{"id":7420,"date":"2024-06-06T15:45:37","date_gmt":"2024-06-06T07:45:37","guid":{"rendered":"https:\/\/www.btccccc.cc\/invwp\/?p=7420"},"modified":"2024-06-06T15:45:37","modified_gmt":"2024-06-06T07:45:37","slug":"%e9%85%92%e9%ac%bc%e6%bc%ab%e6%ad%a5%e7%9a%84%e6%95%b0%e5%ad%a6-%e9%9a%8f%e6%9c%ba%e8%bf%87%e7%a8%8b-%e5%bc%a0%e5%a4%a9%e8%93%89%e4%b8%93%e6%a0%8f","status":"publish","type":"post","link":"https:\/\/www.invbus.com\/blog\/?p=7420","title":{"rendered":"\u9152\u9b3c\u6f2b\u6b65\u7684\u6570\u5b66\u2014\u2014\u968f\u673a\u8fc7\u7a0b | \u5f20\u5929\u84c9\u4e13\u680f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>\u7f16\u8005\u6309\uff1a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u51e0\u7bc7\u4e3b\u8981\u4ecb\u7ecd\u4e86\u6982\u7387\u4e0e\u7edf\u8ba1\u4e2d\u7684\u4e24\u4e2a\u91cd\u8981\u5b66\u6d3e\uff1a<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655415734&amp;idx=2&amp;sn=3c455c263b593a18d5755a081cd702e8&amp;chksm=f3a66fdbc4d1e6cdafd127c6265760db662de34a620085f59fbed5d635d462bd7469e3c30d5c&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u9891\u7387\u5b66\u6d3e<\/a>\u548c<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655416427&amp;idx=3&amp;sn=d4950b9a4d509e357178110284c688a5&amp;chksm=f3a67206c4d1fb1065fd17ad9d4d367e9cb504b6e6604a94a3ef6d83f309ba4779a2cd003814&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u8d1d\u53f6\u65af\u5b66\u6d3e<\/a>\uff0c\u4ece\u800c\u5f15\u7533\u51fa\u4e86\u6982\u7387\u4e0e\u7edf\u8ba1\u9886\u57df\u6700\u57fa\u672c\u7684\u95ee\u9898\uff1a\u4ec0\u4e48\u662f\u6982\u7387\u3001\u5b83\u53c8\u4ece\u4f55\u800c\u6765\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u6b64\u7bc7\u5219\u5c06\u4ee5\u6982\u7387\u4e0e\u7edf\u8ba1\u4e2d\u4e00\u4e2a\u91cd\u8981\u7684\u6982\u5ff5\u2014\u2014\u968f\u673a\u8fc7\u7a0b\u4f5c\u4e3a\u8d77\u70b9\uff0c\u53bb\u63a2\u8ba8\u4e00\u4e2a\u9152\u9b3c\u56de\u5bb6\u7684\u53ef\u80fd\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u64b0\u6587 | \u5f20\u5929\u84c9&nbsp;\uff08\u7f8e\u56fd\u5fb7\u5dde\u5927\u5b66\u5965\u65af\u6c40\u5206\u6821\u7406\u8bba\u7269\u7406\u535a\u58eb\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8d23\u7f16 | \u5415\u6d69\u7136<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6982\u7387\u8bba\u4e13\u680f<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">2017-03-16&nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655413624&amp;idx=1&amp;sn=0c6643bec24f2f6131b7eac7d0420670&amp;chksm=f3a66715c4d1ee03b55a4a03c89558d8e99f46df452fcf1bce273aa9e3b3989bda27a932acc3&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u4e0a\u5e1d\u6559\u4eba\u63b7\u9ab0\u5b50\u2014\u2014\u201c\u795e\u7ae5\u201d\u5e15\u65af\u5361\u4e0e\u6982\u7387\u8bba<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2017-03-31 &nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655413915&amp;idx=2&amp;sn=1772b467cab4a886ce3f13969650ab41&amp;chksm=f3a664f6c4d1ede0261c20b6d9745deb6e2162d72fb42c9dcb4e8f9178a26c809cd4edd8b520&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u4f3c\u662f\u800c\u975e\u7684\u7b54\u6848\uff1a\u6982\u7387\u8bba\u6096\u8bba<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2017-04-18 &nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655414229&amp;idx=2&amp;sn=7d6b702363a67f5b29bba7f99cae403c&amp;chksm=f3a665b8c4d1ecae1a1cb384c4eb5f5e4dd3dd83dd3ff809e84b6b90530a483ef4417848429e&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u522b\u76f8\u4fe1\u76f4\u89c9\uff1a\u6982\u7387\u8bba\u5e2e\u52a9\u4fa6\u7834\u201c\u8d22\u52a1\u9020\u5047\u201d<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2017-05-15 &nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655414880&amp;idx=2&amp;sn=ed580b38f96a93a4cbe258b75512350c&amp;chksm=f3a6680dc4d1e11b053ea3d15dae984daa795ab7671ca814049babfc0cb903bac6e02d8627d4&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u8d4c\u5f92\u8c2c\u8bef\uff1a\u8d4c\u535a\u4e0e\u5927\u6570\u5b9a\u5f8b<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2017-06-24 &nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655415734&amp;idx=2&amp;sn=3c455c263b593a18d5755a081cd702e8&amp;chksm=f3a66fdbc4d1e6cdafd127c6265760db662de34a620085f59fbed5d635d462bd7469e3c30d5c&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u65e0\u6240\u4e0d\u5728\u7684\u6982\u7387\u5206\u5e03\u949f\u578b\u66f2\u7ebf<\/a>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2017-07-26 &nbsp;<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655416427&amp;idx=3&amp;sn=d4950b9a4d509e357178110284c688a5&amp;chksm=f3a67206c4d1fb1065fd17ad9d4d367e9cb504b6e6604a94a3ef6d83f309ba4779a2cd003814&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u6982\u7387\u4e4b\u672c\u8d28\u2014\u4ece\u4e3b\u89c2\u6982\u7387\u5230\u91cf\u5b50\u8d1d\u53f6\u65af<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u25cf\u3000\u25cf\u3000\u25cf<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u60f3\u8c61\u5728\u66fc\u54c8\u987f\u4e1c\u897f\u5357\u5317\u683c\u70b9\u5316\u7684\u8857\u9053\u4e2d\u6709\u4e00\u4e2a\u5c0f\u9189\u6c49\uff0c\u4ed6\u6bcf\u6b21\u5230\u8fbe\u4e00\u4e2a\u4ea4\u53c9\u8def\u53e3\u65f6\u90fd\u4f1a\u968f\u673a\u9009\u62e9\u524d\u540e\u5de6\u53f3\u56db\u4e2a\u65b9\u5411\u5176\u4e2d\u7684\u4e00\u4e2a\uff0c\u7136\u540e\u7ee7\u7eed\u524d\u8fdb\uff08\u6216\u540e\u9000\uff09\uff1b\u5728\u8d70\u5230\u4e0b\u4e00\u4e2a\u8def\u53e3\u65f6\u53c8\u968f\u673a\u9009\u62e9\u4e00\u6b21\u65b9\u5411\u2026\u2026\u5982\u6b64\u7ee7\u7eed\u4e0b\u53bb\uff0c\u4ed6\u6240\u7ecf\u8fc7\u7684\u8def\u5f84\u4f1a\u5177\u6709\u4ec0\u4e48\u6837\u7684\u7279\u70b9\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u5b66\u5bb6\u4eec\u5c06\u8fd9\u6837\u7684\u95ee\u9898\u79f0\u4e4b\u4e3a\u201c\u9152\u9b3c\u6f2b\u6b65\u201d\uff0c\u751a\u81f3\u5c06\u9152\u9b3c\u7684\u8def\u5f84\u62bd\u8c61\u4e3a\u4e00\u4e2a\u6570\u5b66\u6a21\u578b\uff1a\u65e0\u89c4\u884c\u8d70\uff0c\u6216\u79f0\u968f\u673a\u6e38\u8d70\uff08random walk\uff09\u3002\u800c\u56e0\u66fc\u54c8\u987f\u7684\u9152\u9b3c\u53ea\u80fd\u5728\u4e8c\u7ef4\u7684\u57ce\u5e02\u5730\u9762\u4e0a\u6e38\u8361\uff0c\u6240\u4ee5\u8fd9\u4e5f\u662f\u4e00\u79cd\u201c\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u201d\uff0c\u89c1\u56fe1\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/0635431hyot1y6oj21jgam.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/0635431hyot1y6oj21jgam.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe1\uff1a\u9152\u9b3c\u6f2b\u6b65\u548c\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u8def\u5f84<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u968f\u673a\u8fc7\u7a0b\u4e0e\u4f2f\u52aa\u5229\u8fc7\u7a0b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e0\u89c4\u884c\u8d70\u662f\u4e00\u7c7b\u968f\u673a\u8fc7\u7a0b\u3002\u4f55\u8c13\u968f\u673a\u8fc7\u7a0b\uff1f\u4e4b\u524d\u6211\u4eec\u4ee5\u4e22\u786c\u5e01\u4e3a\u4f8b\u4ecb\u7ecd\u4e86<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655413624&amp;idx=1&amp;sn=0c6643bec24f2f6131b7eac7d0420670&amp;chksm=f3a66715c4d1ee03b55a4a03c89558d8e99f46df452fcf1bce273aa9e3b3989bda27a932acc3&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u968f\u673a\u53d8\u91cf<\/a>\uff0c\u968f\u673a\u8fc7\u7a0b\u5c31\u662f\u4e00\u7cfb\u5217\u968f\u673a\u53d8\u91cf\u7684\u96c6\u5408\u3002\u6bd4\u5982\u8bf4\uff0c\u6bcf\u4e22\u4e00\u6b21\u786c\u5e01\uff0c\u4fbf\u4ea7\u751f\u4e00\u4e2a\u968f\u673a\u53d8\u91cfX\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u4e00\u6b21\u53c8\u4e00\u6b21\u5730\u4e22\u4e0b\u53bb\uff0c\u4fbf\u4ea7\u751f\u51fa\u4e00\u7cfb\u5217\u7684\u968f\u673a\u53d8\u91cfX1\uff0cX2\u2026\u2026 Xi&nbsp;\u2026\u2026\uff0c\u9152\u9b3c\u7684\u6f2b\u6b65\u4e5f\u7c7b\u4f3c\uff0c\u603b\u7684\u8def\u5f84\u662f\u9152\u9b3c\u591a\u6b21\u968f\u673a\u9009\u62e9\u884c\u8d70\u7684\u6240\u6709\u8def\u5f84\u7684\u96c6\u5408\u3002\u968f\u673a\u53d8\u91cf\u5e8f\u5217\u96c6\u5408\u8d77\u6765\uff0c\u4fbf\u5f62\u6210\u4e86\u201c\u968f\u673a\u8fc7\u7a0b\u201d\u3002\u968f\u673a\u8fc7\u7a0b\u4e2d\u7684Xi\uff0c\u53ef\u770b\u4f5c\u662f\u65f6\u95f4 ti&nbsp;\u7684\u201c\u51fd\u6570\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0e\u7ecf\u5178\u7269\u7406\u5b66\u7c7b\u4f3c\uff0c\u7269\u7406\u7cfb\u7edf\u968f\u65f6\u95f4\u6f14\u5316\u7684\u8fc7\u7a0b\uff0c\u8981\u9075\u5faa\u725b\u987f\u7269\u7406\u5b66\u7684\u89c4\u5f8b\u3002\u968f\u673a\u8fc7\u7a0b\u4e5f\u6709\u5b83\u7684\u8fd0\u52a8\u89c4\u5f8b\u3002\u4f46\u4e0d\u540c\u7684\u662f\uff0c\u968f\u673a\u8fc7\u7a0b\u7684\u53d8\u91cf\u662f\u53d6\u503c\u4e0d\u786e\u5b9a\u7684\u968f\u673a\u53d8\u91cf\uff0c\u8fd9\u4f7f\u5f97\u968f\u673a\u8fc7\u7a0b\u76f8\u6bd4\u4e8e\u201c\u4e0d\u968f\u673a\u7684\u8fc7\u7a0b\u201d\u66f4\u96be\u4ee5\u5904\u7406\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u5904\u8fd8\u5e94\u4ecb\u7ecd\u4e00\u4e2a\u65b0\u7684\u5b9a\u4e49\u2014\u2014\u4f2f\u52aa\u5229\u8fc7\u7a0b\u3002\u4e22\u4e00\u6b21\u786c\u5e01\u4ea7\u751f\u4e00\u4e2a\u53d6\u503c\u4e3a1\u62160\u7684\u968f\u673a\u53d8\u91cfX\uff0c\u90a3\u4e48\uff0c\u63a5\u8fde\u4e22\u4e0b\u53bb\u4ea7\u751f\u7684\u968f\u673a\u53d8\u91cf\u7684\u96c6\u5408\u5c31\u88ab\u79f0\u4e3a\u4f2f\u52aa\u5229\u8fc7\u7a0b\u3002\u4f2f\u52aa\u5229\u8fc7\u7a0b\u662f\u4e00\u4e2a\u65f6\u95f4\u79bb\u6563\uff0c\u53d6\u503c\u4e5f\u79bb\u6563\u7684\u968f\u673a\u8fc7\u7a0b\uff0c\u5176\u4e2d\u968f\u673a\u53d8\u91cf\u7684\u6837\u672c\u7a7a\u95f4\u53ea\u6709\u4e24\u4e2a\u53d6\u503c\uff1a\u6210\u529f\uff081\uff09\u3001\u6216\u5931\u8d25\uff080\uff09\uff0c\u6210\u529f\u7684\u6982\u7387\u4e3ap\u3002\u4f8b\u5982\uff0c\u63b7\u4e00\u4e2a6\u9762\u5bf9\u79f0\u7684\u9ab0\u5b50\uff0c\u5982\u679c\u5c06\u201c3\u201d\u51fa\u73b0\u7684\u6982\u7387\u5b9a\u4e3a\u6210\u529f\u7684\u8bdd\uff0c\u5219\u591a\u6b21\u63b7\u9ab0\u5b50\u7684\u7ed3\u679c\u662f\u4e00\u4e2ap=1\/6\u7684\u4f2f\u52aa\u5229\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u9a6c\u5c14\u53ef\u592b\u94fe<\/strong><sup>[1]<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f2f\u52aa\u5229\u8fc7\u7a0b\u6bd4\u8f83\u4e4f\u5473\uff0c\u56e0\u4e3a\u5f97\u5230\u6b63\u9762\u7684\u6982\u7387\u662f\u4e2a\u56fa\u5b9a\u503cp\uff0c\u6bcf\u6b21\u629b\u63b7\u7684\u7ed3\u679c\u4e92\u76f8\u72ec\u7acb\uff0c\u8fd9\u79cd\u72ec\u7acb\u6027\u662f\u6784\u6210\u4e4b\u524d\u6240\u4ecb\u7ecd\u7684<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655414880&amp;idx=2&amp;sn=ed580b38f96a93a4cbe258b75512350c&amp;chksm=f3a6680dc4d1e11b053ea3d15dae984daa795ab7671ca814049babfc0cb903bac6e02d8627d4&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u201c\u8d4c\u5f92\u8c2c\u8bef\u201d<\/a>\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7136\u800c\uff0c\u771f\u5b9e\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\uff0c\u5f80\u5f80\u5b58\u5728\u7740\u4e92\u76f8\u4f9d\u8d56\u7684\u5173\u7cfb\u3002\u6bd4\u5982\u8bf4\uff0c\u8003\u8651\u660e\u5929\u5317\u4eac\u4e0b\u96e8\u6216\u5929\u6674\u7684\u53ef\u80fd\u6027\uff0c\u4e00\u822c\u6765\u8bf4\u4e0e\u5317\u4eac\u4eca\u5929\u3001\u6628\u5929\u7684\u6c14\u5019\u72b6\u51b5\u6709\u5173\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/063544j0nbm0j5fzn9jaue.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/063544j0nbm0j5fzn9jaue.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe2\uff1a\u5178\u578b\u7684\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b80\u5355\u800c\u8a00\uff0c\u5047\u8bbe\u660e\u5929\u4e0b\u96e8\u7684\u6982\u7387\u53ea\u4e0e\u4eca\u5929\u7684\u5929\u6c14\u6709\u5173\uff0c\u5219\u201c\u96e8\u6674\u201d\u7684\u8f6c\u6362\u53ef\u4ee5\u7528\u4e00\u4e2a\u5982\u56fe2a\u7684\u56fe\u5f62\u6765\u63cf\u8ff0\u3002\u56fe\u4e2d\uff0c\u201c\u96e8\u201d\u548c\u201c\u6674\u201d \u4e24\u79cd\u72b6\u6001\u4e4b\u95f4\u88ab\u6570\u6761\u5e26\u7bad\u5934\u7684\u66f2\u7ebf\u8fde\u63a5\u3002\u8fd9\u4e9b\u8fde\u7ebf\u8868\u793a\u4ece\u4eca\u5929\u7684\u72b6\u6001\uff0c\u5982\u4f55\u9884\u6d4b\u660e\u5929\u7684\u72b6\u6001\u3002\u6bd4\u5982\u8bf4\uff0c\u4ece\u72b6\u6001\u201c\u96e8\u201d\u51fa\u53d1\u6709\u4e24\u6761\u8fde\u7ebf\uff1a\u7ed3\u675f\u4e8e\u72b6\u6001\u201c\u6674\u201d\u7684\u53f3\u8fb9\u90a3\u4e00\u6761\u6807\u4e0a\u4e86\u201c0.6\u201d\uff0c\u610f\u601d\u662f\u8bf4\uff1a\u201c\u4eca\u5929\u96e8\u660e\u5929\u6674\u7684\u6982\u7387\u662f60%\u201d\uff1b\u5de6\u8fb9\u66f2\u7ebf\u7ed5\u4e86\u4e00\u5708\u53c8\u8fd4\u56de\u201c\u96e8\u201d\uff0c\u6807\u8bc60.4\uff0c\u5373\u201c\u660e\u5929\u7ee7\u7eed\u4e0b\u96e8\u7684\u6982\u7387\u662f40%\u201d\u3002\u53ef\u4ee5\u7c7b\u4f3c\u5730\u7406\u89e3\u4ece\u72b6\u6001\u201c\u6674\u201d\u51fa\u53d1\u7684\u4e24\u6761\u66f2\u7ebf\uff1a\u5982\u679c\u4eca\u5929\u6674\uff0c\u90a3\u4e48\u660e\u5929\u670980%\u7684\u53ef\u80fd\u6027\u6674\uff0c20%\u7684\u53ef\u80fd\u6027\u4e0b\u96e8\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65f6\u95f4\u4e0a\u79bb\u6563\u7684\u8fc7\u7a0b\uff0c\u4e5f\u88ab\u79f0\u4e3a\u201c\u94fe\u201d\uff0c\u4e0a\u8ff0\u4f8b\u5b50\u662f\u4e00\u4e2a\u5178\u578b\u7684\u3001\u4e5f\u662f\u6700\u7b80\u5355\u7684\u9a6c\u5c14\u53ef\u592b\u94fe\uff0c\u5b83\u4e5f\u5f97\u540d\u4e8e\u4fc4\u7f57\u65af\u6570\u5b66\u5bb6\u5b89\u5fb7\u70c8\u00b7\u9a6c\u5c14\u53ef\u592b\uff08Andreyevich Markov\uff0c1856\uff0d1922\uff09\u3002\u9a6c\u5c14\u53ef\u592b\u94fe\u5177\u6709\u9a6c\u5c14\u53ef\u592b\u6027\u8d28\uff0c\u4e5f\u88ab\u79f0\u4e3a\u201c\u65e0\u8bb0\u5fc6\u6027\u201d\u6216\u201c\u65e0\u540e\u6548\u6027\u201d\uff0c\u5373\u4e0b\u4e00\u72b6\u6001\u7684\u6982\u7387\u5206\u5e03\u53ea\u7531\u5f53\u524d\u72b6\u6001\u51b3\u5b9a\uff0c\u4e0e\u8fc7\u53bb\u7684\u4e8b\u4ef6\u65e0\u5173\u3002\u53cd\u6620\u5230\u4e0a\u8ff0\u6848\u4f8b\u4e2d\uff0c\u660e\u5929\u201c\u6674\u96e8\u201d\u7684\u6982\u7387\u53ea\u4e0e\u4eca\u5929\u7684\u72b6\u6001\u6709\u5173\uff0c\u800c\u4e0e\u6628\u5929\u4ee5\u53ca\u66f4\u65e9\u4e4b\u524d\u7684\u6c14\u5019\u5747\u65e0\u5173\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9664\u4e86\u7528\u56fe\u5f62\u6765\u8868\u793a\u9a6c\u5c14\u53ef\u592b\u94fe\u4e4b\u5916\uff0c\u201c\u96e8\u6674\u201d\u53d8\u6362\u5173\u7cfb\u4e5f\u53ef\u4ee5\u7528\u56fe2b\u7684\u8f6c\u6362\u77e9\u9635P\u6765\u63cf\u8ff0\u3002\u77e9\u9635\u4e2d\u7684\u6570\u503c\uff0c\u8868\u793a\u7cfb\u7edf\u6f14\u5316\u201c\u4e00\u6b65\u201d\u540e\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u79fb\u6982\u7387\u3002\u77e9\u9635\u8868\u793a\u4e2d\u7684\u72b6\u6001\u662f\u4e00\u4e2a\u77e2\u91cf\uff0c\u56fe2b\u4e2d\uff0c\u4eca\u5929\u7684\u72b6\u6001\u88ab\u8868\u793a\u4e3a\u4e00\u4e2a\u5206\u91cf\u4e3a0.3\u548c0.7\u7684\u77e2\u91cf\uff0c\u660e\u5929\u7684\u72b6\u6001\u5219\u7531P\u4e58\u4ee5\u4eca\u5929\u4e4b\u72b6\u6001\u800c\u5f97\u5230\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/063545136tv3l1s33l63vh.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/063545136tv3l1s33l63vh.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe3\uff1a\u65f6\u9f50\u9a6c\u5c14\u53ef\u592b\u94fe<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4e0a\u8ff0\u77e9\u9635\u4e2d\u7684\u8f6c\u79fb\u6982\u7387\u5e76\u4e0d\u968f\u65f6\u95f4\u800c\u53d8\u5316\uff0c\u5373\u77e9\u9635\u4e2d\u7684\u5404\u4e2a\u5143\uff080.4, 0.6, 0.2, 0.8\uff09\u7684\u6570\u503c\u662f\u56fa\u5b9a\u7684\uff0c\u8fd9\u79cd\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u9875\u53eb\u505a\u65f6\u9f50\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u3002\u6bd4\u5982\u8bf4\uff0c\u5982\u56fe3\u6240\u793a\uff0c\u5047\u8bbe\u5317\u4eac\u4efb\u4f55\u4e00\u5929\u7684\u201c\u6674\u96e8\u201d\u72b6\u6001\u90fd\u7531\u524d\u4e00\u5929\u7684\u72b6\u6001\u4e58\u4ee5\u540c\u6837\u7684\u8f6c\u6362\u77e9\u9635P\u800c\u5f97\u5230\uff0c\u5219\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u65f6\u9f50\u7684\u3002\u901a\u5e38\u8003\u8651\u7684\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\uff0c\u90fd\u88ab\u5047\u5b9a\u662f\u201c\u65f6\u9f50\u201d\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9664\u4e86\u201c\u65f6\u9f50\u201d\u6027\u4e4b\u5916\uff0c\u4eba\u4eec\u8fd8\u5bf9\u957f\u65f6\u95f4\u540e\u8d8b\u4e8e\u7a33\u5b9a\u72b6\u6001\u7684\u9a6c\u5c14\u79d1\u592b\u8fc7\u7a0b\u9887\u4e3a\u611f\u5174\u8da3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u4e00\u5468\u5185\u7684\u80a1\u7968\u5e02\u573a\u53ea\u7528\u7b80\u5355\u76843\u79cd\u72b6\u6001\u8868\u793a\uff1a\u725b\u5e02\u3001\u718a\u5e02\u3001\u505c\u6ede\u4e0d\u524d\u3002\u5176\u8f6c\u79fb\u6982\u7387\u5982\u56fe4\u6240\u793a\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/063546a044sd73k4067q3u.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/063546a044sd73k4067q3u.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe4\uff1a\u80a1\u7968\u5e02\u573a\u7684\u6781\u9650\u6982\u7387\u5206\u5e03<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u65f6\u95f4\u8db3\u591f\u957f\u7684\u65f6\u5019\uff0c\u8fd9\u4e2a\u9a6c\u5c14\u53ef\u592b\u94fe\u4ea7\u751f\u7684\u4e00\u7cfb\u5217\u968f\u673a\u72b6\u6001\u8d8b\u5411\u4e00\u4e2a\u6781\u9650\u5411\u91cf\uff0c\u5373\u56fe4\u4e2d\u53f3\u4e0b\u89d2\u6240\u793a\u7684\u77e2\u91cfXlimit&nbsp;=[0.47, 0.3, 0.23]\uff0c\u4e5f\u5c31\u662f\u7cfb\u7edf\u6700\u540e\u7684\u7a33\u6001\u5411\u91cf\u3002\u6309\u7167\u8fd9\u4e2a\u7279\u6b8a\u7684\u80a1\u7968\u5e02\u573a\u6a21\u578b\uff0c\u957f\u8fdc\u7684\u5e02\u573a\u8d8b\u52bf\u8d8b\u4e8e\u7a33\u5b9a\uff0c\u5373\u6bcf\u5468\u7684\u80a1\u7968\u60c5\u51b5\u662f\uff1a47%\u7684\u6982\u7387\u662f\u725b\u5e02\u300130%\u718a\u5e02\u300123%\u505c\u6ede\u4e0d\u524d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u9152\u9b3c\u5931\u8db3\u3001\u8d4c\u5f92\u7834\u4ea7\u53ca\u9e1f\u513f\u56de\u5bb6<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e0\u89c4\u884c\u8d70\u53ef\u4ee5\u770b\u505a\u662f\u9a6c\u5c14\u79d1\u592b\u94fe\u7684\u7279\u4f8b[2]\uff0c\u5b83\u7684\u72b6\u6001\u7a7a\u95f4\u4e0d\u662f\u50cf\u4e0a\u8ff0\u629b\u786c\u5e01\u7b49\u4f8b\u5b50\u4e2d\u90a3\u79cd\u7531\u7b80\u5355\u7684\u51e0\u79cd\u6709\u9650\u7684\u57fa\u672c\u72b6\u6001\u6784\u6210\u7684\uff0c\u800c\u662f\u7531\u65e0\u9650\u5ef6\u4f38\u7684\u201c\u7269\u7406\u7a7a\u95f4\u201d\u6784\u6210\uff0c\u8fd9\u513f\u7684\u201c\u7a7a\u95f4\u201d\u53ef\u4ee5\u662f\u4efb\u610f\u7ef4\u5ea6\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\uff0c\u4e3a\u4ec0\u4e48\u8bf4\u9152\u9b3c\u6f2b\u6b65\u662f\u9a6c\u5c14\u53ef\u592b\u94fe\u5462\uff1f\u56e0\u4e3a\uff0c\u9189\u6c49\u5728\u65f6\u523b ti+1&nbsp;\u7684\u72b6\u6001\uff08\u5373\u4f4d\u7f6e\uff09\u4ec5\u7531\u4ed6\u5728\u65f6\u523b ti&nbsp;\u7684\u72b6\u6001\uff08xi, yi\uff09\uff0c\u4ee5\u53ca\u4ed6\u968f\u673a\u9009\u62e9\u7684\u65b9\u5411\u6240\u51b3\u5b9a\uff0c\u4e0e\u8fc7\u53bb\uff08ti&nbsp;\u4e4b\u524d\uff09\u8d70\u8fc7\u7684\u8def\u5f84\u65e0\u5173\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u518d\u6765\u8ba8\u8bba\u4e00\u4e2a\u201c\u9152\u9b3c\u6389\u4e0b\u60ac\u5d16\u201d\u7684\u8da3\u9898\u3002\u524d\u6587\u66fe\u7ecf\u4ecb\u7ecd\u8fc7<a href=\"http:\/\/mp.weixin.qq.com\/s?__biz=MzIyNDA2NTI4Mg==&amp;mid=2655415734&amp;idx=2&amp;sn=3c455c263b593a18d5755a081cd702e8&amp;chksm=f3a66fdbc4d1e6cdafd127c6265760db662de34a620085f59fbed5d635d462bd7469e3c30d5c&amp;scene=21#wechat_redirect\" target=\"_blank\" rel=\"noreferrer noopener\">\u9ad8\u5c14\u987f\u9489\u677f\u5b9e\u9a8c<\/a>\uff0c\u53ef\u4f5c\u4e3a\u4e00\u7ef4\u65e0\u89c4\u884c\u8d70\u7684\u4f8b\u5b50\u3002\u9ad8\u5c14\u987f\u9489\u677f\u867d\u7136\u8c8c\u4f3c\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\uff0c\u4f46\u56e0\u4e3a\u5c0f\u7403\u5728\u5782\u76f4\u65b9\u5411\u7684\u8fd0\u52a8\u5e76\u4e0d\u662f\u968f\u673a\u7684\uff0c\u800c\u662f\u6bcf\u6b21\u56fa\u5b9a\u5411\u4e0b1\u683c\uff0c\u56e0\u6b64\u53ef\u4ee5\u89c6\u4f5c\u4e00\u4e2a\u5411\u4e0b\u7684\u65f6\u95f4\u8f74\uff0c\u800c\u6c34\u5e73\u65b9\u5411\u5219\u662f\u4e00\u4e2a\u4e00\u7ef4\u65e0\u89c4\u884c\u8d70\uff0c\u89c1\u56fe5\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/0635478u4i2kt8be22422j.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/0635478u4i2kt8be22422j.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe5\uff1a\u6c42\u4e00\u7ef4\u9152\u9b3c\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u56fe5\u4e2d\uff0c\u9489\u677f\u7684\u6c34\u5e73\u65b9\u5411\u4e3ax\u8f74\uff0c\u5782\u76f4\u5411\u4e0b\u4e3a\u65f6\u95f4\u8f74\u3002\u60ac\u5d16\u5904\u8bbe\u4e3ax=0\uff08\u56fe5\u5de6\u8fb9\u865a\u7ebf\uff09\u3002\u5047\u8bbe\u9152\u9b3c\uff08\u9876\u7aef\u7684\u5c0f\u7403\uff09\u8d77\u59cb\u65f6\u4f4d\u4e8ex=n\u7684\u683c\u70b9\u4f4d\u7f6e\uff0c\u5373\u79bb\u60ac\u5d16\u6709n\u683c\u4e4b\u9065\u3002\u9152\u9b3c\u671d\u4e0b\u6f2b\u6b65\u8fc7\u7a0b\u4e2d\u7684\u6bcf\u4e00\u6b65\uff0c\u5411\u53f3\uff08x\u589e\u5927\uff09\u6982\u7387\u4e3ap\uff0c\u5411\u5de6\u6982\u7387\u4e3a\uff081-p\uff09\u3002\u73b0\u5728\u95ee\uff1a\u9152\u9b3c\u4ece\u4f4d\u7f6en\u6f2b\u6e38\uff0c\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387\u662f\u591a\u5c11\uff08\u60ac\u5d16\u7684\u4f4d\u7f6e\u5728x=0\u5904\uff0c\u6240\u4ee5\uff0c\u5f53\u968f\u673a\u53d8\u91cfx\u7684\u503c\u5230\u8fbe0\uff0c\u53ef\u4f5c\u4e3a\u9152\u9b3c\u6389\u4e0b\u4e86\u60ac\u5d16\u7684\u5224\u636e\uff09\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5148\u8003\u8651\u4e00\u4e2a\u7b80\u5316\u7684\u5177\u4f53\u95ee\u9898\uff0c\u6bd4\u5982\u8bf4\uff0c\u8bbe\u9152\u9b3c\u6f2b\u6b65\u65f6\u5411\u53f3\u8d70\u7684\u6982\u7387p=2\/3\uff0c\u5411\u5de6\u8d70\u7684\u6982\u7387\u4e3aq=1-p=1\/3\uff0c\u90a3\u4e48\uff0c\u9152\u9b3c\u4ecex=1\u7684\u4f4d\u7f6e\u5f00\u59cb\u6f2b\u6e38\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u8bb8\u6709\u4eba\u4f1a\u5f88\u5feb\u5c31\u5f97\u51fa\u7b54\u6848\uff1a\u9152\u9b3c\u4ecex=1\u5411\u5de6\u8d70\u4e00\u6b65\u5c31\u5230\u4e86\u60ac\u5d16\uff0c\u800c\u4ed6\u5411\u5de6\u8d70\u7684\u6982\u7387\u4e3a1\/3\u3002\u90a3\u4e48\uff0c\u4ed6\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387\u4e0d\u5c31\u662f1\/3\u5417\uff1f\u4e8b\u60c5\u5e76\u4e0d\u662f\u90a3\u4e48\u7b80\u5355\u30021\/3\u662f\u9152\u9b3c\u7b2c\u4e00\u6b65\u5411\u5de6\u8d70\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387\uff0c\u4f46\u4ed6\u7b2c\u4e00\u6b65\u5411\u53f3\u8d70\u4ecd\u7136\u6709\u53ef\u80fd\u6389\u4e0b\u60ac\u5d16\uff0c\u6bd4\u5982\u8bf4\uff0c\u53f3\u8d70\u4e00\u6b65\u4e4b\u540e\u53c8\u518d\u5de6\u8d70\u4e24\u6b65\u4e0d\u4e5f\u4e00\u6837\u5230\u8fbex=0\u7684\u683c\u70b9\u5417\uff1f\u6240\u4ee5\uff0c\u6389\u4e0b\u60ac\u5d16\u7684\u603b\u6982\u7387\u6bd41\/3\u8981\u5927\uff0c\u8981\u52a0\u4e0a\u7b2c\u4e00\u6b65\u5411\u53f3\u8d70\u5230\u4e86x=2\u7684\u70b9\u4f46\u540e\u6765\u4ecd\u7136\u6389\u4e0b\u60ac\u5d16\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u66f4\u6e05\u695a\u5730\u5206\u6790\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u9152\u9b3c\u4ecex=1\u5904\u6f2b\u6b65\u5230x=0\u5904\u7684\u6982\u7387\u8bb0\u4e3aP1\u3002\u8fd9\u4e2a\u6982\u7387\u663e\u7136\u5c31\u662f\u521a\u624d\u7b80\u5316\u95ee\u9898\u4e2d\u8981\u6c42\u89e3\u7684\uff1a\u4ecex=1\u5904\u5f00\u59cb\u6f2b\u6b65\u6389\u5165\u60ac\u5d16\u7684\u6982\u7387\u3002\u540c\u65f6\uff0c\u4ece\u8fd9\u4e2a\u95ee\u9898\u7684\u5e73\u79fb\u5bf9\u79f0\u6027\u8003\u8651\uff0cP1\u4e5f\u662f\u9152\u9b3c\u4ece\u4efb\u4f55x=k\u5de6\u79fb\u4e00\u4e2a\u683c\u70b9\uff0c\u6f2b\u6b65\uff08\u4e0d\u7ba1\u591a\u5c11\u6b65\uff09\u5230\u8fbex=k-1\u683c\u70b9\u4f4d\u7f6e\u7684\u6982\u7387\u3002\u9700\u8981\u6ce8\u610f\uff1a\u9152\u9b3c\u8d70\u4e00\u6b65\uff0c\u4e0e\u4ed6\u7684\u683c\u70b9\u4f4d\u7f6e\u79fb\u52a8\u4e00\u683c\u662f\u4e24\u7801\u4e8b\uff0c\u4f4d\u7f6e\u4ecex=k\u5de6\u79fb\u5230x=k-1\uff0c\u4e5f\u8bb8\u8981\u8d70\u597d\u51e0\u6b65\uff0c\u8fd9\u4e0e\u4e24\u70b9\u4e4b\u95f4\u7684\u201c\u8def\u5f84\u4e0e\u4f4d\u79fb\u201d\u662f\u4e00\u4e2a\u9053\u7406\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9664\u4e86P1\u4e4b\u5916\uff0c\u5c06\u4ecex=2\u5904\u5f00\u59cb\u6f2b\u6b65\u6389\u5165\u60ac\u5d16\u7684\u6982\u7387\u8bb0\u4e3aP2=P<sub>1<\/sub><sup>2<\/sup>&nbsp;\uff0cx=3\u5904\u7684\u6982\u7387\u8bb0\u4e3aP3=P<sub>1<\/sub><sup>3<\/sup>\u2026\u2026\u4ee5\u6b64\u7c7b\u63a8\uff0c\u5982\u521a\u624d\u6240\u5206\u6790\u7684\uff0c\u5bf9P1\u53ef\u4ee5\u5217\u51fa\u4e00\u4e2a\u7b49\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P1&nbsp;= 1-p+pP<sub>1<\/sub><sup>2<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0cp\u662f\u9152\u9b3c\u671d\u60ac\u5d16\u53cd\u65b9\u5411\u6e38\u8d70\u7684\u6982\u7387\u3002\u7531\u6b64\u53ef\u4ee5\u89e3\u51faP1&nbsp;= 1\u6216\u8005P1= (1-p)\/p\u3002\u5bf9\u8fd9\u4e2a\u95ee\u9898\u6709\u610f\u4e49\u7684\u89e3\u662fP1= (1-p)\/p\uff0cPn=P<sub>1<\/sub><sup>n<\/sup>&nbsp;\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53p=1\/2\u65f6\uff0cP1=1\uff0c\u610f\u5473\u7740\u9152\u9b3c\u6700\u7ec8\u4e00\u5b9a\u4f1a\u6389\u4e0b\u60ac\u5d16\uff1b\u5f53p&lt;1\/2\uff0cP1&gt;1\uff0cPn\u4e5f\u4e00\u6837\uff0c\u4f46\u6982\u7387\u6700\u591a\u53ea\u80fd\u4e3a1\u3002\u6240\u4ee5\uff0c\u5982\u679c\u9152\u9b3c\u671d\u60ac\u5d16\u53cd\u65b9\u5411\u7684\u6982\u7387\u4e0d\u8db31\/2\u7684\u8bdd\uff0c\u65e0\u8bba\u4ed6\u5f00\u59cb\u65f6\u8ddd\u79bb\u60ac\u5d16\u591a\u8fdc\uff0c\u9152\u9b3c\u4e5f\u662f\u80af\u5b9a\u8981\u6389\u4e0b\u60ac\u5d16\u7684\uff1b\u5982\u679cp=2\/3\uff0c\u7b97\u51faP1=1\/2\uff0cPn=(1\/2)<sup>n<\/sup>\uff0cn\u8d8a\u5927\uff0c\u5373\u9152\u9b3c\u521d\u59cb\u4f4d\u7f6e\u79bb\u60ac\u5d16\u8d8a\u8fdc\uff0c\u5931\u8db3\u7684\u53ef\u80fd\u6027\u4fbf\u8d8a\u5c0f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e0\u89c4\u884c\u8d70\u6a21\u578b\u7684\u5e94\u7528\u8303\u56f4\u5f88\u5e7f\uff0c\u9152\u9b3c\u5931\u8db3\u60ac\u5d16\u7684\u95ee\u9898\u4e5f\u6709\u8bb8\u591a\u4e0d\u540c\u7684\u6545\u4e8b\u7248\u672c\uff0c\u4f46\u63cf\u8ff0\u7684\u6570\u5b66\u6a21\u578b\u57fa\u672c\u4e00\u81f4\u3002\u6bd4\u5982\u8bf4\uff0c\u8d4c\u5f92\u7834\u4ea7\u95ee\u9898\u5c31\u662f\u5176\u4e2d\u4e00\u4f8b\uff1a\u8d4c\u5f92\u5728\u8d4c\u573a\u8d4c\u535a\uff0c\u8d62\u7684\u6982\u7387\u662fp\uff0c\u8f93\u7684\u6982\u73871-p\uff0c\u6bcf\u6b21\u7684\u8d4c\u6ce8\u4e3a1\u5143\uff0c\u5047\u8bbe\u8d4c\u5f92\u6700\u5f00\u59cb\u65f6\u6709\u8d4c\u91d1n\u5143\uff0c\u8d62\u4e86\u8d4c\u91d1\u52a0\u4e00\u5143\uff0c\u8f93\u4e86\u8d4c\u91d1\u51cf\u4e00\u5143\u3002\u95ee\uff1a\u8d4c\u5f92\u8f93\u5149\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f\u8fd9\u4e2a\u95ee\u9898\u4e0e\u4e0a\u9762\u89e3\u51b3\u7684\u9152\u9b3c\u60ac\u5d16\u95ee\u9898\u7684\u6570\u5b66\u6a21\u578b\u5b8c\u5168\u4e00\u6837\uff0c\u8d4c\u91d1\u7684\u6570\u76ee\u5bf9\u5e94\u4e8e\u9152\u9b3c\u6f2b\u6b65\u4e2d\u7684\u4e00\u7ef4\u8ddd\u79bbx\uff0c\u60ac\u5d16\u4f4d\u7f6ex=0\u4fbf\u5bf9\u5e94\u4e8e\u8d4c\u91d1\u8f93\u5149\u8d4c\u5f92\u7834\u4ea7\u3002\u4ece\u4e0a\u9762\u5206\u6790\u53ef\u77e5\uff0c\u5373\u4f7fp=1\/2\uff0c\u9152\u9b3c\u4e5f\u5fc5\u5b9a\u6389\u4e0b\u60ac\u5d16\uff0c\u5373\u8d4c\u5f92\u6700\u7ec8\u4e00\u5b9a\u7834\u4ea7\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9152\u9b3c\u5931\u8db3\u95ee\u9898\u8fd8\u53ef\u4ee5\u7a0d\u52a0\u53d8\u6362\u6784\u6210\u4e00\u4e9b\u65b0\u578b\u7684\u8da3\u9898\u3002\u6bd4\u5982\u8bf4\uff0c\u5047\u8bbe\u9152\u9b3c\u7684\u8def\u4e0a\u4e24\u8fb9\u90fd\u6709\u60ac\u5d16\uff0c\u8ba1\u7b97\u5206\u522b\u6389\u5230\u4e24\u8fb9\u60ac\u5d16\u7684\u6982\u7387\uff1b\u8d4c\u535a\u95ee\u9898\u4e0a\uff0c\u4fbf\u76f8\u5f53\u4e8e\u4e24\u4e2a\u8d4c\u5f92A\u548cB\u8d4c\u535a\uff0c\u770b\u8c01\u5148\u8f93\u5149\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u53ef\u4ee5\u5047\u8bbe\u9152\u9b3c\u7684\u8def\u4e0a\u6839\u672c\u6ca1\u6709\u60ac\u5d16\uff0c\u4e14\u8def\u7684\u4e24\u5934\u90fd\u53ef\u4ee5\u65e0\u9650\u5ef6\u4f38\uff0c\u9152\u9b3c\u4ece\u81ea\u5bb6\u95e8\u53e3\u51fa\u53d1\uff0c\u8981\u4f60\u8ba1\u7b97\uff0c\u9152\u9b3c\u51fa\u53bb\u6f2b\u6e38\u4e4b\u540e\uff0c\u6700\u540e\u8fd8\u80fd\u591f\u56de\u5230\u5bb6\u7684\u6982\u7387\u7b49\u4e8e\u591a\u5c11\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7c4d\u5308\u7259\u5229\u6570\u5b66\u5bb6\u6ce2\u5229\u4e9a\uff08George P\u00f3lya\uff0c1887\uff0d1985\uff09\u8ba4\u771f\u7814\u7a76\u4e86\u4ee5\u4e0a\u6240\u63d0\u7684\u201c\u9152\u9b3c\u56de\u5bb6\u201d\u95ee\u9898[3]\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6839\u636e\u521a\u624d\u7684\u8ba8\u8bba\uff0c\u9152\u9b3c\u968f\u673a\u6e38\u8d70\u5728\u957f\u5ea6\u65e0\u9650\uff08\u4e00\u7ef4\uff09\u6ca1\u6709\u60ac\u5d16\u7684\u8def\u4e0a\uff0c\u65f6\u5de6\u65f6\u53f3\uff0c\u4f46\u53ea\u8981\u65f6\u95f4\u8db3\u591f\u957f\uff0c\u4ed6\u6700\u7ec8\u603b\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u3002\u56e0\u6b64\uff0c\u6700\u7ec8\u56de\u5bb6\u7684\u6982\u7387\u662f100% \u3002\u4e8c\u7ef4\u7684\u60c5\u5f62\u4e5f\u7c7b\u4f3c\uff0c\u53ea\u8981\u65f6\u95f4\u8db3\u591f\u957f\uff0c\u8fd9\u4e2a\u9189\u9b3c\u603b\u80fd\u56de\u5230\u5bb6\uff0c\u6982\u7387\u4ecd\u7136\u662f 100% \u3002\u6ce2\u5229\u4e9a\u5728 1921 \u5e74\u8bc1\u660e\u4e86\u8fd9\u70b9\uff0c\u4f46\u4e09\u7ef4\u7684\u7b54\u6848\u53c8\u5982\u4f55\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ce2\u5229\u4e9a\u4ee4\u4eba\u5403\u60ca\u5730\u8bc1\u660e\u4e86\u5728\u7ef4\u6570\u6bd42\u66f4\u9ad8\u7684\u60c5\u51b5\u4e0b\uff0c\u9152\u9b3c\u56de\u5bb6\u7684\u6982\u7387\u8fdc\u5c0f\u4e8e1\uff01\u6bd4\u5982\uff0c\u5728\u4e09\u7ef4\u7f51\u683c\u4e2d\u968f\u673a\u6e38\u8d70\uff0c\u6700\u7ec8\u80fd\u56de\u5230\u51fa\u53d1\u70b9\u7684\u6982\u7387\u53ea\u6709 34% \uff0c\u8fd9\u4e5f\u88ab\u79f0\u4e3a\u6ce2\u5229\u4e9a\u5b9a\u7406\uff08\u89c1\u56fe6\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/album\/201708\/18\/063548mjbm35bspzi57zgj.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/album\/201708\/18\/063548mjbm35bspzi57zgj.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u25ba<\/strong>\u56fe6\uff1a\u201c\u9152\u9b3c\u5c0f\u9e1f\u56de\u5bb6\u201d\u5b9a\u7406<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9152\u9b3c\u4e0d\u53ef\u80fd\u5728\u7a7a\u4e2d\u6e38\u8d70\uff0c\u800c\u9e1f\u513f\u7684\u6d3b\u52a8\u7a7a\u95f4\u5374\u662f\u4e09\u7ef4\u7684\uff0c\u56e0\u6b64\uff0c\u7f8e\u56fd\u65e5\u88d4\u6570\u5b66\u5bb6\u89d2\u8c37\u9759\u592b\uff08Shizuo Kakutani\uff0c1911\u20132004\uff09\u5c06\u6ce2\u5229\u4e9a\u5b9a\u7406\u7528\u4e00\u53e5\u901a\u4fd7\u53c8\u5341\u5206\u98ce\u8da3\u7684\u8bed\u8a00\u6765\u603b\u7ed3\uff1a\u559d\u9189\u7684\u9152\u9b3c\u603b\u80fd\u627e\u5230\u56de\u5bb6\u7684\u8def\uff0c\u559d\u9189\u7684\u5c0f\u9e1f\u5219\u53ef\u80fd\u6c38\u8fdc\u4e5f\u56de\u4e0d\u4e86\u5bb6[4]\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u65e0\u89c4\u884c\u8d70\u4e5f\u662f\u7269\u7406\u5b66\u4e2d\u5e03\u6717\u8fd0\u52a8\u7684\u6570\u5b66\u6a21\u578b\uff0c\u6b32\u77e5\u8be6\u60c5\uff0c\u4e14\u542c\u4e0b\u56de\u5206\u89e3\u3002<img decoding=\"async\" src=\"http:\/\/pic.zhishifenzi.com\/3\/af\/zsfz1531326714.3876744.png\" class=\"\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53c2\u8003\u6587\u732e\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30101\u3011\u7ef4\u57fa\u767e\u79d1\uff1a\u9a6c\u5c14\u53ef\u592b\u94fe<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E9%93%BE\">https:\/\/zh.wikipedia.org\/wiki\/%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E9%93%BE<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30102\u3011wikipedia\uff1ahttps:\/\/en.wikipedia.org\/wiki\/Random_walk<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30103\u3011Finch, S. R. &#8220;P\u00f3lya&#8217;s Random Walk Constant.&#8221; \u00a75.9 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 322-331, 2003.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30104\u3011A joke by Shizuo Kakutani at a UCLA colloquium talk as attributed in Rick Durrett&#8217;s book Probability:Theory and Examples.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><em>2017\/08\/13<\/em><br>http:\/\/zhishifenzi.com\/column\/newcolumn\/1102.html<br><a href=\"https:\/\/blog.sciencenet.cn\/blog-677221-1071588.html\">https:\/\/blog.sciencenet.cn\/blog-677221-1071588.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7f16\u8005\u6309\uff1a \u524d\u51e0\u7bc7\u4e3b\u8981\u4ecb\u7ecd\u4e86\u6982\u7387\u4e0e\u7edf\u8ba1\u4e2d\u7684\u4e24\u4e2a\u91cd\u8981\u5b66\u6d3e\uff1a\u9891\u7387\u5b66\u6d3e\u548c\u8d1d\u53f6\u65af\u5b66\u6d3e\uff0c\u4ece\u800c\u5f15\u7533\u51fa\u4e86\u6982\u7387\u4e0e\u7edf\u8ba1\u9886\u57df\u6700\u57fa\u672c\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[22],"class_list":["post-7420","post","type-post","status-publish","format-standard","hentry","category-investment","tag-22"],"_links":{"self":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7420"}],"version-history":[{"count":0,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/7420\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.invbus.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}