{"id":2377,"date":"2026-06-05T18:53:17","date_gmt":"2026-06-05T10:53:17","guid":{"rendered":"http:\/\/www.preluna.xyz\/?p=2377"},"modified":"2026-06-11T18:59:55","modified_gmt":"2026-06-11T10:59:55","slug":"%e4%b8%ba%e4%bb%80%e4%b9%88%e5%af%86%e5%ba%a6%e5%87%bd%e6%95%b0%e7%9a%84%e7%a7%af%e5%88%86%e6%98%af%e6%9c%9f%e6%9c%9b%e5%91%a2%ef%bc%9f","status":"publish","type":"post","link":"http:\/\/www.preluna.xyz\/index.php\/2026\/06\/05\/%e4%b8%ba%e4%bb%80%e4%b9%88%e5%af%86%e5%ba%a6%e5%87%bd%e6%95%b0%e7%9a%84%e7%a7%af%e5%88%86%e6%98%af%e6%9c%9f%e6%9c%9b%e5%91%a2%ef%bc%9f\/preluna\/text\/","title":{"rendered":"\u4e3a\u4ec0\u4e48\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u662f\u671f\u671b\u5462\uff1f"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u4e25\u683c\u8bf4\uff0c<strong>\u4e0d\u662f\u201c\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u662f\u671f\u671b\u201d<\/strong>\uff0c\u800c\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u5bc6\u5ea6\u51fd\u6570 f(x) \u7684\u79ef\u5206 = \u6982\u7387\n\u968f\u673a\u53d8\u91cf X \u4e58\u4ee5\u5bc6\u5ea6\u51fd\u6570 f(x) \u540e\u518d\u79ef\u5206 = \u671f\u671b\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u5c31\u662f\u8bf4\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b f(x) dx = 1\n\u222b x f(x) dx = E(X)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u662f\u968f\u673a\u53d8\u91cf\u7684\u51fd\u6570 <code>g(X)<\/code>\uff0c\u5219\u6709\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E&#91;g(X)] = \u222b g(x) f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u771f\u6b63\u8981\u7406\u89e3\u7684\u662f\uff1a<strong>\u4e3a\u4ec0\u4e48\u671f\u671b\u8981\u5199\u6210\u201c\u53d6\u503c \u00d7 \u8fd9\u4e2a\u53d6\u503c\u9644\u8fd1\u7684\u6982\u7387\u5bc6\u5ea6\u201d\u518d\u79ef\u5206\u3002<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00\u3001\u5148\u4ece\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\u770b\u671f\u671b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\u6700\u5bb9\u6613\u7406\u89e3\u3002\u5047\u8bbe\u968f\u673a\u53d8\u91cf <code>X<\/code> \u7684\u53ef\u80fd\u53d6\u503c\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x\u2081, x\u2082, x\u2083, ...\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u5e94\u6982\u7387\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(X = x\u2081), P(X = x\u2082), P(X = x\u2083), ...\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\u6570\u5b66\u671f\u671b\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = x\u2081P(X = x\u2081) + x\u2082P(X = x\u2082) + x\u2083P(X = x\u2083) + ...\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u5c31\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u03a3 x\u1d62 P(X = x\u1d62)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u516c\u5f0f\u7684\u542b\u4e49\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u671f\u671b = \u6bcf\u4e2a\u53d6\u503c \u00d7 \u8fd9\u4e2a\u53d6\u503c\u51fa\u73b0\u7684\u6982\u7387\uff0c\u7136\u540e\u5168\u90e8\u52a0\u8d77\u6765\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>X = 1 \u7684\u6982\u7387\u662f 0.2\nX = 2 \u7684\u6982\u7387\u662f 0.3\nX = 3 \u7684\u6982\u7387\u662f 0.5\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u4e48\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = 1 \u00d7 0.2 + 2 \u00d7 0.3 + 3 \u00d7 0.5\n     = 2.3\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a <code>2.3<\/code> \u4e0d\u662f\u8bf4 <code>X<\/code> \u4e00\u5b9a\u80fd\u53d6\u5230 2.3\uff0c\u800c\u662f\u957f\u671f\u5e73\u5747\u7ed3\u679c\u8d8b\u8fd1\u4e8e 2.3\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4e0d\u80fd\u76f4\u63a5\u5199 P(X = x)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u7684\u95ee\u9898\u5728\u4e8e\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(X = \u67d0\u4e00\u4e2a\u5177\u4f53\u503c) = 0\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982 <code>X<\/code> \u670d\u4ece\u67d0\u4e2a\u8fde\u7eed\u5206\u5e03\uff0c\u95ee\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(X = 1)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u901a\u5e38\u7b49\u4e8e 0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4e0d\u80fd\u50cf\u79bb\u6563\u578b\u90a3\u6837\u5199\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u03a3 x P(X = x)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\u6bcf\u4e00\u4e2a\u70b9\u7684\u6982\u7387\u90fd\u662f 0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u53ef\u4ee5\u8ba8\u8bba\u533a\u95f4\u6982\u7387\uff0c\u6bd4\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(a &lt; X &lt; b)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e2a\u6982\u7387\u7531\u5bc6\u5ea6\u51fd\u6570\u79ef\u5206\u5f97\u5230\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(a &lt; X &lt; b) = \u222b&#91;a,b] f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u5bc6\u5ea6\u51fd\u6570 <code>f(x)<\/code> \u4e0d\u662f\u6982\u7387\u672c\u8eab\uff0c\u800c\u662f\u63cf\u8ff0\u6982\u7387\u5728\u6570\u8f74\u4e0a\u5982\u4f55\u5206\u5e03\u7684\u201c\u5bc6\u5ea6\u201d\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001\u8fde\u7eed\u578b\u671f\u671b\u4e3a\u4ec0\u4e48\u662f \u222b x f(x) dx\uff1f<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u4ee5\u628a\u8fde\u7eed\u533a\u95f4\u5207\u6210\u5f88\u591a\u5f88\u5c0f\u7684\u5c0f\u6bb5\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\u5982\u628a\u533a\u95f4\u5206\u6210\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#91;x\u2081, x\u2081 + \u0394x]\n&#91;x\u2082, x\u2082 + \u0394x]<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">[x\u2083, x\u2083 + \u0394x] &#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 <code>\u0394x<\/code> \u5f88\u5c0f\u65f6\uff0c\u5728 <code>x\u1d62<\/code> \u9644\u8fd1\u7684\u4e00\u5c0f\u6bb5\u6982\u7387\u5927\u7ea6\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(x\u1d62 &lt; X &lt; x\u1d62 + \u0394x) \u2248 f(x\u1d62)\u0394x\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5c31\u662f\u5bc6\u5ea6\u51fd\u6570\u7684\u542b\u4e49\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\u8fd9\u4e2a\u5c0f\u533a\u95f4\u5bf9\u671f\u671b\u7684\u8d21\u732e\u5927\u7ea6\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u53d6\u503c \u00d7 \u8be5\u5c0f\u533a\u95f4\u6982\u7387\n\u2248 x\u1d62 \u00d7 f(x\u1d62)\u0394x\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u6240\u6709\u5c0f\u533a\u95f4\u8d21\u732e\u52a0\u8d77\u6765\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) \u2248 \u03a3 x\u1d62 f(x\u1d62)\u0394x\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53 <code>\u0394x \u2192 0<\/code> \u65f6\uff0c\u6c42\u548c\u5c31\u53d8\u6210\u79ef\u5206\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u222b x f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\u8fde\u7eed\u578b\u671f\u671b\u516c\u5f0f\u672c\u8d28\u4e0a\u5c31\u662f\u79bb\u6563\u578b\u516c\u5f0f\u7684\u8fde\u7eed\u7248\u672c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u79bb\u6563\u578b\uff1aE(X) = \u03a3 x\u1d62 P(X = x\u1d62)\n\n\u8fde\u7eed\u578b\uff1aE(X) = \u222b x f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u4ee5\u8fd9\u6837\u8bb0\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u79bb\u6563\uff1a\u6982\u7387\u662f P(X = x\u1d62)\n\u8fde\u7eed\uff1a\u5c0f\u533a\u95f4\u6982\u7387\u7ea6\u4e3a f(x)dx\n\n\u6240\u4ee5\uff1a\n\u03a3 x \u00d7 \u6982\u7387  \u2192  \u222b x \u00d7 f(x) dx\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u672c\u8eab\u4e0d\u662f\u671f\u671b\uff0c\u800c\u662f\u603b\u6982\u7387<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bc6\u5ea6\u51fd\u6570\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b(-\u221e,+\u221e) f(x) dx = 1\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u56e0\u4e3a\u968f\u673a\u53d8\u91cf\u4e00\u5b9a\u4f1a\u843d\u5728\u6574\u4e2a\u5b9e\u6570\u8303\u56f4\u5185\uff0c\u6240\u4ee5\u603b\u6982\u7387\u4e3a 1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u53ea\u5bf9\u67d0\u4e2a\u533a\u95f4\u79ef\u5206\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b&#91;a,b] f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f97\u5230\u7684\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P(a \u2264 X \u2264 b)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u4e0d\u662f\u671f\u671b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8981\u5f97\u5230\u671f\u671b\uff0c\u5fc5\u987b\u4e58\u4e0a\u53d6\u503c <code>x<\/code>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u222b(-\u221e,+\u221e) x f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4ec0\u4e48\u8981\u4e58 <code>x<\/code>\uff1f\u56e0\u4e3a\u671f\u671b\u4e0d\u662f\u5355\u7eaf\u7b97\u6982\u7387\uff0c\u800c\u662f\u7b97\u201c\u52a0\u6743\u5e73\u5747\u503c\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bc6\u5ea6\u51fd\u6570 <code>f(x)<\/code> \u8d1f\u8d23\u63d0\u4f9b\u6743\u91cd\uff0c<code>x<\/code> \u662f\u5bf9\u5e94\u7684\u53d6\u503c\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e94\u3001\u4e00\u4e2a\u7b80\u5355\u4f8b\u5b50\uff1a\u5747\u5300\u5206\u5e03<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>X ~ U(0,1)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u7684\u5bc6\u5ea6\u51fd\u6570\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>f(x) = 1, 0 &lt; x &lt; 1\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u603b\u6982\u7387\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b&#91;0,1] f(x) dx = \u222b&#91;0,1] 1 dx = 1\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u8bf4\u660e <code>X<\/code> \u843d\u5728 <code>[0,1]<\/code> \u5185\u7684\u6982\u7387\u4e3a 1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u671f\u671b\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u222b&#91;0,1] x f(x) dx\n     = \u222b&#91;0,1] x dx\n     = 1\/2\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc <code>1\/2<\/code> \u8868\u793a\uff0c\u5728 <code>[0,1]<\/code> \u4e0a\u5747\u5300\u53d6\u6570\uff0c\u957f\u671f\u5e73\u5747\u503c\u662f 0.5\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b f(x) dx \u7b97\u7684\u662f\u6982\u7387\u9762\u79ef\n\u222b x f(x) dx \u7b97\u7684\u662f\u52a0\u6743\u5e73\u5747\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u516d\u3001\u5982\u679c\u662f\u4e8c\u7ef4\u5bc6\u5ea6\u51fd\u6570\u600e\u4e48\u529e\uff1f<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c <code>(X,Y)<\/code> \u6709\u8054\u5408\u5bc6\u5ea6\u51fd\u6570 <code>f(x,y)<\/code>\uff0c\u90a3\u4e48\u603b\u6982\u7387\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b\u222b f(x,y) dxdy = 1\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u671f\u671b\u5206\u522b\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X) = \u222b\u222b x f(x,y) dxdy\n\nE(Y) = \u222b\u222b y f(x,y) dxdy\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u6c42 <code>E[g(X,Y)]<\/code>\uff0c\u5219\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E&#91;g(X,Y)] = \u222b\u222b g(x,y) f(x,y) dxdy\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u5728\u8003\u7814\u6982\u7387\u8bba\u4e2d\u975e\u5e38\u5e38\u89c1\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(XY) = \u222b\u222b xy f(x,y) dxdy\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc <code>xy<\/code> \u662f\u51fd\u6570\u503c\uff0c<code>f(x,y)<\/code> \u662f\u6982\u7387\u5bc6\u5ea6\u6743\u91cd\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e03\u3001\u8003\u7814\u91cc\u6700\u5bb9\u6613\u6df7\u6dc6\u7684\u5730\u65b9<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u5e38\u89c1\u7684\u9519\u8bef\u662f\u628a\u4e0b\u9762\u51e0\u4e2a\u5f0f\u5b50\u6df7\u5728\u4e00\u8d77\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b f(x) dx = 1\n\u222b&#91;a,b] f(x) dx = P(a \u2264 X \u2264 b)\n\u222b x f(x) dx = E(X)\n\u222b g(x) f(x) dx = E&#91;g(X)]\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u4eec\u7684\u533a\u522b\u5728\u4e8e\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u8868\u8fbe\u5f0f<\/th><th>\u542b\u4e49<\/th><\/tr><\/thead><tbody><tr><td><code>\u222b f(x) dx<\/code><\/td><td>\u603b\u6982\u7387<\/td><\/tr><tr><td><code>\u222b[a,b] f(x) dx<\/code><\/td><td>\u533a\u95f4\u6982\u7387<\/td><\/tr><tr><td><code>\u222b x f(x) dx<\/code><\/td><td><code>X<\/code> \u7684\u671f\u671b<\/td><\/tr><tr><td><code>\u222b x\u00b2 f(x) dx<\/code><\/td><td><code>E(X\u00b2)<\/code><\/td><\/tr><tr><td><code>\u222b g(x) f(x) dx<\/code><\/td><td><code>E[g(X)]<\/code><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5c24\u5176\u8981\u6ce8\u610f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X\u00b2) \u2260 &#91;E(X)]\u00b2\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X\u00b2) = \u222b x\u00b2 f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u4e0d\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u222b x f(x) dx)\u00b2\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u516b\u3001\u4e00\u53e5\u8bdd\u603b\u7ed3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u672c\u8eab\u4e0d\u662f\u671f\u671b\uff0c\u800c\u662f\u6982\u7387\uff1b\u671f\u671b\u662f\u201c\u53d6\u503c\u7684\u52a0\u6743\u5e73\u5747\u201d\u3002\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\u4e2d\uff0c\u67d0\u4e00\u70b9\u6ca1\u6709\u6982\u7387\uff0c\u53ea\u6709\u5c0f\u533a\u95f4\u6982\u7387\uff0c\u800c\u5c0f\u533a\u95f4\u6982\u7387\u8fd1\u4f3c\u4e3a <code>f(x)dx<\/code>\uff0c\u6240\u4ee5\u8fde\u7eed\u578b\u671f\u671b\u5c31\u4ece\u79bb\u6563\u578b\u7684<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u03a3 x\u1d62P(X = x\u1d62)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u53d8\u6210\u4e86<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u222b x f(x) dx\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\u53ef\u4ee5\u8bb0\u6210\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u6982\u7387 = \u5bf9\u5bc6\u5ea6\u79ef\u5206\n\u671f\u671b = \u5bf9\u201c\u53d6\u503c \u00d7 \u5bc6\u5ea6\u201d\u79ef\u5206\n\u51fd\u6570\u7684\u671f\u671b = \u5bf9\u201c\u51fd\u6570\u503c \u00d7 \u5bc6\u5ea6\u201d\u79ef\u5206\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/www.preluna.xyz\/wp-content\/uploads\/2026\/06\/28-1024x524.jpg'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"524\" data-original=\"http:\/\/www.preluna.xyz\/wp-content\/uploads\/2026\/06\/28-1024x524.jpg\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-2381\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9898\u7684\u7b54\u6848\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>n \u81f3\u5c11\u4e3a 8000\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u9898\u7528\u7684\u4e0d\u662f\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0c\u800c\u662f<strong>\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f<\/strong>\u3002\u4e25\u683c\u8bf4\uff0c\u5b83\u5c5e\u4e8e\u201c\u7528\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\u4f30\u8ba1\u6982\u7387\u201d\u7684\u9898\uff0c\u548c\u5207\u6bd4\u96ea\u592b\u5927\u6570\u5b9a\u5f8b\u7684\u601d\u60f3\u76f8\u901a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9898\u76ee\u53ea\u544a\u8bc9\u4e86\u5bff\u547d <code>X<\/code> \u7684\u6570\u5b66\u671f\u671b\u4e3a <code>\u03bc<\/code>\uff0c\u65b9\u5dee\u4e3a <code>\u03c3\u00b2 = 400<\/code>\uff0c\u6ca1\u6709\u544a\u8bc9\u5bff\u547d\u670d\u4ece\u4ec0\u4e48\u5206\u5e03\u3002\u56e0\u6b64\u4e0d\u80fd\u76f4\u63a5\u6309\u6b63\u6001\u5206\u5e03\u7b97\u7cbe\u786e\u6982\u7387\uff0c\u4e5f\u4e0d\u80fd\u9ed8\u8ba4\u7528\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u53bb\u8fd1\u4f3c\u3002\u8003\u7814\u6570\u5b66\u91cc\uff0c\u53ea\u7ed9\u671f\u671b\u548c\u65b9\u5dee\u3001\u8981\u6c42\u4fdd\u8bc1\u67d0\u4e2a\u6982\u7387\u4e0d\u5c0f\u4e8e\u591a\u5c11\uff0c\u6700\u5e38\u89c1\u5c31\u662f\u7528\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u5148\u8bbe\u968f\u673a\u62bd\u53d6\u7684 <code>n<\/code> \u4e2a\u5668\u4ef6\u5bff\u547d\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>X\u2081, X\u2082, ... , X\u2099\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u4eec\u76f8\u4e92\u72ec\u7acb\uff0c\u4e14\u6765\u81ea\u540c\u4e00\u79cd\u5668\u4ef6\uff0c\u6240\u4ee5\u4e00\u822c\u9ed8\u8ba4\u540c\u5206\u5e03\u3002\u56e0\u6b64\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X\u2096) = \u03bc\nD(X\u2096) = \u03c3\u00b2 = 400\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6837\u672c\u5747\u503c\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>X\u0304 = (1\/n)(X\u2081 + X\u2082 + ... + X\u2099)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5148\u6c42 <code>X\u0304<\/code> \u7684\u6570\u5b66\u671f\u671b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X\u0304)\n= E&#91;(1\/n)(X\u2081 + X\u2082 + ... + X\u2099)]\n= (1\/n)&#91;E(X\u2081) + E(X\u2082) + ... + E(X\u2099)]\n= (1\/n)(n\u03bc)\n= \u03bc\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5 <code>X\u0304<\/code> \u662f <code>\u03bc<\/code> \u7684\u65e0\u504f\u4f30\u8ba1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u518d\u6c42 <code>X\u0304<\/code> \u7684\u65b9\u5dee\u3002\u56e0\u4e3a <code>X\u2081, X\u2082, ... , X\u2099<\/code> \u76f8\u4e92\u72ec\u7acb\uff0c\u6240\u4ee5\u548c\u7684\u65b9\u5dee\u7b49\u4e8e\u65b9\u5dee\u4e4b\u548c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>D(X\u0304)\n= D&#91;(1\/n)(X\u2081 + X\u2082 + ... + X\u2099)]\n= (1\/n\u00b2)D(X\u2081 + X\u2082 + ... + X\u2099)\n= (1\/n\u00b2)&#91;D(X\u2081) + D(X\u2082) + ... + D(X\u2099)]\n= (1\/n\u00b2)(n\u03c3\u00b2)\n= \u03c3\u00b2\/n\n= 400\/n\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\u6700\u5173\u952e\u7684\u4e00\u6b65\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>D(aX) = a\u00b2D(X)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5 <code>(1\/n)<\/code> \u63d0\u51fa\u6765\u540e\u53d8\u6210\u4e86 <code>(1\/n\u00b2)<\/code>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X - E(X)| &lt; \u03b5} \u2265 1 - D(X)\/\u03b5\u00b2\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u73b0\u5728\u628a <code>X<\/code> \u6362\u6210\u6837\u672c\u5747\u503c <code>X\u0304<\/code>\uff0c\u56e0\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>E(X\u0304) = \u03bc\nD(X\u0304) = 400\/n\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; \u03b5} \u2265 1 - D(X\u0304)\/\u03b5\u00b2\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u9898\u76ee\u8981\u6c42\u7684\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; 1} \u2265 0.95\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e5f\u5c31\u662f\u53d6 <code>\u03b5 = 1<\/code>\uff0c\u4ee3\u5165\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; 1}\n\u2265 1 - D(X\u0304)\/1\u00b2\n= 1 - 400\/n\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u4fdd\u8bc1\u9898\u76ee\u8981\u6c42\u6210\u7acb\uff0c\u53ea\u8981\u8ba9\u53f3\u8fb9\u4e0d\u5c0f\u4e8e <code>0.95<\/code>\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>1 - 400\/n \u2265 0.95\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u89e3\u8fd9\u4e2a\u4e0d\u7b49\u5f0f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>400\/n \u2264 0.05\nn \u2265 400\/0.05\nn \u2265 8000\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>n \u81f3\u5c11\u4e3a 8000\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9898\u7684\u516c\u5f0f\u8f6c\u6362\u4e3b\u7ebf\u53ef\u4ee5\u538b\u7f29\u6210\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>D(X\u0304) = \u03c3\u00b2\/n = 400\/n\n\nP{|X\u0304 - \u03bc| &lt; 1}\n\u2265 1 - D(X\u0304)\/1\u00b2\n= 1 - 400\/n\n\n1 - 400\/n \u2265 0.95\n\nn \u2265 8000\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u5173\u4e8e\u201c\u505a\u9898\u65f6\u5982\u4f55\u5224\u65ad\u8be5\u7528\u54ea\u4e2a\u6781\u9650\u5b9a\u7406\u201d\uff0c\u53ef\u4ee5\u6309\u9898\u5e72\u4fe1\u53f7\u6765\u5224\u65ad\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u9898\u76ee\u53ea\u7ed9\u4e86\u6570\u5b66\u671f\u671b\u548c\u65b9\u5dee\uff0c\u5e76\u4e14\u8981\u6c42\u7c7b\u4f3c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; \u03b5} \u2265 \u67d0\u4e2a\u6570\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216\u8005\u8981\u6c42\u201c\u4e3a\u4e86\u4f7f\u6837\u672c\u5747\u503c\u4e0e\u603b\u4f53\u5747\u503c\u7684\u504f\u5dee\u5c0f\u4e8e\u67d0\u503c\u7684\u6982\u7387\u81f3\u5c11\u4e3a\u591a\u5c11\u201d\uff0c\u8fd9\u901a\u5e38\u7528<strong>\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f<\/strong>\u3002\u56e0\u4e3a\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\u4e0d\u8981\u6c42\u77e5\u9053\u603b\u4f53\u5206\u5e03\uff0c\u53ea\u8981\u6c42\u65b9\u5dee\u5b58\u5728\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u9898\u76ee\u95ee\u7684\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u5f53 n \u2192 \u221e \u65f6\uff0cX\u0304 \u662f\u5426\u4f9d\u6982\u7387\u6536\u655b\u4e8e \u03bc\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216\u8005\u95ee\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u8bc1\u660e X\u0304 \u2192 \u03bc\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u7c7b\u9898\u4e00\u822c\u7528<strong>\u5927\u6570\u5b9a\u5f8b<\/strong>\u3002\u5b83\u5173\u5fc3\u7684\u662f\u6837\u672c\u5747\u503c\u662f\u5426\u7a33\u5b9a\u8d8b\u8fd1\u603b\u4f53\u5747\u503c\uff0c\u4e0d\u662f\u8ba9\u4f60\u7b97\u5177\u4f53\u7684 <code>n<\/code>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u9898\u76ee\u51fa\u73b0\u5927\u91cf\u72ec\u7acb\u540c\u5206\u5e03\u968f\u673a\u53d8\u91cf\u7684\u548c\uff0c\u5e76\u4e14\u95ee\u8fd1\u4f3c\u6982\u7387\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{a &lt; X\u2081 + X\u2082 + ... + X\u2099 &lt; b}\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216\u8005\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{a &lt; X\u0304 &lt; b}\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e76\u4e14 <code>n<\/code> \u8f83\u5927\uff0c\u5e38\u5e38\u7528<strong>\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406<\/strong>\uff0c\u628a\u548c\u6216\u5747\u503c\u6807\u51c6\u5316\u540e\u8fd1\u4f3c\u4e3a\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(X\u2081 + ... + X\u2099 - n\u03bc)\/(\u03c3\u221an) \u8fd1\u4f3c\u670d\u4ece N(0,1)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216\u8005\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(X\u0304 - \u03bc)\/(\u03c3\/\u221an) \u8fd1\u4f3c\u670d\u4ece N(0,1)\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9898\u5982\u679c\u5f3a\u884c\u7528\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0c\u4f1a\u5f97\u5230\u8fd1\u4f3c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; 1}\n\u2248 P{|Z| &lt; \u221an\/20}\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8981\u6c42\u7ea6\u7b49\u4e8e\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>2\u03a6(\u221an\/20) - 1 \u2265 0.95\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8e\u662f\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u221an\/20 \u2265 1.96\nn \u2265 1536.64\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5373 <code>n \u2248 1537<\/code>\u3002\u4f46\u662f\u8fd9\u4e2a\u7ed3\u679c\u53ea\u662f<strong>\u6b63\u6001\u8fd1\u4f3c\u7ed3\u679c<\/strong>\uff0c\u4e0d\u662f\u4e25\u683c\u4fdd\u8bc1\u3002\u9898\u76ee\u6ca1\u6709\u8bf4\u5bff\u547d\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u4e5f\u6ca1\u6709\u8bf4\u7528\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u8fd1\u4f3c\uff0c\u6240\u4ee5\u4e0d\u80fd\u628a <code>1537<\/code> \u5f53\u4f5c\u672c\u9898\u6807\u51c6\u7b54\u6848\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u9898\u6807\u51c6\u505a\u6cd5\u7528\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\uff0c\u7ed3\u679c\u662f <code>8000<\/code>\u3002\u5b83\u6bd4\u8f83\u4fdd\u5b88\uff0c\u4f46\u5b83\u4e0d\u4f9d\u8d56\u603b\u4f53\u5206\u5e03\uff0c\u6240\u4ee5\u80fd\u4fdd\u8bc1\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P{|X\u0304 - \u03bc| &lt; 1} \u2265 0.95\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">\u8003\u7814\u91cc\u53ef\u4ee5\u8fd9\u6837\u5feb\u901f\u8bc6\u522b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u53ea\u7ed9 E(X)\u3001D(X)\uff0c\u8981\u6c42\u6982\u7387\u4e0b\u754c \u2192 \u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\n\n\u95ee\u6837\u672c\u5747\u503c\u662f\u5426\u8d8b\u4e8e\u603b\u4f53\u5747\u503c \u2192 \u5927\u6570\u5b9a\u5f8b\n\n\u95ee\u5927\u91cf\u72ec\u7acb\u968f\u673a\u53d8\u91cf\u548c\u7684\u8fd1\u4f3c\u5206\u5e03\u6216\u8fd1\u4f3c\u6982\u7387 \u2192 \u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\n\n\u660e\u786e\u7ed9\u51fa\u6b63\u6001\u5206\u5e03 \u2192 \u76f4\u63a5\u7528\u6b63\u6001\u5206\u5e03\u6807\u51c6\u5316\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u9898\u6700\u6838\u5fc3\u7684\u8bc6\u522b\u70b9\u5c31\u662f\uff1a<strong>\u53ea\u7ed9\u5747\u503c\u548c\u65b9\u5dee\uff0c\u6ca1\u6709\u7ed9\u5206\u5e03\uff0c\u5374\u8981\u6c42\u6982\u7387\u81f3\u5c11\u4e3a 0.95<\/strong>\u3002\u56e0\u6b64\u5e94\u8be5\u7528\u5207\u6bd4\u96ea\u592b\u4e0d\u7b49\u5f0f\uff0c\u800c\u4e0d\u662f\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e25\u683c\u8bf4\uff0c\u4e0d\u662f\u201c\u5bc6\u5ea6\u51fd\u6570\u7684\u79ef\u5206\u662f\u671f\u671b\u201d\uff0c\u800c\u662f\uff1a \u4e5f\u5c31\u662f\u8bf4\uff1a \u5982\u679c\u662f\u968f\u673a\u53d8\u91cf\u7684\u51fd\u6570 g(X)\uff0c\u5219\u6709\uff1a \u6240\u4ee5\u771f\u6b63\u8981\u7406 [&hellip;]<\/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-2377","post","type-post","status-publish","format-standard","hentry","category-text"],"_links":{"self":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2377","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=2377"}],"version-history":[{"count":2,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2377\/revisions"}],"predecessor-version":[{"id":2383,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2377\/revisions\/2383"}],"wp:attachment":[{"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=2377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=2377"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.preluna.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=2377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}