{"id":2385,"date":"2026-06-17T15:24:01","date_gmt":"2026-06-17T07:24:01","guid":{"rendered":"http:\/\/www.preluna.xyz\/?p=2385"},"modified":"2026-06-17T15:24:02","modified_gmt":"2026-06-17T07:24:02","slug":"%e5%88%86%e5%b8%83%e7%b1%bb%e5%9e%8b%e7%9a%84%e7%ae%80%e5%86%99","status":"publish","type":"post","link":"http:\/\/www.preluna.xyz\/index.php\/2026\/06\/17\/%e5%88%86%e5%b8%83%e7%b1%bb%e5%9e%8b%e7%9a%84%e7%ae%80%e5%86%99\/preluna\/text\/","title":{"rendered":"\u5206\u5e03\u7c7b\u578b\u7684\u7b80\u5199"},"content":{"rendered":"\n

U\u3001N\u3001P<\/code> \u90fd\u662f\u201c\u5206\u5e03\u7c7b\u578b\u7684\u7b80\u5199\u201d\u3002<\/p>\n\n\n\n

\u4f8b\u5982\uff1a<\/p>\n\n\n\n

X ~ U(0,6)<\/code><\/p>\n\n\n\n

\u8bfb\u4f5c\uff1a\u968f\u673a\u53d8\u91cf X<\/code> \u670d\u4ece\u533a\u95f4 (0,6)<\/code> \u4e0a\u7684\u5747\u5300\u5206\u5e03\u3002<\/p>\n\n\n\n

\u5176\u4e2d\u7b26\u53f7 ~<\/code> \u8868\u793a\u201c\u670d\u4ece\u2026\u2026\u5206\u5e03\u201d\u3002\u5728\u8003\u7814\u6570\u5b66\u4e00\u7684\u6982\u7387\u8bba\u4e2d\uff0c\u6700\u5e38\u89c1\u7684\u5206\u5e03\u4e3b\u8981\u6709\u4ee5\u4e0b\u51e0\u7c7b\u3002<\/p>\n\n\n\n

\u4e00\u3001\u6700\u6838\u5fc3\u7684\u516d\u79cd\u5e38\u89c1\u5206\u5e03<\/h2>\n\n\n\n

1. 0-1\u5206\u5e03\uff1aB(1,p)<\/h3>\n\n\n\n

\u5199\u4f5c\uff1a<\/p>\n\n\n\n

X ~ B(1,p)<\/code><\/p>\n\n\n\n

\u6216\u8005\u76f4\u63a5\u5199\u6210\uff1a<\/p>\n\n\n\n

P{X=1}=p\uff0cP{X=0}=1-p<\/code><\/p>\n\n\n\n

\u53c2\u6570 p<\/code> \u8868\u793a\u4e8b\u4ef6\u6210\u529f\u7684\u6982\u7387\uff0c\u6ee1\u8db3\uff1a<\/p>\n\n\n\n

0 < p < 1<\/code><\/p>\n\n\n\n

\u968f\u673a\u53d8\u91cf\u53ea\u80fd\u53d6\u4e24\u4e2a\u503c\uff1a<\/p>\n\n\n\n

X = 0 \u6216 1<\/code><\/p>\n\n\n\n

\u5176\u6570\u5b57\u7279\u5f81\u4e3a\uff1a<\/p>\n\n\n\n

E(X) = p<\/code><\/p>\n\n\n\n

D(X) = p(1-p)<\/code><\/p>\n\n\n\n

\u03c3(X) = \u221a[p(1-p)]<\/code><\/p>\n\n\n\n

\u8fd9\u91cc\u7684 \u03c3(X)<\/code> \u8868\u793a\u6807\u51c6\u5dee\u3002<\/p>\n\n\n\n

0-1\u5206\u5e03\u53ef\u4ee5\u7406\u89e3\u4e3a\u53ea\u8fdb\u884c\u4e00\u6b21\u8bd5\u9a8c\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n

    \n
  • \u4ea7\u54c1\u5408\u683c\u8bb0\u4e3a1\uff0c\u4e0d\u5408\u683c\u8bb0\u4e3a0\uff1b<\/li>\n\n\n\n
  • \u6295\u7bee\u547d\u4e2d\u8bb0\u4e3a1\uff0c\u672a\u547d\u4e2d\u8bb0\u4e3a0\uff1b<\/li>\n\n\n\n
  • \u4e8b\u4ef6\u53d1\u751f\u8bb0\u4e3a1\uff0c\u4e0d\u53d1\u751f\u8bb0\u4e3a0\u3002<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    2. \u4e8c\u9879\u5206\u5e03\uff1aB(n,p)<\/h3>\n\n\n\n

    \u5199\u4f5c\uff1a<\/p>\n\n\n\n

    X ~ B(n,p)<\/code><\/p>\n\n\n\n

    \u6709\u65f6\u4e5f\u5199\u4f5c\uff1a<\/p>\n\n\n\n

    X ~ Bin(n,p)<\/code><\/p>\n\n\n\n

    \u53c2\u6570\u542b\u4e49\u4e3a\uff1a<\/p>\n\n\n\n

      \n
    • n<\/code>\uff1a\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u7684\u6b21\u6570\uff1b<\/li>\n\n\n\n
    • p<\/code>\uff1a\u6bcf\u6b21\u8bd5\u9a8c\u6210\u529f\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n\n\n\n

      \u968f\u673a\u53d8\u91cf X<\/code> \u8868\u793a n<\/code> \u6b21\u8bd5\u9a8c\u4e2d\u6210\u529f\u7684\u6b21\u6570\uff0c\u56e0\u6b64\uff1a<\/p>\n\n\n\n

      X = 0,1,2,\u2026,n<\/code><\/p>\n\n\n\n

      \u6982\u7387\u8d28\u91cf\u51fd\u6570\u4e3a\uff1a<\/p>\n\n\n\n

      P{X=k} = C\u2099\u1d4f p\u1d4f(1-p)\u207f\u207b\u1d4f<\/code><\/p>\n\n\n\n

      \u6570\u5b57\u7279\u5f81\u4e3a\uff1a<\/p>\n\n\n\n

      E(X) = np<\/code><\/p>\n\n\n\n

      D(X) = np(1-p)<\/code><\/p>\n\n\n\n

      \u03c3(X) = \u221a[np(1-p)]<\/code><\/p>\n\n\n\n

      \u4e8c\u9879\u5206\u5e03\u548c0-1\u5206\u5e03\u7684\u5173\u7cfb\u662f\uff1a<\/p>\n\n\n\n

      B(1,p)<\/code> \u5c31\u662f\u53ea\u8fdb\u884c\u4e00\u6b21\u8bd5\u9a8c\u7684\u4e8c\u9879\u5206\u5e03\u3002<\/p>\n\n\n\n

      \u56e0\u6b64\uff0c0-1\u5206\u5e03\u662f\u4e8c\u9879\u5206\u5e03\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/p>\n\n\n\n

      \n\n\n\n

      3. \u6cca\u677e\u5206\u5e03\uff1aP(\u03bb)<\/h3>\n\n\n\n

      \u5199\u4f5c\uff1a<\/p>\n\n\n\n

      X ~ P(\u03bb)<\/code><\/p>\n\n\n\n

      \u6709\u4e9b\u6559\u6750\u4e5f\u4f1a\u5199\u6210\uff1a<\/p>\n\n\n\n

      X ~ \u03c0(\u03bb)<\/code><\/p>\n\n\n\n

      \u6216\u8005\uff1a<\/p>\n\n\n\n

      X ~ Poisson(\u03bb)<\/code><\/p>\n\n\n\n

      \u53c2\u6570 \u03bb<\/code> \u8868\u793a\u5355\u4f4d\u65f6\u95f4\u3001\u5355\u4f4d\u9762\u79ef\u6216\u5355\u4f4d\u8303\u56f4\u5185\u4e8b\u4ef6\u53d1\u751f\u7684\u5e73\u5747\u6b21\u6570\uff0c\u6ee1\u8db3\uff1a<\/p>\n\n\n\n

      \u03bb > 0<\/code><\/p>\n\n\n\n

      \u968f\u673a\u53d8\u91cf\u53d6\u503c\u4e3a\uff1a<\/p>\n\n\n\n

      X = 0,1,2,\u2026<\/code><\/p>\n\n\n\n

      \u6982\u7387\u8d28\u91cf\u51fd\u6570\u4e3a\uff1a<\/p>\n\n\n\n

      P{X=k} = e\u207b\u03bb \u03bb\u1d4f\/k!<\/code><\/p>\n\n\n\n

      \u6cca\u677e\u5206\u5e03\u6700\u91cd\u8981\u7684\u7ed3\u8bba\u662f\uff1a<\/p>\n\n\n\n

      E(X) = \u03bb<\/code><\/p>\n\n\n\n

      D(X) = \u03bb<\/code><\/p>\n\n\n\n

      \u03c3(X) = \u221a\u03bb<\/code><\/p>\n\n\n\n

      \u4e5f\u5c31\u662f\u8bf4\uff0c\u6cca\u677e\u5206\u5e03\u7684\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u76f8\u7b49\uff0c\u90fd\u7b49\u4e8e\u53c2\u6570 \u03bb<\/code>\u3002<\/p>\n\n\n\n

      \u4f8b\u5982\u4e0a\u4e00\u9898\u4e2d\u7684\uff1a<\/p>\n\n\n\n

      X\u2083 ~ P(3)<\/code><\/p>\n\n\n\n

      \u8868\u793a X\u2083<\/code> \u670d\u4ece\u53c2\u6570\u4e3a3\u7684\u6cca\u677e\u5206\u5e03\uff0c\u56e0\u6b64\uff1a<\/p>\n\n\n\n

      E(X\u2083)=3<\/code><\/p>\n\n\n\n

      D(X\u2083)=3<\/code><\/p>\n\n\n\n

      \u03c3(X\u2083)=\u221a3<\/code><\/p>\n\n\n\n

      \u770b\u5230\u6cca\u677e\u5206\u5e03\u65f6\uff0c\u57fa\u672c\u53ef\u4ee5\u76f4\u63a5\u5199\u51fa\uff1a<\/p>\n\n\n\n

      \u5747\u503c = \u65b9\u5dee = \u03bb<\/code><\/p>\n\n\n\n

      \n\n\n\n

      4. \u5747\u5300\u5206\u5e03\uff1aU(a,b)<\/h3>\n\n\n\n

      \u5199\u4f5c\uff1a<\/p>\n\n\n\n

      X ~ U(a,b)<\/code><\/p>\n\n\n\n

      \u5176\u4e2d\uff1a<\/p>\n\n\n\n

        \n
      • a<\/code>\uff1a\u533a\u95f4\u5de6\u7aef\u70b9\uff1b<\/li>\n\n\n\n
      • b<\/code>\uff1a\u533a\u95f4\u53f3\u7aef\u70b9\uff1b<\/li>\n\n\n\n
      • \u5fc5\u987b\u6ee1\u8db3 a < b<\/code>\u3002<\/li>\n<\/ul>\n\n\n\n

        \u8868\u793a\u968f\u673a\u53d8\u91cf X<\/code> \u5728\u533a\u95f4 (a,b)<\/code> \u4e0a\u5747\u5300\u5206\u5e03\u3002<\/p>\n\n\n\n

        \u5176\u6982\u7387\u5bc6\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n

        f(x) = 1\/(b-a)\uff0ca < x < b\n       0\uff0c\u5176\u4ed6\n<\/code><\/pre>\n\n\n\n
        \u6570\u5b57\u7279\u5f81\u4e3a\uff1a<\/p>\n\n\n\n
        E(X) = (a+b)\/2<\/code><\/p>\n\n\n\n
        D(X) = (b-a)\u00b2\/12<\/code><\/p>\n\n\n\n
        \u03c3(X) = (b-a)\/\u221a12<\/code><\/p>\n\n\n\n
        \u7531\u4e8e b>a<\/code>\uff0c\u6240\u4ee5\u6807\u51c6\u5dee\u4e5f\u53ef\u4ee5\u5199\u6210\uff1a<\/p>\n\n\n\n
        \u03c3(X) = (b-a)\/(2\u221a3)<\/code><\/p>\n\n\n\n
        \u4f8b\u5982\u4e0a\u4e00\u9898\uff1a<\/p>\n\n\n\n
        X\u2081 ~ U(0,6)<\/code><\/p>\n\n\n\n
        \u5176\u4e2d\uff1a<\/p>\n\n\n\n
        a=0\uff0cb=6<\/code><\/p>\n\n\n\n
        \u56e0\u6b64\uff1a<\/p>\n\n\n\n
        E(X\u2081) = (0+6)\/2 = 3<\/code><\/p>\n\n\n\n
        D(X\u2081) = (6-0)\u00b2\/12 = 3<\/code><\/p>\n\n\n\n
        \u03c3(X\u2081) = \u221a3<\/code><\/p>\n\n\n\n
        \u5747\u5300\u5206\u5e03\u7684\u671f\u671b\u5c31\u662f\u533a\u95f4\u4e2d\u70b9\uff0c\u65b9\u5dee\u7531\u533a\u95f4\u957f\u5ea6\u51b3\u5b9a\u3002<\/p>\n\n\n\n
        \u5feb\u901f\u8bb0\u5fc6\uff1a<\/p>\n\n\n\n
        \u5747\u503c\u770b\u4e2d\u70b9\uff0c\u65b9\u5dee\u770b\u957f\u5ea6\u5e73\u65b9\u9664\u4ee512\u3002<\/code><\/p>\n\n\n\n
        \n\n\n\n
        5. \u6307\u6570\u5206\u5e03\uff1aE(\u03bb) \u6216 Exp(\u03bb)<\/h3>\n\n\n\n
        \u5199\u4f5c\uff1a<\/p>\n\n\n\n
        X ~ E(\u03bb)<\/code><\/p>\n\n\n\n
        \u6216\u8005\uff1a<\/p>\n\n\n\n
        X ~ Exp(\u03bb)<\/code><\/p>\n\n\n\n
        \u7531\u4e8e\u7b26\u53f7 E<\/code> \u4e5f\u5e38\u7528\u6765\u8868\u793a\u6570\u5b66\u671f\u671b\uff0c\u56e0\u6b64\u6709\u4e9b\u6559\u6750\u66f4\u559c\u6b22\u4f7f\u7528 Exp(\u03bb)<\/code>\u3002<\/p>\n\n\n\n
        \u53c2\u6570 \u03bb<\/code> \u79f0\u4e3a\u7387\u53c2\u6570\u6216\u5f3a\u5ea6\u53c2\u6570\uff0c\u6ee1\u8db3\uff1a<\/p>\n\n\n\n
        \u03bb > 0<\/code><\/p>\n\n\n\n
        \u6307\u6570\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n
        f(x) = \u03bbe\u207b\u03bbx\uff0cx > 0\n       0\uff0cx \u2264 0\n<\/code><\/pre>\n\n\n\n
        \u6570\u5b57\u7279\u5f81\u4e3a\uff1a<\/p>\n\n\n\n
        E(X) = 1\/\u03bb<\/code><\/p>\n\n\n\n
        D(X) = 1\/\u03bb\u00b2<\/code><\/p>\n\n\n\n
        \u03c3(X) = 1\/\u03bb<\/code><\/p>\n\n\n\n
        \u6240\u4ee5\u6307\u6570\u5206\u5e03\u5177\u6709\u4e00\u4e2a\u5bb9\u6613\u8bb0\u5fc6\u7684\u7279\u70b9\uff1a<\/p>\n\n\n\n
        \u6807\u51c6\u5dee = \u6570\u5b66\u671f\u671b = 1\/\u03bb<\/code><\/p>\n\n\n\n
        \u4f46\u65b9\u5dee\u662f\uff1a<\/p>\n\n\n\n
        D(X)=1\/\u03bb\u00b2<\/code><\/p>\n\n\n\n
        \u4e0d\u8981\u628a\u65b9\u5dee\u8bef\u5199\u6210 1\/\u03bb<\/code>\u3002<\/p>\n\n\n\n
        \u6307\u6570\u5206\u5e03\u901a\u5e38\u7528\u4e8e\u8868\u793a\uff1a<\/p>\n\n\n\n
          \n
        • \u5143\u4ef6\u7684\u5bff\u547d\uff1b<\/li>\n\n\n\n
        • \u7b49\u5f85\u65f6\u95f4\uff1b<\/li>\n\n\n\n
        • \u4e24\u6b21\u4e8b\u4ef6\u53d1\u751f\u4e4b\u95f4\u7684\u65f6\u95f4\u95f4\u9694\u3002<\/li>\n<\/ul>\n\n\n\n
          \u6307\u6570\u5206\u5e03\u8fd8\u5177\u6709\u65e0\u8bb0\u5fc6\u6027\uff1a<\/p>\n\n\n\n
          P{X>s+t | X>s} = P{X>t}<\/code><\/p>\n\n\n\n
          \u8fd9\u662f\u8003\u7814\u4e2d\u8f83\u5e38\u8003\u7684\u6027\u8d28\u3002<\/p>\n\n\n\n
          \n\n\n\n
          6. \u6b63\u6001\u5206\u5e03\uff1aN(\u03bc,\u03c3\u00b2)<\/h3>\n\n\n\n
          \u5199\u4f5c\uff1a<\/p>\n\n\n\n
          X ~ N(\u03bc,\u03c3\u00b2)<\/code><\/p>\n\n\n\n
          \u53c2\u6570\u542b\u4e49\u4e3a\uff1a<\/p>\n\n\n\n
            \n
          • \u03bc<\/code>\uff1a\u6570\u5b66\u671f\u671b\uff0c\u4e5f\u5c31\u662f\u5747\u503c\uff1b<\/li>\n\n\n\n
          • \u03c3\u00b2<\/code>\uff1a\u65b9\u5dee\uff1b<\/li>\n\n\n\n
          • \u03c3<\/code>\uff1a\u6807\u51c6\u5dee\u3002<\/li>\n<\/ul>\n\n\n\n
            \u56e0\u6b64\uff1a<\/p>\n\n\n\n
            E(X) = \u03bc<\/code><\/p>\n\n\n\n
            D(X) = \u03c3\u00b2<\/code><\/p>\n\n\n\n
            \u03c3(X) = \u03c3<\/code><\/p>\n\n\n\n
            \u8fd9\u91cc\u5fc5\u987b\u7279\u522b\u6ce8\u610f\uff1a\u6309\u7167\u56fd\u5185\u8003\u7814\u6570\u5b66\u6559\u6750\u7684\u901a\u5e38\u7ea6\u5b9a\uff0c\u6b63\u6001\u5206\u5e03\u7684\u7b2c\u4e8c\u4e2a\u53c2\u6570\u662f\u65b9\u5dee<\/strong>\uff0c\u4e0d\u662f\u6807\u51c6\u5dee\u3002<\/p>\n\n\n\n
            \u4f8b\u5982\uff1a<\/p>\n\n\n\n
            X ~ N(0,4)<\/code><\/p>\n\n\n\n
            \u8868\u793a\uff1a<\/p>\n\n\n\n
            \u03bc=0<\/code><\/p>\n\n\n\n
            \u03c3\u00b2=4<\/code><\/p>\n\n\n\n
            \u6240\u4ee5\uff1a<\/p>\n\n\n\n
            E(X)=0<\/code><\/p>\n\n\n\n
            D(X)=4<\/code><\/p>\n\n\n\n
            \u03c3(X)=2<\/code><\/p>\n\n\n\n
            \u4e0d\u80fd\u8ba4\u4e3a\u6807\u51c6\u5dee\u662f4\u3002<\/p>\n\n\n\n
            \u6b63\u6001\u5206\u5e03\u7684\u6982\u7387\u5bc6\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n
            f(x) = 1\/(\u221a(2\u03c0)\u03c3) \u00b7 e\u207b[(x-\u03bc)\u00b2\/(2\u03c3\u00b2)]\n<\/code><\/pre>\n\n\n\n
            \u5f53\uff1a<\/p>\n\n\n\n
            \u03bc=0\uff0c\u03c3\u00b2=1<\/code><\/p>\n\n\n\n
            \u79f0\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff0c\u5199\u4f5c\uff1a<\/p>\n\n\n\n
            X ~ N(0,1)<\/code><\/p>\n\n\n\n
            \u6807\u51c6\u6b63\u6001\u5206\u5e03\u4e00\u822c\u7528\u5927\u5199\u5b57\u6bcd Z<\/code> \u8868\u793a\uff1a<\/p>\n\n\n\n
            Z ~ N(0,1)<\/code><\/p>\n\n\n\n
            \u82e5\uff1a<\/p>\n\n\n\n
            X ~ N(\u03bc,\u03c3\u00b2)<\/code><\/p>\n\n\n\n
            \u5219\u6807\u51c6\u5316\u4ee5\u540e\uff1a<\/p>\n\n\n\n
            Z = (X-\u03bc)\/\u03c3 ~ N(0,1)<\/code><\/p>\n\n\n\n
            \n\n\n\n
            \u4e8c\u3001\u516d\u79cd\u6838\u5fc3\u5206\u5e03\u603b\u7ed3\u8868<\/h2>\n\n\n\n
            \u5206\u5e03<\/th>\u5e38\u7528\u8bb0\u53f7<\/th>\u53c2\u6570\u542b\u4e49<\/th>\u6570\u5b66\u671f\u671b E(X)<\/th>\u65b9\u5dee D(X)<\/th>\u6807\u51c6\u5dee \u03c3(X)<\/th><\/tr><\/thead>
            0-1\u5206\u5e03<\/td>B(1,p)<\/code><\/td>p<\/code>\u4e3a\u6210\u529f\u6982\u7387<\/td>p<\/code><\/td>p(1-p)<\/code><\/td>\u221a[p(1-p)]<\/code><\/td><\/tr>
            \u4e8c\u9879\u5206\u5e03<\/td>B(n,p)<\/code><\/td>n<\/code>\u4e3a\u6b21\u6570\uff0cp<\/code>\u4e3a\u6210\u529f\u6982\u7387<\/td>np<\/code><\/td>np(1-p)<\/code><\/td>\u221a[np(1-p)]<\/code><\/td><\/tr>
            \u6cca\u677e\u5206\u5e03<\/td>P(\u03bb)<\/code><\/td>\u03bb<\/code>\u4e3a\u5e73\u5747\u53d1\u751f\u6b21\u6570<\/td>\u03bb<\/code><\/td>\u03bb<\/code><\/td>\u221a\u03bb<\/code><\/td><\/tr>
            \u5747\u5300\u5206\u5e03<\/td>U(a,b)<\/code><\/td>a\u3001b<\/code>\u4e3a\u533a\u95f4\u7aef\u70b9<\/td>(a+b)\/2<\/code><\/td>(b-a)\u00b2\/12<\/code><\/td>(b-a)\/\u221a12<\/code><\/td><\/tr>
            \u6307\u6570\u5206\u5e03<\/td>E(\u03bb)<\/code>\u3001Exp(\u03bb)<\/code><\/td>\u03bb<\/code>\u4e3a\u7387\u53c2\u6570<\/td>1\/\u03bb<\/code><\/td>1\/\u03bb\u00b2<\/code><\/td>1\/\u03bb<\/code><\/td><\/tr>
            \u6b63\u6001\u5206\u5e03<\/td>N(\u03bc,\u03c3\u00b2)<\/code><\/td>\u03bc<\/code>\u4e3a\u5747\u503c\uff0c\u03c3\u00b2<\/code>\u4e3a\u65b9\u5dee<\/td>\u03bc<\/code><\/td>\u03c3\u00b2<\/code><\/td>\u03c3<\/code><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
            \u8fd9\u5f20\u8868\u662f\u8003\u7814\u6982\u7387\u8bba\u4e2d\u5fc5\u987b\u719f\u7ec3\u638c\u63e1\u7684\u5185\u5bb9\u3002<\/p>\n\n\n\n
            \n\n\n\n
            \u4e09\u3001\u6570\u5b66\u671f\u671b\u3001\u65b9\u5dee\u3001\u6807\u51c6\u5dee\u4e4b\u95f4\u7684\u5173\u7cfb<\/h2>\n\n\n\n
            1. \u6570\u5b66\u671f\u671b<\/h3>\n\n\n\n
            \u6570\u5b66\u671f\u671b\u53cd\u6620\u968f\u673a\u53d8\u91cf\u53d6\u503c\u7684\u201c\u5e73\u5747\u4f4d\u7f6e\u201d\u6216\u201c\u4e2d\u5fc3\u4f4d\u7f6e\u201d\u3002<\/p>\n\n\n\n
            \u8bb0\u4f5c\uff1a<\/p>\n\n\n\n
            E(X)<\/code><\/p>\n\n\n\n
            \u4f8b\u5982\uff1a<\/p>\n\n\n\n
            X ~ N(3,4)<\/code><\/p>\n\n\n\n
            \u8868\u793a\u5b83\u7684\u5747\u503c\u57283\u9644\u8fd1\uff0c\u56e0\u6b64\uff1a<\/p>\n\n\n\n
            E(X)=3<\/code><\/p>\n\n\n\n
            \u4f46\u6570\u5b66\u671f\u671b\u4e0d\u4e00\u5b9a\u662f\u968f\u673a\u53d8\u91cf\u771f\u6b63\u53ef\u4ee5\u53d6\u5230\u7684\u503c\u3002<\/p>\n\n\n\n
            \u4f8b\u5982\u63b7\u4e00\u6b21\u9ab0\u5b50\uff0c\u671f\u671b\u4e3a\uff1a<\/p>\n\n\n\n
            E(X)=3.5<\/code><\/p>\n\n\n\n
            \u4f46\u9ab0\u5b50\u4e0d\u53ef\u80fd\u63b7\u51fa3.5\u3002<\/p>\n\n\n\n
            \n\n\n\n
            2. \u65b9\u5dee<\/h3>\n\n\n\n
            \u65b9\u5dee\u53cd\u6620\u968f\u673a\u53d8\u91cf\u76f8\u5bf9\u4e8e\u5747\u503c\u7684\u6ce2\u52a8\u7a0b\u5ea6\u3002<\/p>\n\n\n\n
            \u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n
            D(X) = E{[X-E(X)]\u00b2}<\/code><\/p>\n\n\n\n
            \u8003\u7814\u8ba1\u7b97\u4e2d\u66f4\u5e38\u4f7f\u7528\uff1a<\/p>\n\n\n\n
            D(X) = E(X\u00b2)-[E(X)]\u00b2<\/code><\/p>\n\n\n\n
            \ue200genui\ue202{“probability_statistics_learning_block”:{“type_id”:”VARIANCE”}}\ue201<\/p>\n\n\n\n
            \u8fd9\u4e24\u4e2a\u516c\u5f0f\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n\n\n\n
            \u901a\u5e38\u505a\u9898\u65f6\uff1a<\/p>\n\n\n\n
              \n
            • \u5df2\u77e5\u5206\u5e03\uff0c\u76f4\u63a5\u5957\u5206\u5e03\u7684\u65b9\u5dee\u516c\u5f0f\uff1b<\/li>\n\n\n\n
            • \u5df2\u77e5\u5bc6\u5ea6\u6216\u5206\u5e03\u5f8b\uff0c\u9700\u8981\u8ba1\u7b97 E(X)<\/code> \u548c E(X\u00b2)<\/code>\uff1b<\/li>\n\n\n\n
            • \u5df2\u77e5 E(X)<\/code> \u548c D(X)<\/code>\uff0c\u53ef\u4ee5\u53cd\u63a8\u51fa E(X\u00b2)<\/code>\u3002<\/li>\n<\/ul>\n\n\n\n
              \u5e38\u7528\u8f6c\u6362\u4e3a\uff1a<\/p>\n\n\n\n
              E(X\u00b2) = D(X)+[E(X)]\u00b2<\/code><\/p>\n\n\n\n
              \u4f8b\u5982\uff1a<\/p>\n\n\n\n
              E(X)=2\uff0cD(X)=5<\/code><\/p>\n\n\n\n
              \u5219\uff1a<\/p>\n\n\n\n
              E(X\u00b2)=5+2\u00b2=9<\/code><\/p>\n\n\n\n
              \u8fd9\u91cc\u4e00\u5b9a\u8981\u6ce8\u610f\uff1a<\/p>\n\n\n\n
              D(X)<\/code> \u4e0d\u7b49\u4e8e E(X\u00b2)<\/code>\u3002<\/p>\n\n\n\n
              \n\n\n\n
              3. \u6807\u51c6\u5dee<\/h3>\n\n\n\n
              \u6807\u51c6\u5dee\u5c31\u662f\u65b9\u5dee\u7684\u7b97\u672f\u5e73\u65b9\u6839\uff1a<\/p>\n\n\n\n
              \u03c3(X) = \u221aD(X)<\/code><\/p>\n\n\n\n
              \u65b9\u5dee\u7684\u5355\u4f4d\u662f\u539f\u5355\u4f4d\u7684\u5e73\u65b9\uff0c\u800c\u6807\u51c6\u5dee\u4e0e\u968f\u673a\u53d8\u91cf\u672c\u8eab\u5355\u4f4d\u76f8\u540c\u3002<\/p>\n\n\n\n
              \u4f8b\u5982\u67d0\u4ea7\u54c1\u957f\u5ea6\u7684\u5355\u4f4d\u662f\u5398\u7c73\uff1a<\/p>\n\n\n\n
                \n
              • \u6570\u5b66\u671f\u671b\u7684\u5355\u4f4d\u662f\u5398\u7c73\uff1b<\/li>\n\n\n\n
              • \u65b9\u5dee\u7684\u5355\u4f4d\u662f\u5e73\u65b9\u5398\u7c73\uff1b<\/li>\n\n\n\n
              • \u6807\u51c6\u5dee\u7684\u5355\u4f4d\u662f\u5398\u7c73\u3002<\/li>\n<\/ul>\n\n\n\n
                \u56e0\u6b64\u6807\u51c6\u5dee\u6bd4\u65b9\u5dee\u66f4\u5bb9\u6613\u76f4\u63a5\u53cd\u6620\u6ce2\u52a8\u5927\u5c0f\u3002<\/p>\n\n\n\n
                \n\n\n\n
                \u56db\u3001\u7ebf\u6027\u53d8\u6362\u4e0b\u7684\u671f\u671b\u3001\u65b9\u5dee\u548c\u6807\u51c6\u5dee<\/h2>\n\n\n\n
                \u82e5\uff1a<\/p>\n\n\n\n
                Y = aX+b<\/code><\/p>\n\n\n\n
                \u5219\u6570\u5b66\u671f\u671b\u4e3a\uff1a<\/p>\n\n\n\n
                E(Y) = aE(X)+b<\/code><\/p>\n\n\n\n
                \u65b9\u5dee\u4e3a\uff1a<\/p>\n\n\n\n
                D(Y) = a\u00b2D(X)<\/code><\/p>\n\n\n\n
                \u6807\u51c6\u5dee\u4e3a\uff1a<\/p>\n\n\n\n
                \u03c3(Y) = |a|\u03c3(X)<\/code><\/p>\n\n\n\n
                \u8fd9\u91cc\u6709\u4e09\u4e2a\u91cd\u8981\u89c4\u5f8b\u3002<\/p>\n\n\n\n
                \u7b2c\u4e00\uff0c\u5e38\u6570 b<\/code> \u4f1a\u6539\u53d8\u5747\u503c\uff0c\u4f46\u4e0d\u4f1a\u6539\u53d8\u65b9\u5dee\u3002<\/p>\n\n\n\n
                \u4f8b\u5982\uff1a<\/p>\n\n\n\n
                Y=X+10<\/code><\/p>\n\n\n\n
                \u5219\uff1a<\/p>\n\n\n\n
                E(Y)=E(X)+10<\/code><\/p>\n\n\n\n
                \u4f46\u662f\uff1a<\/p>\n\n\n\n
                D(Y)=D(X)<\/code><\/p>\n\n\n\n
                \u56e0\u4e3a\u6574\u4f53\u5e73\u79fb\u4e0d\u4f1a\u6539\u53d8\u6570\u636e\u7684\u5206\u6563\u7a0b\u5ea6\u3002<\/p>\n\n\n\n
                \u7b2c\u4e8c\uff0c\u65b9\u5dee\u4e2d\u7684\u7cfb\u6570\u5fc5\u987b\u5e73\u65b9\u3002<\/p>\n\n\n\n
                \u4f8b\u5982\uff1a<\/p>\n\n\n\n
                Y=-2X<\/code><\/p>\n\n\n\n
                \u5219\uff1a<\/p>\n\n\n\n
                D(Y)=(-2)\u00b2D(X)=4D(X)<\/code><\/p>\n\n\n\n
                \u800c\u4e0d\u662f -2D(X)<\/code>\u3002<\/p>\n\n\n\n
                \u7b2c\u4e09\uff0c\u6807\u51c6\u5dee\u4e2d\u7684\u7cfb\u6570\u8981\u53d6\u7edd\u5bf9\u503c\u3002<\/p>\n\n\n\n
                \u03c3(aX+b)=|a|\u03c3(X)<\/code><\/p>\n\n\n\n
                \u6807\u51c6\u5dee\u4e0d\u53ef\u80fd\u662f\u8d1f\u6570\u3002<\/p>\n\n\n\n
                \n\n\n\n
                \u4e94\u3001\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u76f8\u52a0\u65f6\u7684\u65b9\u5dee<\/h2>\n\n\n\n
                \u4e00\u822c\u60c5\u51b5\u4e0b\uff1a<\/p>\n\n\n\n
                D(X+Y)=D(X)+D(Y)+2Cov(X,Y)<\/code><\/p>\n\n\n\n
                D(X-Y)=D(X)+D(Y)-2Cov(X,Y)<\/code><\/p>\n\n\n\n
                \u5176\u4e2d Cov(X,Y)<\/code> \u662f\u534f\u65b9\u5dee\u3002<\/p>\n\n\n\n
                \u82e5 X\u3001Y<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u5219\uff1a<\/p>\n\n\n\n
                Cov(X,Y)=0<\/code><\/p>\n\n\n\n
                \u56e0\u6b64\uff1a<\/p>\n\n\n\n
                D(X+Y)=D(X)+D(Y)<\/code><\/p>\n\n\n\n
                D(X-Y)=D(X)+D(Y)<\/code><\/p>\n\n\n\n
                \u6ce8\u610f\uff0c\u5373\u4f7f\u662f\u76f8\u51cf\uff0c\u65b9\u5dee\u4ecd\u7136\u662f\u76f8\u52a0\uff0c\u56e0\u4e3a\u8d1f\u53f7\u7ecf\u8fc7\u5e73\u65b9\u4ee5\u540e\u6d88\u5931\u3002<\/p>\n\n\n\n
                \u66f4\u4e00\u822c\u5730\uff0c\u5982\u679c X\u2081\u3001X\u2082\u3001\u2026\u3001X\u2099<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u5219\uff1a<\/p>\n\n\n\n
                D(a\u2081X\u2081+a\u2082X\u2082+\u2026+a\u2099X\u2099)<\/code><\/p>\n\n\n\n
                =a\u2081\u00b2D(X\u2081)+a\u2082\u00b2D(X\u2082)+\u2026+a\u2099\u00b2D(X\u2099)<\/code><\/p>\n\n\n\n
                \u8fd9\u5c31\u662f\u7b2c26\u9898\u4f7f\u7528\u7684\u516c\u5f0f\u3002<\/p>\n\n\n\n
                \n\n\n\n
                \u516d\u3001\u7b2c26\u9898\u4e2d\u4e09\u4e2a\u8bb0\u53f7\u7684\u5b8c\u6574\u542b\u4e49<\/h2>\n\n\n\n
                \u9898\u76ee\u7ed9\u51fa\uff1a<\/p>\n\n\n\n
                X\u2081 ~ U(0,6)<\/code><\/p>\n\n\n\n
                \u8bf4\u660e\uff1a<\/p>\n\n\n\n
                X\u2081<\/code> \u670d\u4ece (0,6)<\/code> \u4e0a\u7684\u5747\u5300\u5206\u5e03\u3002<\/p>\n\n\n\n
                \u56e0\u6b64\uff1a<\/p>\n\n\n\n
                E(X\u2081)=3<\/code><\/p>\n\n\n\n
                D(X\u2081)=3<\/code><\/p>\n\n\n\n
                \u03c3(X\u2081)=\u221a3<\/code><\/p>\n\n\n\n
                \u9898\u76ee\u7ed9\u51fa\uff1a<\/p>\n\n\n\n
                X\u2082 ~ N(0,4)<\/code><\/p>\n\n\n\n
                \u8bf4\u660e\uff1a<\/p>\n\n\n\n
                X\u2082<\/code> \u670d\u4ece\u5747\u503c\u4e3a0\u3001\u65b9\u5dee\u4e3a4\u7684\u6b63\u6001\u5206\u5e03\u3002<\/p>\n\n\n\n
                \u56e0\u6b64\uff1a<\/p>\n\n\n\n
                E(X\u2082)=0<\/code><\/p>\n\n\n\n
                D(X\u2082)=4<\/code><\/p>\n\n\n\n
                \u03c3(X\u2082)=2<\/code><\/p>\n\n\n\n
                \u9898\u76ee\u7ed9\u51fa\uff1a<\/p>\n\n\n\n
                X\u2083 ~ P(3)<\/code><\/p>\n\n\n\n
                \u8bf4\u660e\uff1a<\/p>\n\n\n\n
                X\u2083<\/code> \u670d\u4ece\u53c2\u6570\u4e3a3\u7684\u6cca\u677e\u5206\u5e03\u3002<\/p>\n\n\n\n
                \u56e0\u6b64\uff1a<\/p>\n\n\n\n
                E(X\u2083)=3<\/code><\/p>\n\n\n\n
                D(X\u2083)=3<\/code><\/p>\n\n\n\n
                \u03c3(X\u2083)=\u221a3<\/code><\/p>\n\n\n\n
                \u6240\u4ee5\u9898\u76ee\u6c42\uff1a<\/p>\n\n\n\n
                D(X\u2081-2X\u2082+3X\u2083)<\/code><\/p>\n\n\n\n
                \u7531\u4e8e\u4e09\u8005\u76f8\u4e92\u72ec\u7acb\uff1a<\/p>\n\n\n\n
                D(X\u2081-2X\u2082+3X\u2083)<\/code><\/p>\n\n\n\n
                =D(X\u2081)+(-2)\u00b2D(X\u2082)+3\u00b2D(X\u2083)<\/code><\/p>\n\n\n\n
                =3+4\u00d74+9\u00d73<\/code><\/p>\n\n\n\n
                =46<\/code><\/p>\n\n\n\n
                \n\n\n\n
                \u4e03\u3001\u6570\u7406\u7edf\u8ba1\u4e2d\u8fd8\u4f1a\u51fa\u73b0\u7684\u4e09\u4e2a\u5206\u5e03\u8bb0\u53f7<\/h2>\n\n\n\n
                \u9664\u4e86\u524d\u9762\u7684\u5e38\u89c1\u968f\u673a\u53d8\u91cf\u5206\u5e03\uff0c\u5728\u6570\u7406\u7edf\u8ba1\u90e8\u5206\u8fd8\u4f1a\u7ecf\u5e38\u51fa\u73b0 \u03c7\u00b2\u3001t\u3001F<\/code> \u4e09\u79cd\u62bd\u6837\u5206\u5e03\u3002<\/p>\n\n\n\n
                1. \u5361\u65b9\u5206\u5e03\uff1a\u03c7\u00b2(n)<\/h3>\n\n\n\n
                \u5199\u4f5c\uff1a<\/p>\n\n\n\n
                X ~ \u03c7\u00b2(n)<\/code><\/p>\n\n\n\n
                \u5176\u4e2d n<\/code> \u79f0\u4e3a\u81ea\u7531\u5ea6\u3002<\/p>\n\n\n\n
                \u82e5\uff1a<\/p>\n\n\n\n
                X\u2081,X\u2082,\u2026,X\u2099<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u4e14\u90fd\u670d\u4ece N(0,1)<\/code><\/p>\n\n\n\n
                \u5219\uff1a<\/p>\n\n\n\n
                X\u2081\u00b2+X\u2082\u00b2+\u2026+X\u2099\u00b2 ~ \u03c7\u00b2(n)<\/code><\/p>\n\n\n\n
                \u5176\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\u4e3a\uff1a<\/p>\n\n\n\n
                E(X)=n<\/code><\/p>\n\n\n\n
                D(X)=2n<\/code><\/p>\n\n\n\n
                \u03c3(X)=\u221a(2n)<\/code><\/p>\n\n\n\n
                \u81ea\u7531\u5ea6\u5177\u6709\u53ef\u52a0\u6027\uff1a<\/p>\n\n\n\n
                \u82e5 X ~ \u03c7\u00b2(m)<\/code>\uff0cY ~ \u03c7\u00b2(n)<\/code>\uff0c\u4e14\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\uff1a<\/p>\n\n\n\n
                X+Y ~ \u03c7\u00b2(m+n)<\/code><\/p>\n\n\n\n
                \n\n\n\n
                2. t\u5206\u5e03\uff1at(n)<\/h3>\n\n\n\n
                \u5199\u4f5c\uff1a<\/p>\n\n\n\n
                T ~ t(n)<\/code><\/p>\n\n\n\n
                \u5176\u4e2d n<\/code> \u4e3a\u81ea\u7531\u5ea6\u3002<\/p>\n\n\n\n
                \u82e5\uff1a<\/p>\n\n\n\n
                X ~ N(0,1)<\/code><\/p>\n\n\n\n
                Y ~ \u03c7\u00b2(n)<\/code><\/p>\n\n\n\n
                \u4e14 X\u3001Y<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u5219\uff1a<\/p>\n\n\n\n
                T = X\/\u221a(Y\/n) ~ t(n)<\/code><\/p>\n\n\n\n
                \u5f53 n>1<\/code> \u65f6\uff1a<\/p>\n\n\n\n
                E(T)=0<\/code><\/p>\n\n\n\n
                \u5f53 n>2<\/code> \u65f6\uff1a<\/p>\n\n\n\n
                D(T)=n\/(n-2)<\/code><\/p>\n\n\n\n
                \u8003\u7814\u4e2d\u5bf9 t \u5206\u5e03\u66f4\u91cd\u8981\u7684\u4e0d\u662f\u76f4\u63a5\u6c42\u5b83\u7684\u65b9\u5dee\uff0c\u800c\u662f\u8bc6\u522b\u7edf\u8ba1\u91cf\uff1a<\/p>\n\n\n\n
                (X\u0304-\u03bc)\/(S\/\u221an) ~ t(n-1)<\/code><\/p>\n\n\n\n
                \u8fd9\u91cc\u81ea\u7531\u5ea6\u662f n-1<\/code>\u3002<\/p>\n\n\n\n
                \n\n\n\n
                3. F\u5206\u5e03\uff1aF(m,n)<\/h3>\n\n\n\n
                \u5199\u4f5c\uff1a<\/p>\n\n\n\n
                F ~ F(m,n)<\/code><\/p>\n\n\n\n
                \u5176\u4e2d\uff1a<\/p>\n\n\n\n
                  \n
                • m<\/code>\uff1a\u5206\u5b50\u81ea\u7531\u5ea6\uff1b<\/li>\n\n\n\n
                • n<\/code>\uff1a\u5206\u6bcd\u81ea\u7531\u5ea6\u3002<\/li>\n<\/ul>\n\n\n\n
                  \u82e5\uff1a<\/p>\n\n\n\n
                  X ~ \u03c7\u00b2(m)<\/code><\/p>\n\n\n\n
                  Y ~ \u03c7\u00b2(n)<\/code><\/p>\n\n\n\n
                  \u5e76\u4e14\u4e8c\u8005\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\uff1a<\/p>\n\n\n\n
                  (X\/m)\/(Y\/n) ~ F(m,n)<\/code><\/p>\n\n\n\n
                  F\u5206\u5e03\u7684\u4e00\u4e2a\u91cd\u8981\u6027\u8d28\u662f\uff1a<\/p>\n\n\n\n
                  \u82e5\uff1a<\/p>\n\n\n\n
                  F ~ F(m,n)<\/code><\/p>\n\n\n\n
                  \u5219\uff1a<\/p>\n\n\n\n
                  1\/F ~ F(n,m)<\/code><\/p>\n\n\n\n
                  \u6ce8\u610f\u5012\u6570\u4ee5\u540e\uff0c\u4e24\u4e2a\u81ea\u7531\u5ea6\u7684\u4f4d\u7f6e\u4e5f\u8981\u4ea4\u6362\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  \u516b\u3001\u8003\u7814\u4e2d\u6700\u5e38\u89c1\u7684\u7b26\u53f7\u9677\u9631<\/h2>\n\n\n\n
                  1. N(\u03bc,\u03c3\u00b2)\u7684\u7b2c\u4e8c\u4e2a\u53c2\u6570\u662f\u65b9\u5dee<\/h3>\n\n\n\n
                  \u4f8b\u5982\uff1a<\/p>\n\n\n\n
                  X ~ N(2,9)<\/code><\/p>\n\n\n\n
                  \u5219\uff1a<\/p>\n\n\n\n
                  E(X)=2<\/code><\/p>\n\n\n\n
                  D(X)=9<\/code><\/p>\n\n\n\n
                  \u03c3(X)=3<\/code><\/p>\n\n\n\n
                  \u4e0d\u662f\u6807\u51c6\u5dee\u7b49\u4e8e9\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  2. P(\u03bb)\u4e0d\u662f\u6982\u7387P<\/h3>\n\n\n\n
                  \u5355\u72ec\u51fa\u73b0\uff1a<\/p>\n\n\n\n
                  P(A)<\/code><\/p>\n\n\n\n
                  \u8868\u793a\u4e8b\u4ef6 A<\/code> \u7684\u6982\u7387\u3002<\/p>\n\n\n\n
                  \u800c\u51fa\u73b0\uff1a<\/p>\n\n\n\n
                  X ~ P(\u03bb)<\/code><\/p>\n\n\n\n
                  \u8868\u793a X<\/code> \u670d\u4ece\u6cca\u677e\u5206\u5e03\u3002<\/p>\n\n\n\n
                  \u8981\u7ed3\u5408\u4e0a\u4e0b\u6587\u5224\u65ad\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  3. E\u65e2\u53ef\u4ee5\u8868\u793a\u671f\u671b\uff0c\u4e5f\u53ef\u4ee5\u8868\u793a\u6307\u6570\u5206\u5e03<\/h3>\n\n\n\n
                  E(X)<\/code> \u8868\u793a\u968f\u673a\u53d8\u91cf X<\/code> \u7684\u6570\u5b66\u671f\u671b\u3002<\/p>\n\n\n\n
                  X ~ E(\u03bb)<\/code> \u53ef\u80fd\u8868\u793a\u6307\u6570\u5206\u5e03\u3002<\/p>\n\n\n\n
                  \u6240\u4ee5\u90e8\u5206\u6559\u6750\u5199\u4e3a\uff1a<\/p>\n\n\n\n
                  X ~ Exp(\u03bb)<\/code><\/p>\n\n\n\n
                  \u4ee5\u907f\u514d\u6df7\u6dc6\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  4. B(n,p)\u4e2d\u7684B\u53ef\u80fd\u8868\u793a\u4e8c\u9879\u5206\u5e03<\/h3>\n\n\n\n
                  B(1,p)<\/code> \u662f0-1\u5206\u5e03\u3002<\/p>\n\n\n\n
                  B(n,p)<\/code> \u662f\u4e8c\u9879\u5206\u5e03\u3002<\/p>\n\n\n\n
                  \u90e8\u5206\u6559\u6750\u4e5f\u7528 Bin(n,p)<\/code>\uff0c\u542b\u4e49\u76f8\u540c\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  5. \u65b9\u5dee\u3001\u6807\u51c6\u5dee\u4e0d\u80fd\u6df7\u7528<\/h3>\n\n\n\n
                  D(X)=\u03c3\u00b2<\/code><\/p>\n\n\n\n
                  \u03c3(X)=\u221aD(X)<\/code><\/p>\n\n\n\n
                  \u4f8b\u5982\uff1a<\/p>\n\n\n\n
                  D(X)=16<\/code><\/p>\n\n\n\n
                  \u5219\u6807\u51c6\u5dee\u662f\uff1a<\/p>\n\n\n\n
                  \u03c3(X)=4<\/code><\/p>\n\n\n\n
                  \u4e0d\u80fd\u8bf4\u6807\u51c6\u5dee\u4e5f\u662f16\u3002<\/p>\n\n\n\n
                  \n\n\n\n
                  \u4e5d\u3001\u5feb\u901f\u8bb0\u5fc6<\/h2>\n\n\n\n
                  \u53ef\u4ee5\u628a\u516d\u79cd\u6838\u5fc3\u5206\u5e03\u538b\u7f29\u6210\u4e0b\u9762\u51e0\u7ec4\u5173\u7cfb\u3002<\/p>\n\n\n\n
                  \u4e8c\u9879\u5206\u5e03\uff1a<\/p>\n\n\n\n
                  E=np\uff0cD=np(1-p)<\/code><\/p>\n\n\n\n
                  \u6cca\u677e\u5206\u5e03\uff1a<\/p>\n\n\n\n
                  E=D=\u03bb<\/code><\/p>\n\n\n\n
                  \u5747\u5300\u5206\u5e03\uff1a<\/p>\n\n\n\n
                  E=(a+b)\/2\uff0cD=(b-a)\u00b2\/12<\/code><\/p>\n\n\n\n
                  \u6307\u6570\u5206\u5e03\uff1a<\/p>\n\n\n\n
                  E=1\/\u03bb\uff0cD=1\/\u03bb\u00b2<\/code><\/p>\n\n\n\n
                  \u6b63\u6001\u5206\u5e03\uff1a<\/p>\n\n\n\n
                  E=\u03bc\uff0cD=\u03c3\u00b2<\/code><\/p>\n\n\n\n
                  \u6807\u51c6\u5dee\u7edf\u4e00\u4e3a\uff1a<\/p>\n\n\n\n
                  \u03c3=\u221aD<\/code><\/p>\n\n\n\n
                  \u7ebf\u6027\u53d8\u6362\u7edf\u4e00\u4e3a\uff1a<\/p>\n\n\n\n
                  E(aX+b)=aE(X)+b<\/code><\/p>\n\n\n\n
                  D(aX+b)=a\u00b2D(X)<\/code><\/p>\n\n\n\n
                  \u03c3(aX+b)=|a|\u03c3(X)<\/code><\/p>\n\n\n\n
                  \u8fd9\u90e8\u5206\u5728\u9009\u62e9\u9898\u3001\u586b\u7a7a\u9898\u4ee5\u53ca\u6570\u5b57\u7279\u5f81\u8ba1\u7b97\u9898\u4e2d\u51fa\u73b0\u9891\u7387\u5f88\u9ad8\uff0c\u5c24\u5176\u8981\u719f\u7ec3\u8bc6\u522b U\u3001N\u3001P\u3001B\u3001Exp\u3001\u03c7\u00b2\u3001t\u3001F<\/code> \u7684\u53c2\u6570\u542b\u4e49\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
                  U\u3001N\u3001P \u90fd\u662f\u201c\u5206\u5e03\u7c7b\u578b\u7684\u7b80\u5199\u201d\u3002 \u4f8b\u5982\uff1a X ~ U(0,6) \u8bfb\u4f5c\uff1a\u968f\u673a\u53d8\u91cf X \u670d\u4ece\u533a\u95f4 (0,6)  […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[54],"tags":[],"class_list":["post-2385","post","type-post","status-publish","format-standard","hentry","category-text"],"_links":{"self":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2385","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=2385"}],"version-history":[{"count":1,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2385\/revisions"}],"predecessor-version":[{"id":2386,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2385\/revisions\/2386"}],"wp:attachment":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=2385"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=2385"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=2385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}