728\u4e94\u6b21\u5c1d\u8bd5\u4e2d\u81f3\u5c11\u7f5a\u4e2d\u4e24\u6b21\u7684\u6982\u7387\u662f<strong>0.3673<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a\u5c0f\u90e8\u4ef6<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728\u67d0\u5bb6\u5de5\u5382\uff0c\u6240\u6709\u5c0f\u90e8\u4ef6\u4e2d\u6709 2% \u5b58\u5728\u7f3a\u9677\u3002\u5728 10 \u4e2a\u5c0f\u90e8\u4ef6\u7684\u968f\u673a\u6837\u672c\u4e2d\uff0c\u786e\u5b9a\u81f3\u5c11\u4e24\u4e2a\u6709\u7f3a\u9677\u7684\u6982\u7387\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u8ba9\u6211\u4eec\u8ba1\u7b97\u6070\u597d 0 \u6216\u6070\u597d 1 \u6709\u7f3a\u9677\u7684\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = <sub>10<\/sub> C <sub>0<\/sub> * 0.02 <sup>0<\/sup> * (1-0.02) <sup>10-0<\/sup> = 1 * 1 * 0.98 <sup>10<\/sup> = <strong>0.8171<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = <sub>10<\/sub> C <sub>1<\/sub> * 0.02 <sup>1<\/sup> * (1-0.02) <sup>10-1<\/sup> = 10 * 0.02 * 0.98 <sup>9<\/sup> = <strong>0.1667<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u4ee5\u4e0b\u516c\u5f0f\uff0c\u6c42\u51fa\u81f3\u5c11\u4e24\u4e2a\u5c0f\u90e8\u4ef6\u51fa\u73b0\u6545\u969c\u7684\u6982\u7387\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 P(X=0) \u2013 P(X=1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 0.8171 \u2013 0.1667<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = <strong>0.0162<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5728\u8fd9 10 \u4e2a\u968f\u673a\u6837\u672c\u4e2d\uff0c\u81f3\u5c11\u6709\u4e24\u4e2a\u5c0f\u90e8\u4ef6\u6709\u7f3a\u9677\u7684\u6982\u7387\u662f<strong>0.0162<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 3\uff1a\u7410\u4e8b\u95ee\u9898<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u9c8d\u52c3\u6b63\u786e\u56de\u7b54\u4e86 60% \u7684\u7410\u4e8b\u95ee\u9898\u3002\u5982\u679c\u6211\u4eec\u95ee\u4ed6 5 \u4e2a\u7410\u4e8b\u95ee\u9898\uff0c\u6c42\u4ed6\u81f3\u5c11\u6b63\u786e\u56de\u7b54\u4e24\u4e2a\u95ee\u9898\u7684\u6982\u7387\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u6765\u8ba1\u7b97\u5b83\u51c6\u786e\u56de\u7b54 0 \u6216 1 \u7684\u6982\u7387\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=0)<\/strong> = <sub>5<\/sub> C <sub>0<\/sub> * 0.60 <sup>0<\/sup> * (1-0.60) <sup>5-0<\/sup> = 1 * 1 * 0.40 <sup>5<\/sup> = <strong>0.01024<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(X=1)<\/strong> = <sub>5<\/sub> C <sub>1<\/sub> * 0.60 <sup>1<\/sup> * (1-0.60) <sup>5-1<\/sup> = 5 * 0.60 * 0.40 <sup>4<\/sup> = <strong>0.0768<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u4ee5\u4e0b\u516c\u5f0f\uff0c\u6c42\u51fa\u4ed6\u81f3\u5c11\u6b63\u786e\u56de\u7b54\u4e24\u4e2a\u95ee\u9898\u7684\u6982\u7387\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 P(X=0) \u2013 P(X=1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = 1 \u2013 0.01024 \u2013 0.0768<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(X\u22652) = <strong>0.91296<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ed6\u6b63\u786e\u56de\u7b54\u4e94\u4e2a\u95ee\u9898\u4e2d\u81f3\u5c11\u4e24\u4e2a\u7684\u6982\u7387\u662f<strong>0.91296<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5956\u52b1\uff1a\u201c\u81f3\u5c11\u4e24\u4e2a\u201d\u7684\u6982\u7387\u8ba1\u7b97\u5668<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u6b64\u8ba1\u7b97\u5668\u53ef\u4ee5\u6839\u636e\u7ed9\u5b9a\u8bd5\u9a8c\u7684\u6210\u529f\u6982\u7387\u548c\u8bd5\u9a8c\u603b\u6570\u81ea\u52a8\u67e5\u627e\u201c\u81f3\u5c11\u4e24\u6b21\u201d\u6210\u529f\u7684\u6982\u7387\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u901a\u7528\u516c\u5f0f\u6765\u6c42\u51fa\u4e00\u7cfb\u5217\u8bd5\u9a8c\u4e2d\u81f3\u5c11\u4e24\u6b21\u6210\u529f\u7684\u6982\u7387\uff1a P(at least two successe [&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-2820","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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