{"id":6521,"date":"2024-08-06T07:01:01","date_gmt":"2024-08-05T23:01:01","guid":{"rendered":""},"modified":"2024-08-06T07:01:01","modified_gmt":"2024-08-05T23:01:01","slug":"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1","status":"publish","type":"post","link":"https:\/\/mushiming.com\/6521.html","title":{"rendered":"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<h2 id=\"\u4e8c\u6570\u636e\u751f\u6210\">\u4e8c\u3001\u6570\u636e\u751f\u6210<\/h2>\n<blockquote>\n<p>\u539f\u6587\uff1aDS-100\/textbook\/notebooks\/ch02<\/p>\n<p>\u8bd1\u8005\uff1a\u98de\u9f99<\/p>\n<p>\u534f\u8bae\uff1aCC BY-NC-SA 4.0<\/p>\n<p>\u81ea\u8c6a\u5730\u91c7\u7528\u8c37\u6b4c\u7ffb\u8bd1<\/p>\n<\/blockquote>\n<p>\u6570\u636e\u79d1\u5b66\u5f88\u96be\u6210\u4e3a\u6ca1\u6709\u6570\u636e\u7684\u79d1\u5b66\u3002 \u56e0\u6b64\u91cd\u8981\u7684\u662f\uff0c\u6211\u4eec\u901a\u8fc7\u4e86\u89e3\u6211\u4eec\u7684\u6570\u636e\u662f\u5982\u4f55\u751f\u6210\u7684\uff0c\u6765\u542f\u52a8\u4efb\u4f55\u6570\u636e\u5206\u6790\u3002<\/p>\n<p>\u5728\u672c\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u6570\u636e\u6765\u6e90\u3002 \u867d\u7136\u672f\u8bed\u201c\u6570\u636e\u6765\u6e90\u201d\u901a\u5e38\u6307\u7684\u662f\u6570\u636e\u7684\u6574\u4e2a\u5386\u53f2\uff0c\u4ee5\u53ca\u5b83\u968f\u65f6\u95f4\u53d8\u5316\u7684\u4f4d\u7f6e\uff0c\u4f46\u6211\u4eec\u5c06\u5728\u672c\u6559\u79d1\u4e66\u4e2d\u4f7f\u7528\u8fd9\u4e2a\u672f\u8bed\uff0c\u6765\u6307\u4ee3\u6211\u4eec\u7684\u6570\u636e\u7684\u751f\u6210\u8fc7\u7a0b\u3002 \u8bb8\u591a\u4eba\u5f97\u51fa\u4e86\u4e0d\u6210\u719f\u7684\u7ed3\u8bba\uff0c\u56e0\u4e3a\u4ed6\u4eec\u5bf9\u6570\u636e\u7684\u7406\u89e3\u4e0d\u591f\u7ec6\u81f4; \u6211\u4eec\u5c06\u8ba8\u8bba\u4e00\u4e2a\u4f8b\u5b50\u6765\u8bc1\u660e\uff0c\u6982\u7387\u62bd\u6837\u5728\u6570\u636e\u79d1\u5b66\u4e2d\u7684\u91cd\u8981\u6027\u3002<\/p>\n<h3 id=\"dewey-\u51fb\u8d25\u4e86-truman\">Dewey \u51fb\u8d25\u4e86 Truman<\/h3>\n<p>\u5728 1948 \u5e74\u7684\u7f8e\u56fd\u603b\u7edf\u5927\u9009\u4e2d\uff0c\u7ebd\u7ea6\u5dde\u5dde\u957f\u6258\u9a6c\u65af\u675c\u5a01\uff08Thomas Dewey\uff09\u4e0e\u73b0\u4efb\u7684\u675c\u9c81\u95e8\uff08Harry Truman\uff09\u7ade\u4e89\u3002 \u50cf\u5f80\u5e38\u4e00\u6837\uff0c\u4e00\u4e9b\u6295\u7968\u673a\u6784\u8fdb\u884c\u6c11\u610f\u8c03\u67e5\uff0c\u6765\u9884\u6d4b\u54ea\u4e2a\u5019\u9009\u4eba\u66f4\u6709\u53ef\u80fd\u8d62\u5f97\u9009\u4e3e\u3002<\/p>\n<h4 id=\"1936-\u5e74\u4ee5\u524d\u7684\u6c11\u610f\u8c03\u67e5\u707e\u96be\">1936 \u5e74\uff1a\u4ee5\u524d\u7684\u6c11\u610f\u8c03\u67e5\u707e\u96be<\/h4>\n<p>\u5728 1936 \u5e74\uff0c1948 \u5e74\u7684\u4e09\u6b21\u9009\u4e3e\u4e4b\u524d\uff0c\u300a\u6587\u5b66\u6587\u6458\u300b\uff08Literary Digest\uff09\u9884\u8a00\uff0c\u5bcc\u5170\u514b\u6797\u00b7\u5fb7\u62c9\u8bfa\u00b7\u7f57\u65af\u798f\u4f1a\u9047\u5230\u65ad\u5d16\u5f0f\u4e0b\u8dcc\uff0c\u8fd9\u4f7f\u5176\u58f0\u540d\u72fc\u85c9\u3002\u4e3a\u4e86\u505a\u51fa\u8fd9\u4e2a\u65ad\u8a00\uff0c\u8be5\u6742\u5fd7\u6839\u636e\u7535\u8bdd\u548c\u8f66\u7ba1\u5c40\u8c03\u67e5\u4e86 200 \u591a\u4e07\u4eba\u7684\u6837\u672c\u3002 \u4f60\u53ef\u80fd\u77e5\u9053\uff0c\u8fd9\u79cd\u62bd\u6837\u65b9\u6848\u5b58\u5728\u62bd\u6837\u504f\u5dee\uff1a\u90a3\u4e9b\u62e5\u6709\u7535\u8bdd\u548c\u6c7d\u8f66\u7684\u4eba\u5f80\u5f80\u6bd4\u6ca1\u6709\u7684\u4eba\u66f4\u5bcc\u6709\u3002 \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u62bd\u6837\u504f\u5dee\u5982\u6b64\u4e4b\u5927\uff0c\u8db3\u4ee5\u4f7f\u300a\u6587\u5b66\u6587\u6458\u300b\u8ba4\u4e3a\u7f57\u65af\u798f\u53ea\u6709 43% \u7684\u5927\u4f17\u9009\u7968\uff0c\u800c\u4ed6\u6700\u7ec8\u4ee5 61% \u7684\u5927\u4f17\u9009\u7968\u80dc\u51fa\uff0c\u76f8\u5dee\u8fd1 20%\uff0c\u8fd9\u662f\u6709\u53f2\u4ee5\u6765\uff0c\u7531\u6c11\u610f\u8c03\u67e5\u5f15\u53d1\u7684\u6700\u5927\u7684\u9519\u8bef\u3002\u201c\u6587\u5b66\u6587\u6458\u201d\u4e0d\u4e45\u4e4b\u540e\u5c31\u505c\u520a\u4e86 [1]\u3002<\/p>\n<blockquote>\n<p>[1] https:\/\/www.qualtrics.com\/blog\/the-1936-election-a-polling-catastrophe\/<\/p>\n<\/blockquote>\n<h4 id=\"1948-\u5e74\u76d6\u6d1b\u666egallup\u6c11\u610f\u8c03\u67e5\">1948 \u5e74\uff1a\u76d6\u6d1b\u666e\uff08Gallup\uff09\u6c11\u610f\u8c03\u67e5<\/h4>\n<p>\u4e3a\u4e86\u4ece\u8fc7\u53bb\u7684\u9519\u8bef\u4e2d\u5b66\u4e60\uff0c\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u91c7\u7528\u4e86\u4e00\u79cd\u79f0\u4e3a\u914d\u989d\u62bd\u6837\u7684\u65b9\u6cd5\uff0c\u6765\u9884\u6d4b 1948 \u5e74\u9009\u4e3e\u7684\u7ed3\u679c\u3002 \u5728\u4ed6\u4eec\u7684\u62bd\u6837\u65b9\u6848\u4e2d\uff0c\u6bcf\u4f4d\u91c7\u8bbf\u8005\u90fd\u4f1a\u8c03\u67e5\u6765\u81ea\u6bcf\u4e2a\u7279\u5f81\u7c7b\u522b\u7684\u4e00\u5b9a\u6570\u91cf\u7684\u4eba\u3002 \u4f8b\u5982\uff0c\u91c7\u8bbf\u8005\u9700\u8981\u91c7\u8bbf\u4e0d\u540c\u5e74\u9f84\uff0c\u79cd\u65cf\u548c\u6536\u5165\u6c34\u5e73\u7684\u7537\u6027\u548c\u5973\u6027\uff0c\u6765\u5339\u914d\u7f8e\u56fd\u4eba\u53e3\u666e\u67e5\u7684\u4eba\u53e3\u7279\u5f81\u3002 \u8fd9\u786e\u4fdd\u4e86\u6c11\u610f\u8c03\u67e5\u4e0d\u4f1a\u9057\u6f0f\u6295\u7968\u4eba\u7fa4\u7684\u91cd\u8981\u5b50\u5206\u7ec4\u3002<\/p>\n<p>\u4f7f\u7528\u8fd9\u79cd\u65b9\u6cd5\uff0c\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u9884\u6d4b\uff0c\u6258\u9a6c\u65af\u675c\u5a01\u5c06\u6bd4\u54c8\u91cc\u675c\u9c81\u95e8\u591a\u8d62\u5f97 5% \u7684\u5927\u4f17\u9009\u7968\u3002 \u8fd9\u79cd\u5dee\u5f02\u975e\u5e38\u663e\u7740\uff0c\u4f17\u6240\u5468\u77e5\uff0c\u300a\u829d\u52a0\u54e5\u8bba\u575b\u62a5\u300b\uff08 Chicago Tribune\uff09\u7684\u6807\u9898\u662f\u201c\u675c\u5a01\u51fb\u8d25\u675c\u9c81\u95e8\u201d\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/2-1.jpg\" =\"\" =\"\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4 id=\"\u914d\u989d\u62bd\u6837\u7684\u95ee\u9898\">\u914d\u989d\u62bd\u6837\u7684\u95ee\u9898<\/h4>\n<p>\u867d\u7136\u914d\u989d\u62bd\u6837\u786e\u5b9e\u6709\u52a9\u4e8e\u6c11\u610f\u8c03\u67e5\u8005\u51cf\u5c11\u62bd\u6837\u504f\u5dee\uff0c\u4f46\u5b83\u4ee5\u53e6\u4e00\u79cd\u65b9\u5f0f\u5f15\u5165\u4e86\u504f\u5dee\u3002\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u673a\u6784\u5bf9\u5176\u91c7\u8bbf\u8005\u8bf4\uff0c\u53ea\u8981\u4ed6\u4eec\u5b9e\u73b0\u4e86\u914d\u989d\uff0c\u4ed6\u4eec\u5c31\u53ef\u4ee5\u91c7\u8bbf\u4ed6\u4eec\u60f3\u8981\u7684\u4efb\u4f55\u4eba\u3002\u4e3a\u4ec0\u4e48\u91c7\u8bbf\u8005\u7684\u6295\u7968\u7ed3\u679c\u4e0e\u5171\u548c\u515a\u4eba\u4e0d\u6210\u6bd4\u4f8b\uff0c\u4ee5\u4e0b\u662f\u4e00\u4e2a\u53ef\u80fd\u7684\u89e3\u91ca\uff1a\u5f53\u65f6\uff0c\u5171\u548c\u515a\u4eba\u5e73\u5747\u8f83\u5bcc\u88d5\uff0c\u800c\u4e14\u66f4\u6709\u53ef\u80fd\u5c45\u4f4f\u5728\u8f83\u597d\u7684\u793e\u533a\uff0c\u8fd9\u4f7f\u4ed6\u4eec\u66f4\u5bb9\u6613\u53d7\u5230\u91c7\u8bbf\u3002\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u9884\u6d4b\u7684\u5171\u548c\u515a\u7968\u6570\uff0c\u5c06\u6bd4\u4e4b\u524d\u7684 3 \u6b21\u9009\u4e3e\u7684\u5b9e\u9645\u7ed3\u679c\u591a\u51fa 2 % \u81f3 6%\u3002<\/p>\n<p>\u8fd9\u4e9b\u4f8b\u5b50\u5f3a\u8c03\u4e86\u5728\u6570\u636e\u6536\u96c6\u8fc7\u7a0b\u4e2d\uff0c\u5c3d\u53ef\u80fd\u7406\u89e3\u62bd\u6837\u504f\u5dee\u7684\u91cd\u8981\u6027\u3002\u300a\u6587\u5b66\u6587\u6458\u300b\u548c\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u90fd\u9519\u8bef\u5730\u8ba4\u4e3a\uff0c\u5f53\u4ed6\u4eec\u7684\u62bd\u6837\u65b9\u6848\u59cb\u7ec8\u57fa\u4e8e\u4eba\u7c7b\u5224\u65ad\u65f6\uff0c\u4ed6\u4eec\u7684\u65b9\u6cd5\u662f\u6ca1\u6709\u504f\u5dee\u7684\u3002<\/p>\n<p>\u6211\u4eec\u73b0\u5728\u4f9d\u9760\u6982\u7387\u62bd\u6837\uff0c\u4e00\u7ec4\u62bd\u6837\u65b9\u6cd5\uff0c\u4e3a\u6bcf\u4e2a\u6837\u672c\u7684\u5916\u89c2\u8d4b\u4e88\u7cbe\u786e\u7684\u6982\u7387\uff0c\u6765\u5c3d\u53ef\u80fd\u51cf\u5c11\u6570\u636e\u6536\u96c6\u8fc7\u7a0b\u4e2d\u7684\u504f\u5dee\u3002<\/p>\n<h4 id=\"\u5927\u6570\u636e\">\u5927\u6570\u636e\uff1f<\/h4>\n<p>\u5728\u5927\u6570\u636e\u65f6\u4ee3\uff0c\u6211\u4eec\u8bd5\u56fe\u901a\u8fc7\u6536\u96c6\u66f4\u591a\u6570\u636e\u6765\u5e94\u5bf9\u504f\u5dee\u3002 \u6bd5\u7adf\uff0c\u6211\u4eec\u77e5\u9053\u4eba\u53e3\u666e\u67e5\u4f1a\u5411\u6211\u4eec\u63d0\u4f9b\u5b8c\u7f8e\u7684\u4f30\u8ba1\uff1b\u4e0d\u7ba1\u62bd\u6837\u6280\u672f\u5982\u4f55\uff0c\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6837\u672c\u4e0d\u5e94\u8be5\u7ed9\u51fa\u51e0\u4e4e\u5b8c\u7f8e\u7684\u4f30\u8ba1\u503c\u561b\uff1f<\/p>\n<p>\u5728\u8ba8\u8bba\u6982\u7387\u62bd\u6837\u65b9\u6cd5\u6765\u6bd4\u8f83\u4e24\u79cd\u65b9\u6cd5\u4e4b\u540e\uff0c\u6211\u4eec\u5c06\u56de\u5230\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<h3 id=\"\u6982\u7387\u62bd\u6837\">\u6982\u7387\u62bd\u6837<\/h3>\n<p>\u4e0e\u4efb\u610f\u62bd\u6837\u4e0d\u540c\uff0c\u6982\u7387\u62bd\u6837\u5141\u8bb8\u6211\u4eec\uff0c\u4e3a\u62bd\u53d6\u7279\u5b9a\u6837\u672c\u7684\u4e8b\u4ef6\u5206\u914d\u7cbe\u786e\u7684\u6982\u7387\u3002 \u6211\u4eec\u5c06\u9996\u5148\u56de\u987e Data8 \u4e2d\u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\u7136\u540e\u4ecb\u7ecd\u6982\u7387\u62bd\u6837\u7684\u4e24\u79cd\u66ff\u4ee3\u65b9\u6cd5\uff1a\u6574\u7fa4\u62bd\u6837\u548c\u5206\u5c42\u62bd\u6837\u3002<\/p>\n<p>\u5047\u8bbe\u6211\u4eec\u6709 6 \u4e2a\u4e2a\u4f53\u3002 \u6211\u4eec\u5df2\u7ecf\u7ed9\u4e86\u6bcf\u4e2a\u4e2a\u4f53\u4e00\u5c01 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-970be4fa707cabaac0de6542fd12a90b.gif\" =\"\" =\"A-F\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u4fe1\u3002<\/p>\n<h4 id=\"\u7b80\u5355\u968f\u673a\u62bd\u6837\">\u7b80\u5355\u968f\u673a\u62bd\u6837<\/h4>\n<p>\u4ece\u8fd9\u4e2a\u603b\u4f53\u4e2d\u62bd\u53d6\u5927\u5c0f\u4e3a 2 \u7684\u7b80\u5355\u968f\u673a\u6837\u672c\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u5355\u4e2a\u7d22\u5f15\u5361\u7247\u4e0a\u5199\u4e0b <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-970be4fa707cabaac0de6542fd12a90b.gif\" =\"\" =\"A-F\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u6bcf\u4e2a\u5b57\u6bcd\uff0c\u5c06\u6240\u6709\u5361\u7247\u653e\u5165\u4e00\u4e2a\u5e3d\u5b50\u4e2d\uff0c\u5145\u5206\u6df7\u5408\u8fd9\u4e9b\u5361\u7247\uff0c\u7136\u540e\u62bd\u51fa\u4e24\u5f20\u5361\u7247\u800c\u4e0d\u770b\u5b83\u4eec\u3002 \u4e5f\u5c31\u662f\u8bf4\uff0cSRS \u662f\u65e0\u653e\u56de\u968f\u673a\u62bd\u6837\u3002<\/p>\n<p>\u8fd9\u91cc\u662f\u6240\u6709\u53ef\u80fd\u7684\u5927\u5c0f\u4e3a 2 \u7684\u6837\u672c\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-1271f64c0c70bad9a2c94b2e0d6cb71a.gif\" =\"\" =\"\\begin{matrix} AB &amp; BC &amp; CD &amp; DE &amp; EF\\\\ AC&amp;BD&amp;CE&amp;DF&amp;\\\\ AD&amp;BE&amp;CF&amp;&amp;\\\\ AE&amp;BF&amp;&amp;&amp;\\\\ AF&amp;&amp;&amp;&amp;\\\\ \\end{matrix}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c4\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c4\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6211\u4eec\u7684\u5927\u5c0f\u4e3a 6 \u7684\u603b\u4f53\uff0c\u6709 15 \u975e\u53ef\u80fd\u7684\u6837\u672c\uff0c\u5927\u5c0f 2\u3002 \u8ba1\u7b97\u53ef\u80fd\u7684\u6837\u672c\u6570\u91cf\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-980d35bc3500be6859da688d4bfb40d5.gif\" =\"\" =\"\\binom{6}{2} = \\frac{6!}{2!4!} = 15\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c5\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c5\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u7531\u4e8e\u5728 SRS \u4e2d\u6211\u4eec\u968f\u673a\u5747\u5300\u62bd\u6837\uff0c\u8fd9\u4e9b 15 \u975e\u6837\u672c\u4e2d\u7684\u6bcf\u4e2a\u90fd\u662f\u7b49\u53ef\u80fd\u9009\u4e2d\u7684\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-43f7edc01dee06930303a27d4a437ff4.gif\" =\"\" =\"P(AB) = P(CD) = \\ldots = P(DF) = \\frac{1}{15}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c6\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c6\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528\u8fd9\u79cd\u51e0\u7387\u673a\u5236\uff0c\u6765\u56de\u7b54\u6837\u672c\u7ec4\u6210\u7684\u5176\u4ed6\u95ee\u9898\u3002 \u4f8b\u5982\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-903aed24476309827ae2cec60c543ebb.gif\" =\"\" =\"P(A \\text{ in sample}) = \\frac{5}{15} = \\frac{1}{3}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c7\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c7\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6839\u636e\u5bf9\u79f0\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-4c3e4d06b33339c2972345ab3b86e312.gif\" =\"\" =\"P(A \\text{ in sample}) = P(F \\text{ in sample}) = \\frac{1}{3}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c8\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c8\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u53e6\u4e00\u79cd\u8ba1\u7b97 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-cc197a2629da3459df32e6fa7c6f234f.gif\" =\"\" =\" P(A \\text{ in sample}) \" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c9\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c9\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u65b9\u6cd5\u662f\uff0c\u786e\u8ba4\u5bf9\u4e8e\u6837\u672c\u4e2d\u7684 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7fc56270e7a70fa81a5935b72eacbe29.gif\" =\"\" =\"A\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u6211\u4eec\u9700\u8981\u5c06\u5176\u4f5c\u4e3a\u7b2c\u4e00\u4e2a\u5f39\u5b50\u6216\u7b2c\u4e8c\u4e2a\u5f39\u5b50\u6765\u62bd\u53d6\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-e362e2ca8fc64b381822c19a54c5c9ab.gif\" =\"\" =\"\\begin{aligned} P(A \\text{ in sample}) &amp;= P(\\text{A is first or A is second}) \\\\ &amp;= P(\\text{A is first}) + P(\\text{A is second}) \\\\ &amp;= \\frac{1}{6} \\cdot \\frac{5}{5} + \\frac{5}{6} \\cdot \\frac{1}{5} \\\\ &amp;= \\frac{1}{3} \\\\ \\end{aligned}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c11\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c11\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4 id=\"\u6574\u7fa4\u62bd\u6837\">\u6574\u7fa4\u62bd\u6837<\/h4>\n<p>\u5728\u6574\u7fa4\u62bd\u6837\u4e2d\uff0c\u6211\u4eec\u5c06\u603b\u4f53\u5212\u5206\u4e3a\u7c07\u3002 \u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528 SRS \u6765\u968f\u673a\u9009\u62e9\u7c07\u800c\u4e0d\u662f\u4e2a\u4f53\u3002<\/p>\n<p>\u4f5c\u4e3a\u4e00\u4e2a\u4f8b\u5b50\uff0c\u5047\u8bbe\u6211\u4eec\u4ece\u5927\u5c0f\u4e3a 6 \u7684\u603b\u4f53\u9009\u53d6\u4e2a\u4f53\uff0c\u6211\u4eec\u5c06\u4ed6\u4eec\u4e2d\u7684\u6bcf\u4e00\u4e2a\u914d\u5bf9\uff1a<img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-cdfdac1d7a23b2ba11787c5e4e6f118d.gif\" =\"\" =\" (A,B)\\quad (C,D) \\quad (E,F) \" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c12\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c12\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\uff0c\u7ec4\u6210 3 \u4e2a\u4e2a\u4f53\u4e3a 2 \u7684\u7c07\u3002 \u7136\u540e\uff0c\u6211\u4eec\u4f7f\u7528 SRS \u9009\u62e9\u4e00\u4e2a\u7c07\u6765\u4ea7\u751f\u5927\u5c0f\u4e3a 2 \u7684\u6837\u672c\u3002<\/p>\n<p>\u548c\u4ee5\u524d\u4e00\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7fc56270e7a70fa81a5935b72eacbe29.gif\" =\"\" =\"A\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u5728\u6211\u4eec\u6837\u672c\u4e2d\u7684\u6982\u7387\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-d01f63b6ba39b3c0633a67018c4ca39e.gif\" =\"\" =\"P(A \\text{ in sample}) = P(AB \\text{ drawn}) = \\frac{1}{3}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c14\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c14\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u4e0e\u4e4b\u7c7b\u4f3c\uff0c\u4efb\u4f55\u7279\u5b9a\u4e2a\u4f53\u51fa\u73b0\u5728\u6211\u4eec\u7684\u6837\u672c\u4e2d\u7684\u6982\u7387\u662f <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7c1bc20c016ab66f2b43e99fbf038c45.gif\" =\"\" =\" \\frac{1}{3}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c15\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c15\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002 \u8bf7\u6ce8\u610f\uff0c\u8fd9\u4e0e\u6211\u4eec\u7684 SRS \u76f8\u540c\u3002 \u7136\u800c\uff0c\u5f53\u6211\u4eec\u89c2\u5bdf\u6837\u672c\u672c\u8eab\u65f6\uff0c\u6211\u4eec\u770b\u5230\u4e86\u5dee\u5f02\u3002 \u4f8b\u5982\uff0c\u5728 SRS \u4e2d\u83b7\u5f97 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-b86fc6b051f63d73de262d4c34e3a0a9.gif\" =\"\" =\"AB\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c16\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c16\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u673a\u4f1a\u4e0e\u83b7\u5f97 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-4144e097d2fa7a491cec2a7a4322f2bc.gif\" =\"\" =\"AC\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c17\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c17\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u7684\u673a\u4f1a\u76f8\u540c\uff0c\u90fd\u662f <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-56e7f66d849d2a6c1a430d38565c2e35.gif\" =\"\" =\"\\frac{1}{15}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c18\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c18\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" >\u3002 \u4f46\u662f\uff0c\u91c7\u7528\u8fd9\u79cd\u6574\u7fa4\u62bd\u6837\u65b9\u6848\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-d6e0ba2ab427ca9639fc8c8b0eeadb15.gif\" =\"\" =\"\\begin{aligned} P(AB) &amp;= \\frac{1}{3} \\\\ P(AC) &amp;= 0 \\end{aligned}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c19\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c19\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u7531\u4e8e\u5982\u679c\u6211\u4eec\u53ea\u9009\u62e9\u4e00\u4e2a\u7c07\uff0c<img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7fc56270e7a70fa81a5935b72eacbe29.gif\" =\"\" =\"A\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u548c <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-0d61f8370cad1d412f80b84d143e1257.gif\" =\"\" =\"C\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c21\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c21\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u6c38\u8fdc\u4e0d\u4f1a\u51fa\u73b0\u5728\u540c\u4e00\u4e2a\u6837\u672c\u4e2d\u3002<\/p>\n<p>\u6574\u7fa4\u62bd\u6837\u4ecd\u7136\u662f\u62bd\u7387\u91c7\u6837\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u4e3a\u6bcf\u4e2a\u6f5c\u5728\u7684\u62bd\u6837\u5206\u914d\u4e00\u4e2a\u6982\u7387\u3002 \u7136\u800c\uff0c\u6240\u5f97\u6982\u7387\u4e0e\u4f7f\u7528 SRS \u4e0d\u540c\uff0c\u53d6\u51b3\u4e8e\u603b\u4f53\u5982\u4f55\u805a\u96c6\u3002<\/p>\n<p>\u4e3a\u4ec0\u4e48\u4f7f\u7528\u6574\u7fa4\u62bd\u6837\uff1f \u6574\u7fa4\u62bd\u6837\u662f\u6700\u6709\u7528\u7684\uff0c\u56e0\u4e3a\u5b83\u4f7f\u5f97\u6837\u672c\u6536\u96c6\u66f4\u5bb9\u6613\u3002 \u4f8b\u5982\uff0c\u8c03\u67e5 100 \u4e2a\u57ce\u9547\u7684\u4eba\u53e3\u6bd4\u8c03\u67e5\u904d\u5e03\u6574\u4e2a\u7f8e\u56fd\u7684\u6570\u5343\u4eba\u8981\u5bb9\u6613\u5f97\u591a\u3002 \u8fd9\u5c31\u662f\u4eca\u5929\u8bb8\u591a\u6c11\u610f\u8c03\u67e5\u673a\u6784\u4f7f\u7528\u6574\u7fa4\u62bd\u6837\u5f62\u5f0f\u8fdb\u884c\u8c03\u67e5\u7684\u539f\u56e0\u3002<\/p>\n<p>\u6574\u7fa4\u62bd\u6837\u7684\u4e3b\u8981\u7f3a\u70b9\u662f\uff0c\u5b83\u5f80\u5f80\u4f1a\u4ea7\u751f\u66f4\u5927\u7684\u4f30\u8ba1\u5dee\u5f02\u3002 \u8fd9\u901a\u5e38\u610f\u5473\u7740\uff0c\u6211\u4eec\u5728\u4f7f\u7528\u6574\u7fa4\u62bd\u6837\u65f6\u9700\u8981\u66f4\u5927\u7684\u6837\u672c\u3002 \u8bf7\u6ce8\u610f\uff0c\u73b0\u5b9e\u6bd4\u8fd9\u66f4\u590d\u6742\uff0c\u4f46\u6211\u4eec\u5c06\u628a\u7ec6\u8282\u7559\u7ed9\u672a\u6765\u7684\u62bd\u6837\u6280\u672f\u8bfe\u7a0b\u3002<\/p>\n<h4 id=\"\u5206\u5c42\u62bd\u6837\">\u5206\u5c42\u62bd\u6837<\/h4>\n<p>\u5728\u5206\u5c42\u62bd\u6837\u4e2d\uff0c\u6211\u4eec\u5c06\u603b\u4f53\u5206\u6210\u51e0\u5c42\uff0c\u7136\u540e\u6bcf\u5c42\u4ea7\u751f\u4e00\u4e2a\u7b80\u5355\u968f\u673a\u6837\u672c\u3002 \u5728\u6574\u7fa4\u62bd\u6837\u548c\u5206\u5c42\u62bd\u6837\u4e2d\uff0c\u6211\u4eec\u5c06\u4eba\u53e3\u5206\u6210\u51e0\u7ec4\uff1b\u5728\u6574\u7fa4\u62bd\u6837\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u5355\u4e2a SRS \u6765\u9009\u62e9\u7ec4\uff0c\u800c\u5728\u5206\u5c42\u62bd\u6837\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528\u591a\u4e2a SRS\uff0c\u6bcf\u7ec4\u6709\u4e00\u4e2a SRS\u3002<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u5c06\u6211\u4eec\u5927\u5c0f\u4e3a 6 \u7684\u603b\u4f53\u5206\u6210\u4ee5\u4e0b\u51e0\u5c42\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-d989ada5606fd3d7adc85665693e8678.gif\" =\"\" =\"\\begin{matrix} \\text{Strata 1:} &amp; {A,B,C,D} \\\\ \\text{Strata 2:} &amp; {E,F} \\end{matrix}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c22\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c22\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6211\u4eec\u4f7f\u7528 SRS \u4ece\u6bcf\u4e00\u5c42\u4e2d\u9009\u62e9\u4e00\u4e2a\u4e2a\u4f53\uff0c\u6765\u751f\u6210\u4e00\u4e2a\u5927\u5c0f\u4e3a 2 \u7684\u6837\u672c\u3002\u8fd9\u5411\u6211\u4eec\u63d0\u4f9b\u4e86\u4ee5\u4e0b\u53ef\u80fd\u7684\u6837\u672c\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-8d01b3cac9bf4fcbde0c22b93e99aac0.gif\" =\"\" =\"\\begin{aligned} (A,E)\\quad (A,F) \\quad (B,E) \\quad (B,F) \\quad (C,E) \\quad (C,F) \\quad (D,E) \\quad (D,F) \\end{aligned}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c23\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c23\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u518d\u6b21\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97 <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7fc56270e7a70fa81a5935b72eacbe29.gif\" =\"\" =\"A\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u5728\u6211\u4eec\u6837\u672c\u4e2d\u7684\u6982\u7387\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-9d206c973ae429f0d3dfb23bbc31436b.gif\" =\"\" =\"\\begin{aligned} P(A \\text{ in sample}) &amp;= P(A \\text{ selected from Strata 1}) \\\\ &amp;= \\frac{1}{4} \\end{aligned}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c25\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c25\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u4f46\u662f\uff1a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-3230a38ff882eb696c8ef04f5aac538d.gif\" =\"\" =\"\\begin{aligned} P(AB) &amp;= 0 \\end{aligned}\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c26\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c26\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u56e0\u4e3a <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-7fc56270e7a70fa81a5935b72eacbe29.gif\" =\"\" =\"A\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c10\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c10\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u548c <img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/tex-9d5ed678fe57bcca610140957afab571.gif\" =\"\" =\"B\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c28\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c28\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" > \u4e0d\u80fd\u51fa\u73b0\u5728\u540c\u4e00\u4e2a\u6837\u672c\u4e2d\u3002<\/p>\n<p>\u4e0e\u6574\u7fa4\u62bd\u6837\u4e00\u6837\uff0c\u5206\u5c42\u62bd\u6837\u4e5f\u662f\u4e00\u79cd\u6982\u7387\u62bd\u6837\u65b9\u6cd5\uff0c\u5b83\u6839\u636e\u603b\u4f53\u7684\u5206\u5c42\u60c5\u51b5\u4ea7\u751f\u4e0d\u540c\u7684\u6982\u7387\u3002 \u8bf7\u6ce8\u610f\uff0c\u5c31\u50cf\u8fd9\u4e2a\u4f8b\u5b50\uff0c\u5c42\u7684\u5927\u5c0f\u4e0d\u4e00\u5b9a\u76f8\u540c\u3002 \u4f8b\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u804c\u4e1a\u5bf9\u7f8e\u56fd\u8fdb\u884c\u5206\u5c42\uff0c\u7136\u540e\u6839\u636e\u7f8e\u56fd\u804c\u4e1a\u5206\u5e03\uff0c\u4ece\u6bcf\u4e2a\u5c42\u7ea7\u62bd\u53d6\u6837\u672c - \u5982\u679c\u7f8e\u56fd\u53ea\u6709 0.01% \u7684\u4eba\u662f\u7edf\u8ba1\u4eba\u5458\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u4fdd\u6211\u4eec\u6837\u672c\u7684 0.01% \u5c06\u7531\u7edf\u8ba1\u4eba\u5458\u7ec4\u6210\u3002 \u7b80\u5355\u7684\u968f\u673a\u6837\u672c\u53ef\u80fd\u5b8c\u5168\u5ffd\u7565\u4e86\u53ef\u601c\u7684\u7edf\u8ba1\u4eba\u5458\uff01<\/p>\n<p>\u4f60\u53ef\u80fd\u5df2\u7ecf\u60f3\u5230\uff0c\u5206\u5c42\u62bd\u6837\u53ef\u80fd\u88ab\u79f0\u4e3a\u914d\u989d\u62bd\u6837\u7684\u5408\u7406\u65b9\u5f0f\u3002 \u5b83\u5141\u8bb8\u7814\u7a76\u4eba\u5458\u786e\u4fdd\u603b\u4f53\u4e2d\u7684\u5b50\u7ec4\uff0c\u5728\u6837\u672c\u4e2d\u5f97\u5230\u5f88\u597d\u7684\u4ee3\u8868\uff0c\u800c\u4e0d\u7528\u4eba\u4e3a\u5224\u65ad\u6765\u9009\u62e9\u6837\u672c\u4e2d\u7684\u4e2a\u4f53\u3002 \u8fd9\u901a\u5e38\u4f1a\u4f7f\u4f30\u8ba1\u5dee\u5f02\u8f83\u5c0f\u3002 \u7136\u800c\uff0c\u5206\u5c42\u62bd\u6837\u6709\u65f6\u66f4\u96be\u5b8c\u6210\uff0c\u56e0\u4e3a\u6211\u4eec\u6709\u65f6\u4e0d\u77e5\u9053\u6bcf\u4e00\u5c42\u6709\u591a\u5927\u3002 \u5728\u524d\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u6709\u7f8e\u56fd\u4eba\u53e3\u666e\u67e5\u7684\u4f18\u52bf\uff0c\u4f46\u6709\u4e9b\u65f6\u5019\u6211\u4eec\u5e76\u4e0d\u90a3\u4e48\u5e78\u8fd0\u3002<\/p>\n<h4 id=\"\u4e3a\u4ec0\u4e48\u662f\u6982\u7387\u62bd\u6837\">\u4e3a\u4ec0\u4e48\u662f\u6982\u7387\u62bd\u6837\uff1f<\/h4>\n<p>\u6211\u4eec\u5728 Data8 \u4e2d\u770b\u5230\uff0c\u6982\u7387\u62bd\u6837\u4f7f\u6211\u4eec\u80fd\u591f\u91cf\u5316\uff0c\u6211\u4eec\u5bf9\u4f30\u8ba1\u6216\u9884\u6d4b\u7684\u4e0d\u786e\u5b9a\u6027\u3002 \u53ea\u6709\u901a\u8fc7\u8fd9\u4e2a\u7cbe\u786e\u5ea6\uff0c\u6211\u4eec\u624d\u80fd\u8fdb\u884c\u63a8\u65ad\u548c\u5047\u8bbe\u68c0\u9a8c\u3002 \u5f53\u4efb\u4f55\u4eba\u5411\u4f60\u7ed9\u51fa p \u503c\u6216\u7f6e\u4fe1\u5ea6\uff0c\u800c\u6ca1\u6709\u6b63\u786e\u89e3\u91ca\u4ed6\u4eec\u7684\u62bd\u6837\u6280\u672f\u65f6\uff0c\u8981\u5c0f\u5fc3\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u7406\u89e3\u4e86\u6982\u7387\u62bd\u6837\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5351\u5fae\u7684 SRS \u4e0e\u201c\u5927\u6570\u636e\u201d\u76f8\u6bd4\u5982\u4f55\u3002<\/p>\n<h3 id=\"srs-vs-\u5927\u6570\u636e\">SRS vs \u201c\u5927\u6570\u636e\u201d<\/h3>\n<p>\u6211\u4eec\u4e4b\u524d\u63d0\u5230\uff0c\u901a\u8fc7\u4f7f\u7528\u5927\u91cf\u6570\u636e\u6765\u6d88\u9664\u6211\u4eec\u5197\u957f\u7684\u504f\u5dee\u95ee\u9898\uff0c\u662f\u5f88\u6709\u5438\u5f15\u4eba\u7684\u3002\u6309\u7167\u5b9a\u4e49\uff0c\u4eba\u53e3\u666e\u67e5\u786e\u5b9e\u4f1a\u4ea7\u751f\u65e0\u504f\u4f30\u8ba1\u3002\u5982\u679c\u6211\u4eec\u6536\u96c6\u5927\u91cf\u6570\u636e\uff0c\u4e5f\u8bb8\u6211\u4eec\u4e0d\u5fc5\u62c5\u5fc3\u504f\u5dee\u3002<\/p>\n<p>\u5047\u8bbe\u6211\u4eec\u662f 2012 \u5e74\u7684\u6c11\u610f\u8c03\u67e5\u8005\uff0c\u8bd5\u56fe\u9884\u6d4b\u7f8e\u56fd\u603b\u7edf\u9009\u4e3e\u7684\u5927\u4f17\u6295\u7968\uff0c\u5df4\u62c9\u514b\u00b7\u5965\u5df4\u9a6c\u4e0e\u7c73\u7279\u200b\u200b\u00b7\u7f57\u59c6\u5c3c\u7ade\u4e89\u3002\u7531\u4e8e\u6211\u4eec\u77e5\u9053\u51c6\u786e\u7684\u5927\u4f17\u6295\u7968\u7ed3\u679c\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u6bd4\u8f83 SRS \u7684\u9884\u6d4b\uff0c\u4e0e\u5927\u578b\u975e\u968f\u673a\u6570\u636e\u96c6\uff08\u901a\u5e38\u79f0\u4e3a\u884c\u653f\u6570\u636e\u96c6\uff09\u7684\u9884\u6d4b\uff0c\u56e0\u4e3a\u5b83\u4eec\u901a\u5e38\u4f5c\u4e3a\u67d0\u4e9b\u884c\u653f\u5de5\u4f5c\u7684\u4e00\u90e8\u5206\u800c\u6536\u96c6\u3002<\/p>\n<p>\u6211\u4eec\u5c06\u6bd4\u8f83\u5927\u5c0f\u4e3a 400 \u7684 SRS \u548c\u5927\u5c0f\u4e3a 60,000,000 \u7684\u975e\u968f\u673a\u6837\u672c\u3002\u6211\u4eec\u7684\u975e\u968f\u673a\u6837\u672c\u6bd4\u6211\u4eec\u7684 SRS \u5927\u8fd1 15 \u4e07\u500d\uff01\u7531\u4e8e 2012 \u5e74\u5927\u7ea6\u6709 1.2 \u4ebf\u9009\u6c11\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u6211\u4eec\u7684\u975e\u968f\u673a\u6837\u672c\u770b\u4f5c\u4e00\u4e2a\u8c03\u67e5\uff0c\u5176\u4e2d\u7f8e\u56fd\u6240\u6709\u9009\u6c11\u7684\u4e00\u534a\u505a\u51fa\u4e86\u56de\u5e94\uff08\u6ca1\u6709\u8d85\u8fc7 10,000,000 \u4e2a\u9009\u6c11\u7684\u5b9e\u9645\u8c03\u67e5\uff09\u3002<\/p>\n<pre class=\"prettyprint\"><code class=\"language-py hljs bash\"><span class=\"hljs-comment\"># HIDDEN<\/span> total = <span class=\"hljs-number\"><\/span> obama_<span class=\"hljs-literal\">true<\/span>_count = <span class=\"hljs-number\"><\/span> romney_<span class=\"hljs-literal\">true<\/span>_count = <span class=\"hljs-number\"><\/span> obama_<span class=\"hljs-literal\">true<\/span> = obama_<span class=\"hljs-literal\">true<\/span>_count \/ total romney_<span class=\"hljs-literal\">true<\/span> = romney_<span class=\"hljs-literal\">true<\/span>_count \/ total <span class=\"hljs-comment\"># 1 percent off<\/span> obama_big = obama_<span class=\"hljs-literal\">true<\/span> - <span class=\"hljs-number\">0.01<\/span> romney_big = romney_<span class=\"hljs-literal\">true<\/span> + <span class=\"hljs-number\">0.01<\/span><\/code><\/pre>\n<p>\u8fd9\u662f\u4e00\u4e2a\u7ed8\u56fe\uff0c\u6bd4\u8f83\u4e86\u975e\u968f\u673a\u6837\u672c\u7684\u6bd4\u4f8b\u4e0e\u771f\u5b9e\u6bd4\u4f8b\u3002 \u6807\u6709\u771f\u5b9e\u503c\u7684\u6761\u5f62\u663e\u793a\u4e86\uff0c\u6bcf\u4f4d\u5019\u9009\u4eba\u6536\u5230\u7684\u9009\u7968\u7684\u771f\u5b9e\u6bd4\u4f8b\u3002 \u6807\u6709\u201c\u5927\u201d\u7684\u6761\u5f62\u663e\u793a\u4e86\uff0c\u6211\u4eec 6000 \u4e07\u9009\u6c11\u7684\u6570\u636e\u96c6\u4e2d\u7684\u6bd4\u4f8b\u3002<\/p>\n<pre class=\"prettyprint\"><code class=\"language-py hljs bash\">pd.DataFrame({ <span class=\"hljs-string\">'truth'<\/span>: [obama_<span class=\"hljs-literal\">true<\/span>, romney_<span class=\"hljs-literal\">true<\/span>], <span class=\"hljs-string\">'big'<\/span>: [obama_big, romney_big], }, index=[<span class=\"hljs-string\">'Obama'<\/span>, <span class=\"hljs-string\">'Romney'<\/span>], columns=[<span class=\"hljs-string\">'truth'<\/span>, <span class=\"hljs-string\">'big'<\/span>]).plot.bar() plt.title(<span class=\"hljs-string\">'Truth compared to a big non-random dataset'<\/span>) plt.xlabel(<span class=\"hljs-string\">'Candidate'<\/span>) plt.ylabel(<span class=\"hljs-string\">'Proportion of popular vote'<\/span>) plt.ylim(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">0.75<\/span>) None<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/2-2.png\" =\"\" =\"\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c29\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c29\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5c31\u50cf 1948 \u5e74\u7684\u76d6\u6d1b\u666e\u6c11\u610f\u8c03\u67e5\u4e00\u6837\uff0c\u6211\u4eec\u7684\u5927\u6570\u636e\u96c6\u4ec5\u4ec5\u6709\u70b9\u504f\u5411\u5171\u548c\u515a\u5019\u9009\u4eba\u7f57\u59c6\u5c3c\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u8fd9\u4e2a\u6570\u636e\u96c6\u53ef\u4ee5\u5411\u6211\u4eec\u63d0\u4f9b\u51c6\u786e\u7684\u9884\u6d4b\u3002 \u4e3a\u4e86\u68c0\u67e5\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u603b\u4f53\u4e2d\u6a21\u62df\u62bd\u53d6\u5927\u5c0f\u4e3a 400 \u7684\u968f\u673a\u6837\u672c\uff0c\u548c\u5927\u5c0f\u4e3a 60,000,000 \u7684\u5927\u578b\u975e\u968f\u673a\u6837\u672c\u3002 \u6211\u4eec\u5c06\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u4e2d\u7684\u5965\u5df4\u9a6c\u7684\u9009\u7968\u6bd4\u4f8b\uff0c\u5e76\u7ed8\u5236\u6bd4\u4f8b\u5206\u5e03\u56fe\u3002<\/p>\n<pre class=\"prettyprint\"><code class=\"language-py hljs python\">srs_size = <span class=\"hljs-number\">400<\/span> big_size = <span class=\"hljs-number\"><\/span> replications = <span class=\"hljs-number\">10000<\/span> <span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">resample<\/span><span class=\"hljs-params\">(size, prop, replications)<\/span>:<\/span> <span class=\"hljs-keyword\">return<\/span> np.random.binomial(n=size, p=prop, size=replications) \/ size srs_simulations = resample(srs_size, obama_true, replications) big_simulations = resample(big_size, obama_big, replications)<\/code><\/pre>\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u5c06\u7ed8\u5236\u6a21\u62df\u7ed3\u679c\u5e76\u653e\u4e0a\u4e00\u6761\u7ea2\u7ebf\uff0c\u8868\u793a\u6295\u7968\u7ed9\u5965\u5df4\u9a6c\u7684\u9009\u6c11\u7684\u771f\u5b9e\u6bd4\u4f8b\u3002<\/p>\n<pre class=\"prettyprint\"><code class=\"language-py hljs vhdl\">bins = bins=np.arange(<span class=\"hljs-number\">0.47<\/span>, <span class=\"hljs-number\">0.55<\/span>, <span class=\"hljs-number\">0.005<\/span>) plt.hist(srs_simulations, bins=bins, alpha=<span class=\"hljs-number\">0.7<\/span>, normed=True, <span class=\"hljs-keyword\">label<\/span>=<span class=\"hljs-attribute\">'srs<\/span>') plt.hist(big_simulations, bins=bins, alpha=<span class=\"hljs-number\">0.7<\/span>, normed=True, <span class=\"hljs-keyword\">label<\/span>=<span class=\"hljs-attribute\">'big<\/span>') plt.title(<span class=\"hljs-attribute\">'Proportion<\/span> <span class=\"hljs-keyword\">of<\/span> Obama Voters <span class=\"hljs-keyword\">for<\/span> SRS <span class=\"hljs-keyword\">and<\/span> Big Data') plt.xlabel(<span class=\"hljs-attribute\">'Proportion<\/span>') plt.ylabel(<span class=\"hljs-attribute\">'Percent<\/span> per unit') plt.xlim(<span class=\"hljs-number\">0.47<\/span>, <span class=\"hljs-number\">0.55<\/span>) plt.ylim(<span class=\"hljs-number\">0<\/span>, <span class=\"hljs-number\">50<\/span>) plt.axvline(x=obama_true, color=<span class=\"hljs-attribute\">'r<\/span>', <span class=\"hljs-keyword\">label<\/span>=<span class=\"hljs-attribute\">'truth<\/span>') plt.legend() None<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/gitee.com\/wizardforcel\/ds100-textbook-zh\/raw\/master\/img\/2-3.png\" =\"\" =\"\" alt=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1 (https:\/\/mushiming.com\/)  \u7b2c30\u5f20\" title=\"\u6570\u636e\u751f\u6210\u8fc7\u7a0b\u662f\u4ec0\u4e48_\u6570\u636e\u5f00\u53d1  \u7b2c30\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<p>\u6b63\u5982\u4f60\u6240\u770b\u5230\u7684\uff0cSRS \u5206\u5e03\u662f\u5206\u6563\u7684\uff0c\u4f46\u56f4\u7ed5\u7740\u5965\u5df4\u9a6c\u9009\u6c11\u7684\u771f\u5b9e\u603b\u4f53\u6bd4\u4f8b\u3002 \u53e6\u4e00\u65b9\u9762\uff0c\u5927\u578b\u975e\u968f\u673a\u6837\u672c\u521b\u5efa\u7684\u5206\u5e03\u975e\u5e38\u72ed\u7a84\uff0c\u4f46\u6ca1\u6709\u4e00\u4e2a\u6a21\u62df\u6837\u672c\u80fd\u591f\u4ea7\u751f\u771f\u5b9e\u603b\u4f53\u6bd4\u4f8b\u3002 \u5982\u679c\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u975e\u968f\u673a\u6837\u672c\u521b\u5efa\u7f6e\u4fe1\u533a\u95f4\uff0c\u5219\u5b83\u4eec\u90fd\u4e0d\u4f1a\u5305\u542b\u771f\u5b9e\u603b\u4f53\u6bd4\u4f8b\u3002 \u66f4\u7cdf\u7cd5\u7684\u662f\uff0c\u7531\u4e8e\u6837\u672c\u975e\u5e38\u5927\uff0c\u7f6e\u4fe1\u533a\u95f4\u5c06\u975e\u5e38\u72ed\u7a84\u3002\u6211\u4eec\u6700\u7ec8\u4f1a\u786e\u4fe1\u9519\u8bef\u4f30\u8ba1\u3002<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u6211\u4eec\u7684\u62bd\u6837\u65b9\u6cd5\u6709\u504f\u5dee\u65f6\uff0c\u7531\u4e8e\u6211\u4eec\u6536\u96c6\u4e86\u66f4\u591a\u7684\u6570\u636e\uff0c\u6211\u4eec\u7684\u4f30\u8ba1\u4f1a\u53d8\u5f97\u66f4\u7cdf\uff0c\u56e0\u4e3a\u6211\u4eec\u4f1a\u66f4\u52a0\u786e\u4fe1\u4e0d\u6b63\u786e\u7684\u7ed3\u679c\uff0c\u53ea\u6709\u5f53\u6211\u4eec\u7684\u6570\u636e\u96c6\u51e0\u4e4e\u662f\u4eba\u53e3\u666e\u67e5\u65f6\u624d\u4f1a\u53d8\u5f97\u66f4\u52a0\u51c6\u786e\u3002 \u6570\u636e\u7684\u8d28\u91cf\u6bd4\u5b83\u7684\u5927\u5c0f\u91cd\u8981\u5f97\u591a\u3002<\/p>\n<h4 id=\"\u91cd\u8981\u7ed3\u8bba\">\u91cd\u8981\u7ed3\u8bba<\/h4>\n<p>\u5728\u63a5\u53d7\u6570\u636e\u5206\u6790\u7ed3\u679c\u4e4b\u524d\uff0c\u4ed4\u7ec6\u68c0\u67e5\u6570\u636e\u7684\u8d28\u91cf\u662f\u503c\u5f97\u7684\u3002 \u7279\u522b\u662f\uff0c\u6211\u4eec\u5fc5\u987b\u63d0\u51fa\u4ee5\u4e0b\u95ee\u9898\uff1a<\/p>\n<p>\u6570\u636e\u662f\u5426\u4e3a\u4eba\u53e3\u666e\u67e5\uff08\u662f\u5426\u5305\u62ec\u6574\u4e2a\u4eba\u7fa4\uff09\uff1f \u5982\u679c\u662f\u8fd9\u6837\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u603b\u4f53\u7684\u5c5e\u6027\u800c\u4e0d\u5fc5\u4f7f\u7528\u63a8\u65ad\u3002 <br \/> \u5982\u679c\u6570\u636e\u662f\u6837\u672c\uff0c\u90a3\u4e48\u6837\u672c\u662f\u5982\u4f55\u6536\u96c6\u7684\uff1f \u4e3a\u4e86\u6b63\u786e\u8fdb\u884c\u63a8\u65ad\uff0c\u6837\u672c\u5e94\u8be5\u6839\u636e\u6982\u7387\u62bd\u6837\u65b9\u6cd5\u6536\u96c6\u3002 <br \/> \u5728\u4ea7\u751f\u7ed3\u679c\u4e4b\u524d\u5bf9\u6570\u636e\u8fdb\u884c\u4e86\u54ea\u4e9b\u66f4\u6539\uff1f \u8fd9\u4e9b\u53d8\u5316\u662f\u5426\u4f1a\u5f71\u54cd\u6570\u636e\u7684\u8d28\u91cf\uff1f<\/p>\n<p>\u5bf9\u4e8e\u968f\u673a\u548c\u975e\u968f\u673a\u5927\u6837\u672c\u4e4b\u95f4\u7684\u6bd4\u8f83\u7684\u66f4\u591a\u7ec6\u8282\uff0c\u6211\u4eec\u5efa\u8bae\u89c2\u770b\u7edf\u8ba1\u5b66\u5bb6 Xiao-Li Meng 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