{"id":7422,"date":"2024-06-06T15:50:23","date_gmt":"2024-06-06T07:50:23","guid":{"rendered":"https:\/\/www.btccccc.cc\/invwp\/?p=7422"},"modified":"2024-06-06T15:50:23","modified_gmt":"2024-06-06T07:50:23","slug":"%e4%b8%ba%e4%bb%80%e4%b9%88%e9%9a%8f%e6%9c%ba%e6%b8%b8%e8%b5%b0%e7%9a%84%e9%86%89%e6%b1%89%e4%b8%8d%e4%bc%9a%e8%bf%94%e5%9b%9e%e5%8e%9f%e7%82%b9%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/www.invbus.com\/blog\/?p=7422","title":{"rendered":"\u4e3a\u4ec0\u4e48\u968f\u673a\u6e38\u8d70\u7684\u9189\u6c49\u4e0d\u4f1a\u8fd4\u56de\u539f\u70b9\uff1f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u4e00\u3001\u968f\u673a\u6e38\u8d70\u95ee\u9898<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1905\u5e74\uff0c\u82f1\u56fd\u7edf\u8ba1\u5b66\u5bb6Pearson\u5728\u300a\u81ea\u7136\u300b\u6742\u5fd7\u4e0a\u516c\u5f00\u6c42\u89e3\u968f\u673a\u6e38\u8d70\u95ee\u9898\uff08Random Walk 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class=\"wp-block-paragraph\">\u65e5\u672c\u8457\u540d\u6570\u5b66\u5bb6\u89d2\u8c37\u9759\u592b\u901a\u4fd7\u5f62\u8c61\u5730\u5c06Polya\u968f\u673a\u6e38\u8d70\u5b9a\u7406\u8868\u8ff0\u4e3a\uff1a<strong>\u559d\u9189\u7684\u9152\u9b3c\u603b\u80fd\u627e\u5230\u56de\u5bb6\u7684\u8def<\/strong>\u3002\u56e0\u6b64\uff0c\u968f\u673a\u6e38\u8d70\u5b9a\u7406\u4e5f\u88ab\u79f0\u4e3a<strong>\u9152\u9b3c\u56de\u5bb6\u5b9a\u7406<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u3001\u4e0e\u9ad8\u5c14\u987f\u677f\u5b9e\u9a8c\u7ed3\u679c\u4e0d\u7b26<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9ad8\u5c14\u987f\u677f\u662f\u82f1\u56fd\u751f\u7269\u7edf\u8ba1\u5b66\u5bb6\u9ad8\u5c14\u987f\uff08Galton\uff09\u4e13\u95e8\u8bbe\u8ba1\u7528\u6765\u6f14\u793a\u4e00\u7ef4\u968f\u673a\u6e38\u8d70\u53ca\u6b63\u6001\u5206\u5e03\u73b0\u8c61\u7684\u5b9e\u9a8c\u88c5\u7f6e \u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/home\/202010\/29\/154120lon2nm6xqgj6js6t.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/home\/202010\/29\/154120lon2nm6xqgj6js6t.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\u9ad8\u5c14\u987f\u677f.png\" title=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u56fe1 \u9ad8\u5c14\u987f\u677f\u968f\u673a\u6e38\u8d70\u5b9e\u9a8c<\/p>\n\n\n\n<p 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class=\"wp-block-paragraph\">\u5c0f\u7403\u7684\u4e0b\u843d\u8fc7\u7a0b\u5c31\u76f8\u5f53\u4e8e\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u3002\u628a\u5927\u91cf\u5c0f\u7403\u9010\u4e2a\u4ece\u5165\u53e3\u5904\u653e\u4e0b\uff0c\u53ea\u8981\u9ad8\u5c14\u987f\u677f\u7684\u9762\u79ef\u8db3\u591f\u5927\u3001\u9489\u5b50\u6570\u91cf\u8db3\u591f\u591a\uff0c\u843d\u5728\u5e95\u90e8\u683c\u5b50\u5185\u7684\u5c0f\u7403\u5c06\u5f62\u6210\u4e0e\u6b63\u6001\u5206\u5e03\u66f2\u7ebf\u76f8\u4f3c\u7684\u4e2d\u95f4\u9ad8\u3001\u4e24\u8fb9\u4f4e\u7684\u949f\u5f62\u66f2\u7ebf\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u9ad8\u5c14\u987f\u677f\u9762\u79ef\u8db3\u591f\u5927\uff0c\u5c0f\u7403\u5728\u4e0b\u843d\u8fc7\u7a0b\u4e2d\u5c06\u9010\u6e10\u5411\u5de6\u53f3\u4e24\u4e2a\u65b9\u5411\u6269\u6563\uff0c\u8868\u660e\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u7684\u5c0f\u7403\uff08\u9189\u6c49\uff09\u968f\u65f6\u95f4\u8fdc\u79bb\u539f\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e09\u3001\u4e0e\u968f\u673a\u6e38\u8d70\u6a21\u578b\u7684\u6570\u5b57\u7279\u5f81\u4e0d\u4e00\u81f4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300a\u968f\u673a\u8fc7\u7a0b\u300b\u6559\u79d1\u4e66\u7ed9\u51fa\u4e86\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u7684\u6570\u5b66\u6a21\u578b<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D%3DS_%7B0%7D%2BX_%7B1%7D%2BX_%7B2%7D%2B%5Ccdot%5Ccdot%5Ccdot+%2BX_%7Bn%7D'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D%3DS_%7B0%7D%2BX_%7B1%7D%2BX_%7B2%7D%2B%5Ccdot%5Ccdot%5Ccdot+%2BX_%7Bn%7D\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f0f\u4e2d&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=X_%7B1%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u3001&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=X_%7B2%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\uff0c\u2026\uff0c&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=X_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e3a\u72ec\u7acb\u540c\u5206\u5e03&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%EF%BC%88i.i.d.%EF%BC%89\" alt=\"[\u516c\u5f0f]\">&nbsp;\u968f\u673a\u53d8\u91cf\u3002\u5f53&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=S_%7B0%7D%3D0\" alt=\"[\u516c\u5f0f]\">&nbsp;\u65f6\uff0c\u79f0\u4e3a\u4ece\u539f\u70b9\u51fa\u53d1\u7684\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u5411\u5de6\u79fb\u52a8\u4e00\u6b65\u7684\u6982\u7387\u4e0e\u5411\u53f3\u79fb\u52a8\u4e00\u6b65\u7684\u6982\u7387\u76f8\u7b49\uff0c\u6709<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=P%28X_%7Bi%7D%3D1%29%3DP%28X_%7Bi%7D%3D-1%29%3D%5Cfrac%7B1%7D%7B2%7D'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=P%28X_%7Bi%7D%3D1%29%3DP%28X_%7Bi%7D%3D-1%29%3D%5Cfrac%7B1%7D%7B2%7D\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4e8e&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=E%5BX_%7Bi%7D%5D%3D0\" alt=\"[\u516c\u5f0f]\">&nbsp;\uff0c&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=D%5BX_%7Bi%7D%5D%3D1\" alt=\"[\u516c\u5f0f]\">&nbsp;\uff0c\u56e0\u6b64\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u4e3a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=E%5BS_%7Bn%7D%5D%3D0'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=E%5BS_%7Bn%7D%5D%3D0\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=D%5BS_%7Bn%7D%5D%3Dn'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" 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class=\"wp-block-paragraph\">\u65b9\u5dee\u662f\u7528\u6765\u523b\u753b\u968f\u673a\u53d8\u91cf\u504f\u79bb\u5747\u503c\u5206\u6563\u7a0b\u5ea6\u7684\u6570\u5b57\u7279\u5f81\uff0c\u5ea6\u91cf\u7684\u662f\u6240\u6709\u6837\u672c\u8f68\u9053\uff08\u5c0f\u7403\u6216\u9189\u6c49\uff09\u504f\u79bb\u5747\u503c\u7684\u53d1\u6563\u7a0b\u5ea6\uff0c\u56e0\u6b64\uff0c&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=D%5BS_%7Bn%7D%5D%3Dn\" alt=\"[\u516c\u5f0f]\">&nbsp;\u8868\u660e\uff0c\u968f\u7740\u6b65\u6570&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u589e\u52a0\uff0c\u5927\u91cf\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u7684\u5c0f\u7403\u6216\u9189\u6c49\u4f1a\u8fdc\u79bb\u539f\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56fe2\u7ed9\u51fa\u4e86\u5927\u91cf\u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u9189\u6c49\u7684\u6837\u672c\u8f68\u9053\u4eff\u771f\u66f2\u7ebf\uff0c\u663e\u7136\uff0c\u6240\u6709\u6837\u672c\u8f68\u9053\u5728\u7b2c&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">&nbsp;\u6b65\u65f6\u7684\u4f4d\u7f6e\u670d\u4ece&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%EF%BC%880%EF%BC%8Cn%EF%BC%89\" alt=\"[\u516c\u5f0f]\">&nbsp;\u6b63\u6001\u5206\u5e03\u3002\u4ece\u56fe\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u5bf9\u4e8e\u5176\u4e2d\u4efb\u4f55\u4e00\u6761\u6837\u672c\u8f68\u9053\uff08\u9189\u6c49\uff09\uff0c\u90fd\u968f\u6b65\u6570&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u589e\u52a0\u8fdc\u79bb\u539f\u70b9\uff0c\u4e0e\u9ad8\u5c14\u987f\u677f\u7684\u5b9e\u9a8c\u7ed3\u679c\u76f8\u540c \u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/image.sciencenet.cn\/home\/202010\/29\/154305cze1ol3ekcksv1ss.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"http:\/\/image.sciencenet.cn\/home\/202010\/29\/154305cze1ol3ekcksv1ss.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\u968f\u673a\u6e38\u8d70\u4eff\u771f.png\" title=\"\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u56fe2 \u4e00\u7ef4\u7b80\u5355\u968f\u673a\u6e38\u8d70\u6837\u672c\u8f68\u9053<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56db\u3001Polya\u968f\u673a\u6e38\u8d70\u5b9a\u7406\u7684\u8bc1\u660e\u65b9\u6cd5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Polya\u968f\u673a\u6e38\u8d70\u5b9a\u7406\u53ea\u8bc1\u660e\u4e86\u968f\u673a\u6e38\u8d70\u5177\u6709\u5e38\u8fd4\u6027\uff08Recurrence\uff09\uff0c\u5373<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=P%5BS_%7Bn%7D%3D0%EF%BC%8Ci.o.%5D%3D1'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=P%5BS_%7Bn%7D%3D0%EF%BC%8Ci.o.%5D%3D1\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e38\u8fd4\u6027\u53ea\u8868\u793a\u968f\u673a\u53d8\u91cf&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\uff08\u9189\u6c49\u96c6\u5408\uff09\u8fd4\u56de\u539f\u70b9\u65e0\u7a77\u591a\u6b21\u7684\u6982\u7387\u7b49\u4e8e1\uff0c\u4f46\u4e0d\u80fd\u8bf4\u660e\u6837\u672c\u8f68\u9053&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\uff08\u4e00\u4e2a\u9189\u6c49\uff09\u6700\u7ec8\u4e00\u5b9a\u4f1a\u8fd4\u56de\u539f\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6709\u65e0\u6570\u4e2a\u9189\u6c49\u4ece\u539f\u70b9\u51fa\u53d1\uff0c\u5728\u7b2c&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">&nbsp;\u6b65\u65f6\uff0c\u6240\u6709\u9189\u6c49\u7684\u4f4d\u7f6e\u670d\u4ece&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%EF%BC%880%EF%BC%8Cn%EF%BC%89\" alt=\"[\u516c\u5f0f]\">&nbsp;\u6b63\u6001\u5206\u5e03\uff0c\u56e0\u6b64\uff0c\u968f\u673a\u6e38\u8d70\u8fc7\u7a0b\u5177\u6709\u5982\u4e0b\u4e24\u4e2a\u91cd\u8981\u6027\u8d28\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff081\uff09\u968f\u673a\u6e38\u8d70\u662f\u4e00\u4e2a\u6269\u6563\u8fc7\u7a0b\uff0c\u9189\u6c49\u6837\u672c\u6574\u4f53\u5411\u8fdc\u79bb\u539f\u70b9\u7684\u65b9\u5411\u6269\u6563\uff1b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff082\uff09\u5728\u539f\u70b9\u59cb\u7ec8\u53ef\u4ee5\u770b\u5230\u9189\u6c49\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u539f\u70b9\u770b\u5230\u9189\u6c49\u7684\u6982\u7387\u7b49\u4e8e1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Polya\u53ea\u662f\u5229\u7528\u6982\u7387\u8ba1\u7b97\u65b9\u6cd5\u8bc1\u660e\u4e86\u7b2c\u4e8c\u4e2a\u6027\u8d28\uff0c\u5374\u5f97\u51fa\u4e86\u6240\u6709\u9189\u6c49\u6700\u7ec8\u4f1a\u8fd4\u56de\u539f\u70b9\u7684\u7ed3\u8bba\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e94\u3001\u968f\u673a\u6e38\u8d70\u4f4d\u79fb\u516c\u5f0f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pearson\u7684\u968f\u673a\u6e38\u8d70\u95ee\u9898\u662f\u6c42\u89e3\u6837\u672c\u8f68\u9053&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u65f6\u95f4\u6027\u8d28\uff0c\u800c\u975e\u968f\u673a\u53d8\u91cf&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;=0\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=X_%7Bi%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e3a\u72ec\u7acb\u540c\u5206\u5e03\u968f\u673a\u53d8\u91cf\uff0c\u5373&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=X_%7Bi%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u6837\u672c\u8f68\u9053&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u5728\u4e0d\u540c\u65f6\u523b\u4e92\u4e0d\u76f8\u5173\uff0c\u56e0\u6b64&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u65f6\u95f4\u81ea\u76f8\u5173\u51fd\u6570\u4e3a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=R_%7Bx%7D%28k%29%3D%5Cdelta%28k%29'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=R_%7Bx%7D%28k%29%3D%5Cdelta%28k%29\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f0f\u4e2d&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cdelta%28k%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e3a\u5355\u4f4d\u51b2\u51fb\u5e8f\u5217\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6839\u636e\u7ef4\u7eb3-\u8f9b\u94a6\u5b9a\u7406\uff0c\u5e73\u7a33\u968f\u673a\u8fc7\u7a0b\u7684\u81ea\u76f8\u5173\u51fd\u6570\u4e0e\u5176\u529f\u7387\u8c31\u5bc6\u5ea6\u4e4b\u95f4\u6784\u6210\u4e00\u5bf9\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u56e0\u6b64&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u4e3a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=P_%7Bx%7D%28%5Comega%29%3D1'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=P_%7Bx%7D%28%5Comega%29%3D1\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8868\u660e&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u529f\u7387\u8c31\u5bc6\u5ea6\u5728\u6574\u4e2a\u9891\u7387\u8f74\u4e0a\u5747\u5300\u5206\u5e03\uff0c\u56e0\u6b64&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e3a\u767d\u566a\u58f0\u65f6\u95f4\u5e8f\u5217\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u524d\u9762\u4e00\u7ef4\u968f\u673a\u6e38\u8d70\u968f\u673a\u53d8\u91cf&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=S_%7Bn%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u6a21\u578b\uff0c\u53ef\u76f4\u63a5\u5199\u51fa\u6837\u672c\u8f68\u9053&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u6a21\u578b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29%3Dx%281%29%2Bx%282%29%2B%5Ccdot%5Ccdot%5Ccdot%2Bx%28n%29\" alt=\"[\u516c\u5f0f]\">&nbsp;=&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7Bx%28i%29%7D\" alt=\"[\u516c\u5f0f]\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u5c06\u4e0a\u5f0f\u6539\u5199\u4e3a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=s%28n%29%3D%5B%5Cfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7Bx%28i%29%7D%5D%5Ccdot+n%3D%5Cbar%7Bx%28n%29%7D%5Ccdot+n'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29%3D%5B%5Cfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7Bx%28i%29%7D%5D%5Ccdot+n%3D%5Cbar%7Bx%28n%29%7D%5Ccdot+n\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f0f\u4e2d\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cbar%7Bx%28n%29%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e3a&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=x%28i%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u5728\u533a\u95f4&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5B0%EF%BC%8Cn%5D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e0a\u7684\u7b97\u6570\u5e73\u5747\u503c\uff0c\u5176\u7269\u7406\u610f\u4e49\u4e3a\u4e00\u7ef4\u968f\u673a\u6e38\u8d70\u7684\u8d28\u70b9\uff08\u9189\u6c49\uff09\u5728\u533a\u95f4&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5B0%EF%BC%8Cn%5D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e0a\u7684\u5e73\u5747\u901f\u5ea6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\uff0c\u4e00\u7ef4\u968f\u673a\u6e38\u8d70\u7684\u4f4d\u79fb&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7b49\u4e8e\u5176\u5e73\u5747\u901f\u5ea6&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cbar%7Bx%28n%29%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e0e\u6b65\u6570&nbsp;<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">&nbsp;\u7684\u4e58\u79ef\uff0c&nbsp;<img 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src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cbar%7Bx%28n%29%7D\" alt=\"[\u516c\u5f0f]\">&nbsp;\u4e5f\u662f\u968f\u673a\u7684\uff0c\u5176\u65b9\u5dee\u4e3a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/www.zhihu.com\/equation?tex=D%5B%5Cbar%7Bx%28n%29%7D%5D%3D%5Cfrac%7B1%7D%7Bn%7D'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  decoding=\"async\" data-original=\"https:\/\/www.zhihu.com\/equation?tex=D%5B%5Cbar%7Bx%28n%29%7D%5D%3D%5Cfrac%7B1%7D%7Bn%7D\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"[\u516c\u5f0f]\"\/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u00a0<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">\u00a0\u5145\u5206\u5927\u65f6\uff0c<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cbar%7Bx%28n%29%7D\" alt=\"[\u516c\u5f0f]\">\u00a0\u7684\u65b9\u5dee\u8d8b\u4e8e\u96f6\uff0c<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=%5Cbar%7Bx%28n%29%7D\" alt=\"[\u516c\u5f0f]\">\u00a0\u8d8b\u4e8e\u4e00\u4e2a\u5e38\u6570\uff0c\u56e0\u6b64\uff0c\u4e00\u7ef4\u968f\u673a\u6e38\u8d70\u7684\u4f4d\u79fb<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=s%28n%29\" alt=\"[\u516c\u5f0f]\">\u4e0e\u6b65\u6570<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">\u6210\u6b63\u6bd4\uff0c\u968f\u7740\u6b65\u6570\u00a0<img decoding=\"async\" src=\"https:\/\/www.zhihu.com\/equation?tex=n\" alt=\"[\u516c\u5f0f]\">\u00a0\u7684\u589e\u52a0\uff0c\u9189\u6c49\u4f1a\u8fdc\u79bb\u8fdc\u70b9\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u6587\u6765\u81ea\u9ad8\u5b8f\u79d1\u5b66\u7f51\u535a\u5ba2\u3002<br>\u94fe\u63a5\u5730\u5740\uff1a<a href=\"https:\/\/blog.sciencenet.cn\/blog-3418723-1256235.html\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/blog.sciencenet.cn\/blog-3418723-1256235.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u3001\u968f\u673a\u6e38\u8d70\u95ee\u9898 1905\u5e74\uff0c\u82f1\u56fd\u7edf\u8ba1\u5b66\u5bb6Pearson\u5728\u300a\u81ea\u7136\u300b\u6742\u5fd7\u4e0a\u516c\u5f00\u6c42\u89e3\u968f\u673a\u6e38\u8d70\u95ee\u9898\uff08Random W 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