{"id":95892,"date":"2020-04-05T10:51:32","date_gmt":"2020-04-05T02:51:32","guid":{"rendered":"http:\/\/4563.org\/?p=95892"},"modified":"2020-04-05T10:51:32","modified_gmt":"2020-04-05T02:51:32","slug":"%e6%b3%8a%e6%9d%be%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=95892","title":{"rendered":"\u6cca\u677e\u5206\u5e03"},"content":{"rendered":"
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\u6cca\u677e\u5206\u5e03 <\/h1>\n

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\u8cc7\u6df1\u5927\u4f6c : atuocn <\/span> <\/i> 61<\/span> <\/div>\n
<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n
<\/p>\n

\u4f0a\u59cb<\/h1>\n

<\/p>\n

\u5904\u7406\u4e00\u4e2a\u5173\u4e8e\u6b63\u6001\u5206\u5e03\u548c\u03c3\u7684\u95ee\u9898\uff0c\u81ea\u5df1\u6570\u5b66\u7ecf\u8fc7\u8fde\u7eed\u591a\u5e74\u8870\u51cf\uff0c\u6b8b\u503c\u51e0\u4e4e\u4e3a\u96f6\u3002\u6982\u7387\u65b9\u9762\u53ea\u5927\u7ea6\u8bb0\u5f97\u6b63\u6001\u5206\u5e03\u662f\u4e2a\u5012\u949f\u5f62\u66f2\u7ebf -_-!!! \u767e\u5ea6\u7684\u65f6\u5019\uff0c\u770b\u5230\u4e00\u4e2a\u53eb\u6cca\u677e\u5206\u5e03\u7684\uff0c\u56fe\u5f62\u770b\u8d77\u6765\u8c61\u662f\u6b6a\u7684\u6b63\u6001\u5206\u5e03\u3002\u4e00\u65f6\u597d\u5947\uff0c\u4e8e\u662f\u7528\u767e\u5ea6\u767e\u79d1\u7ea7\u7684\u7814\u7a76\u6c34\u5e73\uff0c\u7814\u7a76\u8d77\u6cca\u677e\u5206\u5e03\u3002<\/p>\n

\u5f00\u59cb\u770b\u767e\u5ea6\u767e\u79d1\u7684\u6cca\u677e\u5206\u5e03\u6761\u76ee\uff0c\u611f\u89c9\u61c2\u4e86\u53c8\u611f\u89c9\u6ca1\u61c2\uff0c\u7591\u60d1\u5f88\u591a\uff0c\u4e91\u91cc\u96fe\u91cc\uff1b\u7136\u540e\u53c8\u770b\u4e86\u767e\u79d1\u7684\u6cca\u677e\u5b9a\u7406\uff0c\u4f3c\u4e4e\u660e\u767d\u4e86\u4e00\u4e9b\uff0c\u611f\u89c9\u8fd8\u662f\u6293\u4e0d\u4f4f\uff1b\u6700\u540e\u6cbf\u6cca\u677e\u5b9a\u7406\uff0c\u5f80\u4e0a\u987a\u722c\u5230\u4e8c\u9879\u5206\u5e03\uff0c\u5927\u6982\u7b97\u662f\u6e05\u695a\u4e86\u3002\u867d\u7136\u6ca1\u5565\u4e71\u7528\uff0c\u6d6a\u8d39\u8111\u529b\uff0c\u8fd8\u662f\u8bb0\u4e2a\u7b14\u8bb0\u7559\u4e2a\u75d5\u3002<\/p>\n

\u4e8c\u9879\u5206\u5e03<\/h1>\n

<\/p>\n

    \n
  • \u6bcf\u6b21\u4e8b\u4ef6\u72ec\u7acb\u3002<\/li>\n
  • \u4e8b\u4ef6\u53d1\u751f\u65f6\uff0c\u7ed3\u679c\u8981\u4e48 A,\u8981\u4e48 B, \u53d1\u751f A \u7684\u6982\u7387\u4e3a p\u3002<\/li>\n
  • \u6bcf\u6b21\u5b9e\u9a8c\uff0cp \u4e0d\u53d8\u3002<\/li>\n<\/ul>\n

    n \u6b21\u5b9e\u9a8c\uff08\u7b26\u5408\u4e0a\u8ff0\u6761\u4ef6\u7684\u5b9e\u9a8c\u79f0\u4e3a\u4f2f\u52aa\u5229\u5b9e\u9a8c\uff09\u4e2d A \u53d1\u751f k \u6b21\u7684\u6982\u7387\uff0c\u4e3a\u4e8c\u9879\u5206\u5e03\u3002<\/p>\n

    \u4e8c\u9879\u5206\u5e03\u516c\u5f0f\uff0c\u8bbe\u53d1\u751f\u6b21\u6570\u4e3a\u03be\uff0c\u5f53\u03be=k \u65f6\u7684\u6982\u7387[1]\uff1a<\/p>\n

    P(\u03be=k) = C(n,k) * power(p, k)  * power((1-p), (n-k))  <\/code><\/pre>\n
    \u5176\u4e2d\uff0cC(n,k)\u4e3a\u7ec4\u5408\u6570\u3002power \u4e3a\u6307\u6570\u51fd\u6570\u3002<\/p>\n
    \u6ce8\u610f\uff1a\u6982\u7387 p \u4e3a\u4e8b\u4ef6\u7ed3\u679c\u4e3a A \u7684\u6982\u7387\uff0c\u662f\u4e8b\u4ef6\u672c\u8eab\u7684\u6982\u7387\u7279\u6027\uff0c\u548c\u5b9e\u9a8c\u6b21\u6570\u65e0\u5173\u3002\u4e8c\u9879\u5206\u5e03\u662f\u6c42\u4e8b\u4ef6 A \u53d1\u751f k \u6b21\u7684\u6982\u7387\u3002 \u4e8c\u9879\u5206\u5e03\u7684\u671f\u671b\u4e3a np\uff0c\u65b9\u5dee\u4e3a npq\uff0c\u5176\u4e2d q=1-p\u3002<\/p>\n
    \u6cca\u677e\u5206\u5e03<\/h1>\n
     <\/p>\n
      \n
    1. \u5728\u4e00\u4e2a\u5c0f\u533a\u95f4\u0394t \u5185\uff0c\u53d1\u751f\u4e00\u6b21\u4e8b\u4ef6\u7684\u673a\u7387\u4e0e\u0394t \u6210\u6b63\u6bd4\uff1a\u03bb\u0394t\u3002<\/li>\n
    2. \u5728\u5c0f\u533a\u95f4\u0394t \u5185\u53d1\u751f\u4e24\u6b21\u4ee5\u4e0a\u7684\u673a\u7387\u53ef\u4ee5\u5ffd\u7565\u3002<\/li>\n
    3. \u5728\u4e0d\u91cd\u53e0\u7684\u65f6\u95f4\u6bb5\u843d\u91cc\uff0c\u4e8b\u4ef6\u5404\u81ea\u53d1\u751f\u7684\u6b21\u6570\u662f\u72ec\u7acb\u7684\u3002<\/li>\n<\/ol>\n
      \u5728 T \u65f6\u95f4\u5185\uff0c\u53d1\u751f k \u6b21\u4e8b\u4ef6\u7684\u51e0\u7387\u4e3a\u6cca\u677e\u5206\u5e03\u3002<\/p>\n
      \u6cca\u677e\u5206\u5e03\u516c\u5f0f\uff0c\u5728 T \u65f6\u6bb5\uff0c\u53d1\u751f k \u6b21\u6570\u7684\u6982\u7387[2]\uff1a<\/p>\n
      P(k, T) = (power(\u03bbT, k) \/ k!) * exp(-\u03bbT) <\/code><\/pre>\n
      \u5176\u4e2d exp \u4e3a\u81ea\u7136\u5e38\u6570 e \u7684\u6307\u6570\u51fd\u6570\u3002<\/p>\n
      \u6cca\u677e\u5206\u5e03\u516c\u5f0f\u7684\u671f\u671b\u503c\u548c\u65b9\u5dee\u5747\u4e3a\u03bbT\u3002\u03bbT \u901a\u5e38\u8bb0\u4e3a m\u3002\u8868\u793a\u5728\u533a\u95f4 T \u4e2d\uff0c\u5e73\u5747\u7684\u53d1\u751f\u6b21\u6570\u3002<\/p>\n
        \n
      • \u5e73\u5747\u53d1\u751f\u6b21\u6570\u3002\u5e73\u5747\u53d1\u751f\u6b21\u6570 m\uff0c\u5e76\u4e0d\u662f\u53d1\u751f m \u6b21\u6570\u7684\u6982\u7387\u3002\u591a\u6b21\u7edf\u8ba1 T \u533a\u95f4\u5185\uff0c\u6709\u4e9b\u65f6\u5019\u6b21\u6570\u591a\uff0c\u6709\u4e9b\u65f6\u5019\u6b21\u6570\u5c11\uff0c\u5e73\u5747\u4e0b\u6765\u6b21\u6570\u662f m\u3002<\/li>\n
      • \u6cca\u677e\u5206\u5e03\u4e2d\u5e73\u5747\u53d1\u751f\u6b21\u6570\u548c\u533a\u6bb5 T \u6210\u6b63\u6bd4\u3002\u6bd4\u5982\u6bcf\u5c0f\u65f6\u7684\u5e73\u5747\u7535\u8bdd\u547c\u53eb\u6570\u4e3a m, \u5219\u6bcf\u5206\u949f\u7684\u5e73\u5747\u7535\u8bdd\u547c\u53eb\u6570\u4e3a m\/60\u3002<\/li>\n
      • \u53ef\u4ee5\u7406\u89e3\u4e3a\u5e73\u5747\u53d1\u751f\u6b21\u6570 m \u7684\u901f\u7387\u6216\u8005\u5bc6\u5ea6\u4e3a\u03bb\u3002\u6cca\u677e\u5206\u5e03\u4e2d\u03bb\u6052\u5b9a\u3002<\/li>\n
      • \u03bb\u4e0e\u65f6\u95f4\u533a\u95f4\u65e0\u5173\uff0c\u800c\u5e73\u5747\u6b21\u6570\u4e0e\u65f6\u95f4\u533a\u95f4\u957f\u5ea6\u6709\u5173\uff0c\u03bb\u6709\u70b9\u8c61\u201c\u52a0\u901f\u5ea6\u201d\uff0c\u9664\u4ee5\u4e86 2 \u6b21\u65f6\u95f4\u957f\u5ea6\u3002<\/li>\n<\/ul>\n
        \u6cca\u677e\u5206\u5e03\u516c\u5f0f\u4e2d\uff0c\u53ef\u7528\u5728\u533a\u95f4 T \u4e2d\u5e73\u5747\u7684\u53d1\u751f\u6b21\u6570 m \u4f5c\u4e3a\u53c2\u6570\u3002 \u53e6\u4e00\u79cd\u8bf4\u6cd5\u4e2d\uff0cT \u662f\u5355\u4f4d\u65f6\u95f4\uff0cT=1\u3002\u5e73\u5747\u53d1\u751f\u6b21\u6570\u548c\u53d1\u751f k \u6b21\u7684\u6982\u7387\u90fd\u5728 T=1 \u7684\u5355\u4f4d\u65f6\u95f4\u5185\uff0c\u8fd9\u65f6\u516c\u5f0f\u4e2d\u53c2\u6570\u662f\u03bb\u3002 \u533a\u95f4\u5185\u7684\u5e73\u5747\u53d1\u751f\u6b21\u6570 m\uff0c\u6216\u5355\u4f4d\u65f6\u95f4\u5e73\u5747\u53d1\u751f\u6b21\u6570\u03bb\uff0c\u516c\u5f0f\u5f62\u5f0f\u66f4\u7b80\u5355\u3002\u4f46\u662f\u4e2a\u4eba\u611f\u89c9\u7406\u89e3\u516c\u5f0f\u4e0a\uff0c\u03bbT \u66f4\u597d\u3002<\/p>\n
        \u6cca\u677e\u5206\u5e03\u4e0e\u4e8c\u9879\u5206\u5e03<\/h1>\n
         <\/p>\n
          \n
        • \u6cca\u677e\u5206\u5e03\uff0c\u6761\u4ef6\u2474\uff0c\u2475\u53ef\u77e5\uff0c\u5728\u5f88\u5c0f\u7684\u533a\u6bb5\u0394t \u5185\uff0cP(1, \u0394t) = \u03bb\u0394t\uff0c\u4e14 P(k, \u0394t) = 0, k \u2267 2\u3002 \u5373\uff0c\u4e8b\u4ef6\u53ea\u6709 2 \u79cd\u7ed3\u679c\uff0c\u53d1\u751f\u6216\u4e0d\u53d1\u751f\u3002\u7ed3\u679c\u4e3a\u201c\u53d1\u751f\u201d\u7684\u6982\u7387\u4e3a\u03bb\u0394t\uff0c\u7ed3\u679c\u4e3a\u201c\u4e0d\u53d1\u751f\u201d\u7684\u6982\u7387\u4e3a 1 – \u03bb\u0394t\u3002<\/li>\n
        • \u628a\u533a\u6bb5 T \u5206\u4e3a n \u6bb5\uff0c\u6309\u6cca\u677e\u5206\u5e03\u6761\u4ef6\uff0c\u53ef\u89c6\u4e3a n \u6b21\u4f2f\u52aa\u5229\u5b9e\u9a8c\u3002\u6b64\u65f6\u53d1\u751f k \u6b21\u7684\u6982\u7387\uff0c\u4e3a\u4e8c\u9879\u5206\u5e03\u3002<\/li>\n
        • \u6309\u6cca\u677e\u5206\u5e03\u6761\u4ef6\u2474\uff0c\u533a\u6bb5\u0394t \u5185\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\uff0c\u4e0e\u0394t \u6210\u6b63\u6bd4\uff0c\u5373\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u5bc6\u5ea6\u6052\u5b9a\u4e3a\u03bb<\/li>\n
        • \u7ee7\u7eed\u7ec6\u5206\u0394t\uff0c\u4e8b\u4ef6\u201c\u53d1\u751f\u201d\u7684\u6982\u7387\u5bc6\u5ea6\u03bb\u4e0d\u53d8\uff0c\u800c\u4e8b\u4ef6\u201c\u53d1\u751f\u201d\u7684\u6982\u7387 p \u5219\u53d8\u5c0f\uff0cn \u53d8\u5927\u3002\u6bcf\u4e00\u6b21\u7ec6\u5206\uff0c\u6307\u5b9a\u7684\u0394t \u4e0b\uff0c\u4ecd\u7b26\u5408\u4f2f\u52aa\u5229\u5b9e\u9a8c \u3002<\/li>\n
        • \u5f53\u0394t \u2192 0\uff0c\u5219 p \u2192 0\uff0cn \u2192 \u221e \u3002\u4e8c\u9879\u5206\u5e03\u7684\u6781\u9650\u4e3a\u6cca\u677e\u5206\u5e03\u3002<\/li>\n
        • \u7531\u4ee5\u4e0a\u63a8\u5bfc\u53ef\u4ee5\uff0c\u82e5\u5b9e\u9a8c\u6b21\u6570 n \u5f88\u5927\uff0c\u800c\u4e8b\u4ef6\u201c\u53d1\u751f\u201d\u7684\u6982\u7387 p \u5f88\u5c0f\uff0c\u4e8c\u9879\u5206\u5e03\u8fd1\u4f3c\u4e8e\u6cca\u677e\u5206\u5e03\u3002 \u901a\u5e38\u5f53 n\u226720, p\u22660.05 \u65f6[3]\uff0c\u53ef\u4ee5\u7528 np = \u03bbT = m \u4ee3\u5165\u6cca\u677e\u5206\u5e03\uff0c\u8fdb\u884c\u8fd1\u4f3c\u8ba1\u7b97\uff0c\u66f4\u65b9\u4fbf\u3002<\/li>\n<\/ul>\n
          \u6cca\u677e\u5206\u5e03\uff0c\u6b63\u6001\u5206\u5e03\uff0c\u4e8c\u9879\u5206\u5e03<\/h1>\n
           <\/p>\n
            \n
          • \u4e8c\u9879\u5206\u5e03\uff0c\u5728 0<p<1\uff0cn \u5f88\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u903c\u8fd1\u6b63\u6001\u5206\u5e03\u3002(p \u4e0d\u53d8, n \u589e\u5927) [4]<\/li>\n
          • \u4e8c\u9879\u5206\u5e03\uff0c\u5728 p \u5f88\u5c0f\uff0cn \u8f83\u5927\u7684\u60c5\u51b5\u4e0b\uff0c\u903c\u8fd1\u6cca\u677e\u5206\u5e03\u3002(\u53c2\u89c1\u6cca\u677e\u5206\u5e03\u63a8\u5bfc\u8fc7\u7a0b\uff0cnp \u4e0d\u53d8\u7ea6\u675f\u4e0b\u4e00\u7cfb\u5217\u4e0d\u540c\u7684\u4e8c\u9879\u5206\u5e03\u903c\u8fd1\uff09\u3002<\/li>\n
          • \u663e\u7136\u6cca\u677e\u5206\u5e03\u4e8e\u6b63\u6001\u5206\u5e03\u6709\u67d0\u79cd\u8fd1\u4f3c\u3002\u6709\u5b9a\u7406\u8868\u660e\u03bb \u2192 \u221e \u65f6\u6cca\u677e\u5206\u5e03\u7684\u6781\u9650\u662f\u6b63\u6001\u5206\u5e03\u3002<\/li>\n
          • \u5f53 p \u5f88\u5c0f\uff0cn \u8f83\u5927\u3002\u7528\u6cca\u677e\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u8ba1\u7b97\u4e8c\u9879\u5206\u5e03\u3002np = \u03bbT = m<\/li>\n
          • \u5f53 p \u4e0d\u63a5\u8fd1\u4e8e 0\uff0c\u4e5f\u4e0d\u63a5\u8fd1\u4e8e 1 \uff08 0.1\u2266p\u22660.9 \uff09\uff0cn \u5145\u5206\u5927\u3002\u7528\u6b63\u6001\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u8ba1\u7b97\u4e8c\u9879\u5206\u5e03\u3002\u03bc=np, \u03c3^2=np(1-p) [4]<\/li>\n<\/ul>\n
            \u8865\u5145\u590d\u4e60\u51e0\u4e2a\u6982\u5ff5<\/h1>\n
             <\/p>\n
              \n
            • \u671f\u671b\u503c\u548c\u5747\u503c\u3002\u671f\u671b\u503c\u662f\u6982\u7387\u8bba\u4e0a\u7684\u6982\u5ff5\uff0c\u5728\u5df2\u77e5\u6982\u7387\u4e0b\u9884\u6d4b\u7684\u5e73\u5747\u503c\u3002\u5747\u503c\u662f\u7edf\u8ba1\u5b66\u4e0a\u7684\u6982\u5ff5\uff0c\u4e8b\u540e\u7edf\u8ba1\u6570\u636e\u8ba1\u7b97\u7684\u5e73\u5747\u503c\u3002 \u53ef\u4ee5\u8bf4\u671f\u671b\u503c\u662f\u5747\u503c\u5728\u6837\u672c\u65e0\u7a77\u5927\u4e0b\u7684\u6781\u9650\u3002\u6982\u7387\u5219\u662f\u7edf\u8ba1\u7684\u9891\u7387\u5728\u6837\u672c\u65e0\u7a77\u5927\u4e0b\u7684\u6781\u9650\u3002<\/li>\n
            • \u6982\u7387\u8d28\u91cf\u51fd\u6570\uff0c\u662f\u63cf\u8ff0\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u3002\u662f\u67d0\u4e2a\u968f\u673a\u503c\u51fa\u73b0\u7684\u6982\u7387\u3002<\/li>\n
            • \u6982\u7387\u5bc6\u5ea6\u51fd\u6570\uff0c\u662f\u63cf\u8ff0\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u7684\u6982\u7387\u5206\u5e03\u3002\u8fde\u7eed\u7684\u968f\u673a\u53d8\u91cf\u533a\u95f4\uff0c\u968f\u673a\u53d8\u91cf X \u7684\u53d6\u503c\u6709\u65e0\u7a77\u4e2a\uff0c\u6240\u4ee5 X \u7b49\u4e8e\u5177\u4f53\u7684\u67d0\u4e2a\u503c k, \u51fa\u73b0\u7684\u6982\u7387\u65e0\u9650\u8d8b\u8fd1\u4e8e\u96f6\u3002 \u867d\u7136 P(X=k)=0\uff0c\u4f46\u5e76\u975e\u4e0d\u53ef\u80fd\u4e8b\u4ef6\u3002\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u843d\u5728\u67d0\u4e2a\u533a\u95f4\u5177\u6709\u4e00\u5b9a\u7684\u6982\u7387\uff0c\u6240\u4ee5\u7528\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u63cf\u8ff0\u3002\u6982\u7387\u5219\u662f\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u3002<\/li>\n<\/ul><\/div>\n
               \u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (2<\/span>)        <\/div>\n
               <\/div>\n<\/p><\/div>\n<\/p><\/div>\n
                \n
              • \n
                \n
                \n
                 \u8cc7\u6df1\u5927\u4f6c : lingll <\/span>  <\/div>\n
                 <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                             \u70b9\u4e2a\u8d5e                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
              • \n
                \n
                \n
                 \u8cc7\u6df1\u5927\u4f6c : IgniteWhite <\/span>  <\/div>\n
                 <\/i>            <\/span> <\/div>\n<\/p><\/div>\n
                                                                             \u70b9\u4e2a\u8d5e                                                            <\/div>\n<\/p><\/div>\n<\/li>\n
              • \n","protected":false},"excerpt":{"rendered":"
                \u6cca\u677e\u5206\u5e03 \u8cc7\u6df1\u5927\u4f6c : atuoc…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[],"tags":[],"_links":{"self":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/95892"}],"collection":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=95892"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/95892\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=95892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=95892"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=95892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}