{"id":2372,"date":"2026-06-04T16:09:08","date_gmt":"2026-06-04T08:09:08","guid":{"rendered":"http:\/\/www.preluna.xyz\/?p=2372"},"modified":"2026-06-04T16:09:09","modified_gmt":"2026-06-04T08:09:09","slug":"%e8%81%94%e5%90%88%e5%af%86%e5%ba%a6%e4%b8%8d%e4%bb%85%e7%9c%8b%e5%85%ac%e5%bc%8f%ef%bc%8c%e8%bf%98%e5%bf%85%e9%a1%bb%e7%9c%8b%e5%8c%ba%e5%9f%9f","status":"publish","type":"post","link":"http:\/\/www.preluna.xyz\/index.php\/2026\/06\/04\/%e8%81%94%e5%90%88%e5%af%86%e5%ba%a6%e4%b8%8d%e4%bb%85%e7%9c%8b%e5%85%ac%e5%bc%8f%ef%bc%8c%e8%bf%98%e5%bf%85%e9%a1%bb%e7%9c%8b%e5%8c%ba%e5%9f%9f\/preluna\/text\/","title":{"rendered":"\u8054\u5408\u5bc6\u5ea6\u4e0d\u4ec5\u770b\u516c\u5f0f\uff0c\u8fd8\u5fc5\u987b\u770b\u533a\u57df"},"content":{"rendered":"\n
\"\"<\/div><\/figure>\n\n\n\n

\u672c\u9898\u7ed9\u51fa\u7684\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u662f\uff1a<\/p>\n\n\n\n

f(x,y) = 12y\u00b2,   0 \u2264 y \u2264 x \u2264 1\n       = 0,      \u5176\u4ed6\n<\/code><\/pre>\n\n\n\n
\u8981\u6c42\uff1a<\/p>\n\n\n\n
E(X), E(Y), E(XY), E(X\u00b2 + Y\u00b2)\n<\/code><\/pre>\n\n\n\n
\u8fd9\u9053\u9898\u7684\u5173\u952e\u4e0d\u5728\u4e8e 12y\u00b2<\/code> \u91cc\u9762\u6709\u6ca1\u6709 x<\/code>\uff0c\u800c\u5728\u4e8e\u5b83\u7684\u53d6\u503c\u533a\u57df\u91cc\u6709 x<\/strong>\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u4e5f\u5c31\u662f\u8bf4\uff0c\u867d\u7136\u5bc6\u5ea6\u51fd\u6570\u8868\u8fbe\u5f0f\u672c\u8eab\u4e0d\u542b x<\/code>\uff0c\u4f46 x<\/code> \u901a\u8fc7\u79ef\u5206\u533a\u57df\u53c2\u4e0e\u4e86\u8ba1\u7b97\u3002\u8003\u7814\u6982\u7387\u8bba\u91cc\u8fd9\u7c7b\u9898\u5f88\u5e38\u89c1\uff1a\u8054\u5408\u5bc6\u5ea6\u4e0d\u4ec5\u770b\u516c\u5f0f\uff0c\u8fd8\u5fc5\u987b\u770b\u533a\u57df\u3002<\/strong><\/p>\n\n\n\n
\n\n\n\n
\u4e00\u3001\u5148\u770b\u79ef\u5206\u533a\u57df<\/h2>\n\n\n\n
\u6761\u4ef6\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u8868\u793a\u5728\u5e73\u9762\u4e0a\u662f\u4e00\u4e2a\u4e09\u89d2\u5f62\u533a\u57df\uff1a<\/p>\n\n\n\n
0 \u2264 x \u2264 1\n0 \u2264 y \u2264 x\n<\/code><\/pre>\n\n\n\n
\u4e5f\u53ef\u4ee5\u6539\u5199\u6210\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 1\ny \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u8fd9\u4e24\u79cd\u5199\u6cd5\u7b49\u4ef7\uff0c\u53ea\u662f\u79ef\u5206\u987a\u5e8f\u4e0d\u540c\u3002<\/p>\n\n\n\n
\u8fd9\u91cc\u4e00\u5b9a\u8981\u6ce8\u610f\uff1a
f(x,y)=12y\u00b2<\/code> \u4e0d\u542b x<\/code>\uff0c\u5e76\u4e0d\u4ee3\u8868 X<\/code> \u4e0d\u91cd\u8981\uff0c\u4e5f\u4e0d\u4ee3\u8868\u53ef\u4ee5\u76f4\u63a5\u628a x<\/code> \u6d88\u6389\u3002\u56e0\u4e3a x<\/code> \u51b3\u5b9a\u4e86 y<\/code> \u7684\u4e0a\u9650\uff0c\u6216\u8005\u8bf4\u533a\u57df\u8fb9\u754c\u91cc\u542b\u6709 x<\/code>\u3002<\/p>\n\n\n\n
\n\n\n\n
\u4e8c\u3001\u5148\u6c42\u8fb9\u7f18\u5bc6\u5ea6<\/h2>\n\n\n\n
1. \u6c42 X \u7684\u8fb9\u7f18\u5bc6\u5ea6 fX(x)<\/h3>\n\n\n\n
\u56fa\u5b9a x<\/code>\uff0c\u6839\u636e\u533a\u57df 0 \u2264 y \u2264 x \u2264 1<\/code>\uff0c\u6709\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 x\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
f_X(x) = \u222b\u2080\u02e3 12y\u00b2 dy\n       = 12 \u00b7 y\u00b3\/3 |\u2080\u02e3\n       = 4x\u00b3\n<\/code><\/pre>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
f_X(x) = 4x\u00b3,  0 \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u4e8e\u662f\uff1a<\/p>\n\n\n\n
E(X) = \u222b\u2080\u00b9 x f_X(x) dx\n     = \u222b\u2080\u00b9 x \u00b7 4x\u00b3 dx\n     = \u222b\u2080\u00b9 4x\u2074 dx\n     = 4\/5\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(X) = 4\/5\n<\/code><\/pre>\n\n\n\n
\u8fd9\u91cc\u5c31\u53ef\u4ee5\u770b\u51fa\uff0c\u867d\u7136\u539f\u6765\u7684\u5bc6\u5ea6 12y\u00b2<\/code> \u4e0d\u542b x<\/code>\uff0c\u4f46\u662f\u79ef\u5206\u4e0a\u9650\u662f x<\/code>\uff0c\u6240\u4ee5\u79ef\u5206\u4e4b\u540e\u5c31\u51fa\u73b0\u4e86 x<\/code>\u3002<\/p>\n\n\n\n
\n\n\n\n
2. \u6c42 Y \u7684\u8fb9\u7f18\u5bc6\u5ea6 fY(y)<\/h3>\n\n\n\n
\u56fa\u5b9a y<\/code>\uff0c\u7531\u533a\u57df\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u5f97\u5230\uff1a<\/p>\n\n\n\n
y \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
f_Y(y) = \u222b\u1d67\u00b9 12y\u00b2 dx\n       = 12y\u00b2 \u00b7 (1 - y)\n<\/code><\/pre>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
f_Y(y) = 12y\u00b2(1-y),  0 \u2264 y \u2264 1\n<\/code><\/pre>\n\n\n\n
\u4e8e\u662f\uff1a<\/p>\n\n\n\n
E(Y) = \u222b\u2080\u00b9 y f_Y(y) dy\n     = \u222b\u2080\u00b9 y \u00b7 12y\u00b2(1-y) dy\n     = \u222b\u2080\u00b9 12y\u00b3(1-y) dy\n     = 12\u222b\u2080\u00b9 (y\u00b3 - y\u2074) dy\n     = 12(1\/4 - 1\/5)\n     = 3\/5\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(Y) = 3\/5\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u4e09\u3001\u6c42 E(XY)<\/h2>\n\n\n\n
\u5bf9\u4e8e\u4e8c\u5143\u968f\u673a\u53d8\u91cf\uff0c\u76f4\u63a5\u7528\u516c\u5f0f\uff1a<\/p>\n\n\n\n
E[g(X,Y)] = \u222c g(x,y) f(x,y) dxdy\n<\/code><\/pre>\n\n\n\n
\u8fd9\u91cc\u53d6\uff1a<\/p>\n\n\n\n
g(X,Y) = XY\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(XY) = \u222c xy \u00b7 12y\u00b2 dxdy\n<\/code><\/pre>\n\n\n\n
\u5728\u533a\u57df 0 \u2264 y \u2264 x \u2264 1<\/code> \u4e0a\u79ef\u5206\u3002\u6309 x<\/code> \u5916\u5c42\u3001y<\/code> \u5185\u5c42\uff1a<\/p>\n\n\n\n
E(XY) = \u222b\u2080\u00b9 \u222b\u2080\u02e3 xy \u00b7 12y\u00b2 dy dx\n      = \u222b\u2080\u00b9 \u222b\u2080\u02e3 12xy\u00b3 dy dx\n<\/code><\/pre>\n\n\n\n
\u56e0\u4e3a\u5185\u5c42\u5bf9 y<\/code> \u79ef\u5206\uff0cx<\/code> \u6682\u65f6\u5f53\u5e38\u6570\uff1a<\/p>\n\n\n\n
= \u222b\u2080\u00b9 12x \u00b7 y\u2074\/4 |\u2080\u02e3 dx\n= \u222b\u2080\u00b9 3x \u00b7 x\u2074 dx\n= \u222b\u2080\u00b9 3x\u2075 dx\n= 3\/6\n= 1\/2\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(XY) = 1\/2\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u56db\u3001\u6c42 E(X\u00b2 + Y\u00b2)<\/h2>\n\n\n\n
\u5229\u7528\u671f\u671b\u7684\u7ebf\u6027\u6027\u8d28\uff1a<\/p>\n\n\n\n
E(X\u00b2 + Y\u00b2) = E(X\u00b2) + E(Y\u00b2)\n<\/code><\/pre>\n\n\n\n
\u5148\u6c42 E(X\u00b2)<\/code>\uff1a<\/p>\n\n\n\n
E(X\u00b2) = \u222b\u2080\u00b9 x\u00b2 f_X(x) dx\n      = \u222b\u2080\u00b9 x\u00b2 \u00b7 4x\u00b3 dx\n      = \u222b\u2080\u00b9 4x\u2075 dx\n      = 4\/6\n      = 2\/3\n<\/code><\/pre>\n\n\n\n
\u518d\u6c42 E(Y\u00b2)<\/code>\uff1a<\/p>\n\n\n\n
E(Y\u00b2) = \u222b\u2080\u00b9 y\u00b2 f_Y(y) dy\n      = \u222b\u2080\u00b9 y\u00b2 \u00b7 12y\u00b2(1-y) dy\n      = \u222b\u2080\u00b9 12y\u2074(1-y) dy\n      = 12\u222b\u2080\u00b9 (y\u2074 - y\u2075) dy\n      = 12(1\/5 - 1\/6)\n      = 2\/5\n<\/code><\/pre>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
E(X\u00b2 + Y\u00b2) = 2\/3 + 2\/5\n           = 10\/15 + 6\/15\n           = 16\/15\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(X\u00b2 + Y\u00b2) = 16\/15\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u4e94\u3001\u6700\u7ec8\u7b54\u6848<\/h2>\n\n\n\n
E(X) = 4\/5\n\nE(Y) = 3\/5\n\nE(XY) = 1\/2\n\nE(X\u00b2 + Y\u00b2) = 16\/15\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u516d\u3001\u91cd\u70b9\u89e3\u91ca\uff1a\u5bc6\u5ea6\u51fd\u6570\u91cc\u6ca1\u6709 x\uff0c\u4e3a\u4ec0\u4e48\u8fd8\u80fd\u7b97\u51fa\u5173\u4e8e x \u7684\u7ed3\u679c\uff1f<\/h2>\n\n\n\n
\u8fd9\u662f\u672c\u9898\u6700\u5bb9\u6613\u8bef\u89e3\u7684\u5730\u65b9\u3002<\/p>\n\n\n\n
\u8054\u5408\u5bc6\u5ea6\u7531\u4e24\u90e8\u5206\u5171\u540c\u51b3\u5b9a\uff1a<\/p>\n\n\n\n
1. \u5bc6\u5ea6\u8868\u8fbe\u5f0f\uff1af(x,y) = 12y\u00b2\n2. \u975e\u96f6\u533a\u57df\uff1a0 \u2264 y \u2264 x \u2264 1\n<\/code><\/pre>\n\n\n\n
\u867d\u7136 12y\u00b2<\/code> \u672c\u8eab\u4e0d\u542b x<\/code>\uff0c\u4f46\u662f\u5b83\u53ea\u5728\u4e09\u89d2\u5f62\u533a\u57df\u5185\u6709\u6548\u3002\u8fd9\u4e2a\u533a\u57df\u7684\u8fb9\u754c\u542b\u6709 x<\/code>\uff0c\u6240\u4ee5\u79ef\u5206\u65f6 x<\/code> \u4f1a\u901a\u8fc7\u79ef\u5206\u4e0a\u4e0b\u9650\u8fdb\u5165\u7ed3\u679c\u3002<\/p>\n\n\n\n
\u6bd4\u5982\u6c42 f_X(x)<\/code> \u65f6\uff1a<\/p>\n\n\n\n
f_X(x) = \u222b 12y\u00b2 dy\n<\/code><\/pre>\n\n\n\n
\u5982\u679c\u4e0d\u770b\u533a\u57df\uff0c\u6839\u672c\u4e0d\u77e5\u9053 y<\/code> \u4ece\u54ea\u91cc\u79ef\u5230\u54ea\u91cc\u3002\u7531 0 \u2264 y \u2264 x \u2264 1<\/code> \u53ef\u77e5\uff1a<\/p>\n\n\n\n
0 \u2264 y \u2264 x\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
f_X(x) = \u222b\u2080\u02e3 12y\u00b2 dy = 4x\u00b3\n<\/code><\/pre>\n\n\n\n
\u8fd9\u91cc\u7684 x<\/code> \u5c31\u662f\u4ece\u79ef\u5206\u4e0a\u9650\u6765\u7684\u3002<\/p>\n\n\n\n
\u56e0\u6b64\u4e0d\u80fd\u8bf4\u201c\u5bc6\u5ea6\u51fd\u6570\u91cc\u6ca1\u6709 x\uff0c\u6240\u4ee5 x \u88ab\u6d88\u6389\u201d\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff1a<\/p>\n\n\n\n
x \u6ca1\u6709\u51fa\u73b0\u5728\u5bc6\u5ea6\u8868\u8fbe\u5f0f\u91cc\uff0c\u4f46\u51fa\u73b0\u5728\u79ef\u5206\u533a\u57df\u91cc\uff1b\n\u8fb9\u7f18\u5bc6\u5ea6\u6216\u671f\u671b\u8ba1\u7b97\u65f6\uff0cx \u4f1a\u901a\u8fc7\u79ef\u5206\u4e0a\u4e0b\u9650\u4f53\u73b0\u51fa\u6765\u3002\n<\/code><\/pre>\n\n\n\n
\u8003\u7814\u4e2d\u9047\u5230\u4e8c\u5143\u5bc6\u5ea6\u9898\uff0c\u7b2c\u4e00\u6b65\u6c38\u8fdc\u4e0d\u662f\u76ef\u7740\u516c\u5f0f\u770b\uff0c\u800c\u662f\u5148\u628a\u975e\u96f6\u533a\u57df\u6574\u7406\u6e05\u695a\u3002\u533a\u57df\u51b3\u5b9a\u79ef\u5206\u9650\uff0c\u79ef\u5206\u9650\u51b3\u5b9a\u6700\u540e\u7ed3\u679c\u3002<\/p>\n\n\n\n
\"\"<\/div><\/figure>\n\n\n\n
\u672c\u9898\u7b54\u6848\u662f\uff1a<\/p>\n\n\n\n
E(Y) = 0\n<\/code><\/pre>\n\n\n\n
\u8fd9\u9053\u9898\u8003\u67e5\u7684\u662f\u201c\u884c\u5217\u5f0f\u5c55\u5f00 + \u968f\u673a\u53d8\u91cf\u72ec\u7acb\u6027 + \u6570\u5b66\u671f\u671b\u7684\u7ebf\u6027\u6027\u201d\u3002<\/p>\n\n\n\n
\u9898\u76ee\u7ed9\u51fa\u968f\u673a\u53d8\u91cf X\u1d62\u2c7c<\/code> \u72ec\u7acb\u540c\u5206\u5e03\uff0c\u5e76\u4e14\uff1a<\/p>\n\n\n\n
E(X\u1d62\u2c7c) = 2\n<\/code><\/pre>\n\n\n\n
\u5b9a\u4e49\u968f\u673a\u53d8\u91cf Y<\/code> \u4e3a\u4e00\u4e2a n \u9636\u884c\u5217\u5f0f\uff1a<\/p>\n\n\n\n
Y =\n| X\u2081\u2081  X\u2081\u2082  ...  X\u2081\u2099 |\n| X\u2082\u2081  X\u2082\u2082  ...  X\u2082\u2099 |\n| ...  ...  ...  ... |\n| X\u2099\u2081  X\u2099\u2082  ...  X\u2099\u2099 |\n<\/code><\/pre>\n\n\n\n
\u8981\u6c42 E(Y)<\/code>\u3002<\/p>\n\n\n\n
\n\n\n\n
\u5148\u770b\u6700\u5c0f\u60c5\u5f62 n = 2<\/code>\uff0c\u8fd9\u6709\u52a9\u4e8e\u7406\u89e3\u672c\u9898\u672c\u8d28\u3002<\/p>\n\n\n\n
\u6b64\u65f6\uff1a<\/p>\n\n\n\n
Y = | X\u2081\u2081  X\u2081\u2082 |\n    | X\u2082\u2081  X\u2082\u2082 |\n  = X\u2081\u2081X\u2082\u2082 - X\u2081\u2082X\u2082\u2081\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(Y) = E(X\u2081\u2081X\u2082\u2082 - X\u2081\u2082X\u2082\u2081)\n     = E(X\u2081\u2081X\u2082\u2082) - E(X\u2081\u2082X\u2082\u2081)\n<\/code><\/pre>\n\n\n\n
\u56e0\u4e3a\u9898\u76ee\u8bf4\u6240\u6709 X\u1d62\u2c7c<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(X\u2081\u2081X\u2082\u2082) = E(X\u2081\u2081)E(X\u2082\u2082) = 2 \u00d7 2 = 4\n<\/code><\/pre>\n\n\n\n
\u540c\u7406\uff1a<\/p>\n\n\n\n
E(X\u2081\u2082X\u2082\u2081) = E(X\u2081\u2082)E(X\u2082\u2081) = 2 \u00d7 2 = 4\n<\/code><\/pre>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
E(Y) = 4 - 4 = 0\n<\/code><\/pre>\n\n\n\n
\u8fd9\u8bf4\u660e\u672c\u9898\u4e0d\u662f\u56e0\u4e3a\u6bcf\u4e2a\u968f\u673a\u53d8\u91cf\u7684\u671f\u671b\u4e3a 0\uff0c\u800c\u662f\u56e0\u4e3a\u884c\u5217\u5f0f\u5c55\u5f00\u540e\u6b63\u8d1f\u9879\u4f1a\u62b5\u6d88\u3002<\/p>\n\n\n\n
\n\n\n\n
\u4e00\u822c\u7684 n<\/code> \u9636\u884c\u5217\u5f0f\u6309\u7167\u6392\u5217\u5c55\u5f00\uff1a<\/p>\n\n\n\n
Y = \u03a3 sgn(\u03c3) X\u2081\u03c3(1) X\u2082\u03c3(2) ... X\u2099\u03c3(n)\n<\/code><\/pre>\n\n\n\n
\u8fd9\u91cc \u03c3<\/code> \u8868\u793a\u5bf9 1,2,...,n<\/code> \u7684\u4e00\u4e2a\u6392\u5217\uff0csgn(\u03c3)<\/code> \u8868\u793a\u8fd9\u4e2a\u6392\u5217\u5bf9\u5e94\u9879\u7684\u6b63\u8d1f\u53f7\u3002<\/p>\n\n\n\n
\u5bf9\u4e24\u8fb9\u53d6\u671f\u671b\uff1a<\/p>\n\n\n\n
E(Y) = E[\u03a3 sgn(\u03c3) X\u2081\u03c3(1) X\u2082\u03c3(2) ... X\u2099\u03c3(n)]\n<\/code><\/pre>\n\n\n\n
\u5229\u7528\u6570\u5b66\u671f\u671b\u7684\u7ebf\u6027\u6027\uff0c\u53ef\u4ee5\u628a\u671f\u671b\u653e\u8fdb\u6c42\u548c\u91cc\uff1a<\/p>\n\n\n\n
E(Y) = \u03a3 sgn(\u03c3) E[X\u2081\u03c3(1) X\u2082\u03c3(2) ... X\u2099\u03c3(n)]\n<\/code><\/pre>\n\n\n\n
\u7531\u4e8e\u6240\u6709 X\u1d62\u2c7c<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u6240\u4ee5\u6bcf\u4e00\u9879\u4e58\u79ef\u7684\u671f\u671b\u53ef\u4ee5\u62c6\u6210\u671f\u671b\u7684\u4e58\u79ef\uff1a<\/p>\n\n\n\n
E[X\u2081\u03c3(1) X\u2082\u03c3(2) ... X\u2099\u03c3(n)]\n= E[X\u2081\u03c3(1)] E[X\u2082\u03c3(2)] ... E[X\u2099\u03c3(n)]\n= 2 \u00d7 2 \u00d7 ... \u00d7 2\n= 2\u207f\n<\/code><\/pre>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
E(Y) = \u03a3 sgn(\u03c3) \u00b7 2\u207f\n     = 2\u207f \u03a3 sgn(\u03c3)\n<\/code><\/pre>\n\n\n\n
\u5173\u952e\u5c31\u53d8\u6210\u4e86\uff1a<\/p>\n\n\n\n
\u03a3 sgn(\u03c3) = ?\n<\/code><\/pre>\n\n\n\n
\u5f53 n \u2265 2<\/code> \u65f6\uff0c\u6240\u6709\u6392\u5217\u4e2d\u6b63\u6392\u5217\u548c\u8d1f\u6392\u5217\u6570\u91cf\u76f8\u7b49\uff0c\u90fd\u662f n!\/2<\/code> \u4e2a\uff0c\u6240\u4ee5\uff1a<\/p>\n\n\n\n
\u03a3 sgn(\u03c3) = \u6b63\u6392\u5217\u4e2a\u6570 - \u8d1f\u6392\u5217\u4e2a\u6570\n         = n!\/2 - n!\/2\n         = 0\n<\/code><\/pre>\n\n\n\n
\u6240\u4ee5\uff1a<\/p>\n\n\n\n
E(Y) = 2\u207f \u00d7 0 = 0\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u8fd9\u9053\u9898\u8fd8\u6709\u4e00\u4e2a\u66f4\u5feb\u7684\u7406\u89e3\u65b9\u5f0f\u3002<\/p>\n\n\n\n
\u56e0\u4e3a\u884c\u5217\u5f0f\u662f\u6309\u4e58\u79ef\u5c55\u5f00\u7684\uff0c\u800c\u5404\u4e2a\u5143\u7d20\u76f8\u4e92\u72ec\u7acb\uff0c\u6240\u4ee5\u53ef\u4ee5\u7406\u89e3\u4e3a\uff1a<\/p>\n\n\n\n
E(Y) = | E(X\u2081\u2081)  E(X\u2081\u2082)  ...  E(X\u2081\u2099) |\n       | E(X\u2082\u2081)  E(X\u2082\u2082)  ...  E(X\u2082\u2099) |\n       |  ...     ...    ...   ...   |\n       | E(X\u2099\u2081)  E(X\u2099\u2082)  ...  E(X\u2099\u2099) |\n<\/code><\/pre>\n\n\n\n
\u800c\u6bcf\u4e2a E(X\u1d62\u2c7c)<\/code> \u90fd\u7b49\u4e8e 2\uff0c\u56e0\u6b64\uff1a<\/p>\n\n\n\n
E(Y) =\n| 2  2  ...  2 |\n| 2  2  ...  2 |\n| ... ... ... |\n| 2  2  ...  2 |\n<\/code><\/pre>\n\n\n\n
\u8fd9\u4e2a\u884c\u5217\u5f0f\u7684\u6bcf\u4e00\u884c\u5b8c\u5168\u76f8\u540c\u3002\u53ea\u8981 n \u2265 2<\/code>\uff0c\u884c\u5217\u5f0f\u4e2d\u6709\u4e24\u884c\u76f8\u540c\uff0c\u6240\u4ee5\u884c\u5217\u5f0f\u4e3a 0\u3002<\/p>\n\n\n\n
\u56e0\u6b64\uff1a<\/p>\n\n\n\n
E(Y) = 0\n<\/code><\/pre>\n\n\n\n
\n\n\n\n
\u8fd9\u9053\u9898\u5bb9\u6613\u9519\u5728\u4e24\u4e2a\u5730\u65b9\u3002<\/p>\n\n\n\n
\u7b2c\u4e00\uff0c\u8bef\u4ee5\u4e3a\u8981\u6c42 E(Y)<\/code> \u5fc5\u987b\u77e5\u9053 X\u1d62\u2c7c<\/code> \u7684\u5177\u4f53\u5206\u5e03\u3002\u5176\u5b9e\u4e0d\u7528\u3002\u56e0\u4e3a\u884c\u5217\u5f0f\u5c55\u5f00\u540e\uff0c\u6bcf\u4e00\u9879\u90fd\u662f\u82e5\u5e72\u4e2a\u76f8\u4e92\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u7684\u4e58\u79ef\uff0c\u53ea\u9700\u8981\u7528\u5230\u6bcf\u4e2a\u53d8\u91cf\u7684\u671f\u671b\u3002<\/p>\n\n\n\n
\u7b2c\u4e8c\uff0c\u673a\u68b0\u5730\u5199\u6210\uff1a<\/p>\n\n\n\n
E(det X) = det(E(X))\n<\/code><\/pre>\n\n\n\n
\u8fd9\u4e2a\u5199\u6cd5\u5728\u672c\u9898\u4e2d\u53ef\u4ee5\u7528\uff0c\u4f46\u4e0d\u80fd\u65e0\u6761\u4ef6\u4e71\u7528\u3002\u5b83\u4e4b\u6240\u4ee5\u6210\u7acb\uff0c\u662f\u56e0\u4e3a\u9898\u76ee\u7ed9\u4e86\u6240\u6709 X\u1d62\u2c7c<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u4f7f\u5f97\u6bcf\u4e00\u9879\u4e58\u79ef\u7684\u671f\u671b\u53ef\u4ee5\u62c6\u5f00\u3002\u5982\u679c\u6ca1\u6709\u72ec\u7acb\u6027\uff0c\u4e00\u822c\u4e0d\u80fd\u76f4\u63a5\u8fd9\u6837\u5199\u3002<\/p>\n\n\n\n
\u672c\u9898\u6700\u7a33\u7684\u505a\u6cd5\u662f\u8bb0\u4f4f\uff1a<\/p>\n\n\n\n
\u884c\u5217\u5f0f\u5c55\u5f00 \u2192 \u5bf9\u6bcf\u9879\u53d6\u671f\u671b \u2192 \u72ec\u7acb\u6027\u62c6\u4e58\u79ef \u2192 \u6b63\u8d1f\u6392\u5217\u62b5\u6d88\n<\/code><\/pre>\n\n\n\n
\u6700\u540e\u7b54\u6848\uff1a<\/p>\n\n\n\n
E(Y) = 0\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u672c\u9898\u7ed9\u51fa\u7684\u8054\u5408\u6982\u7387\u5bc6\u5ea6\u662f\uff1a \u8981\u6c42\uff1a \u8fd9\u9053\u9898\u7684\u5173\u952e\u4e0d\u5728\u4e8e 12y\u00b2 \u91cc\u9762\u6709\u6ca1\u6709 x\uff0c\u800c\u5728\u4e8e\u5b83\u7684\u53d6\u503c\u533a\u57df\u91cc\u6709 x\uff1a […]<\/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-2372","post","type-post","status-publish","format-standard","hentry","category-text"],"_links":{"self":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2372","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=2372"}],"version-history":[{"count":1,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2372\/revisions"}],"predecessor-version":[{"id":2375,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2372\/revisions\/2375"}],"wp:attachment":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=2372"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=2372"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=2372"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}