为什么fX(x)的定义域是-R<x<R：设二维随机变量(X,Y)服从圆域G:x^2+y^2≤R^2上的均匀分布，求关于X以及关 设二维随机变量(X，Y)服从在区域D上的均匀分布

\u8bbe\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf(X,Y)\u670d\u4ece\u56ed\u57dfG\uff1ax^2+y^2<=R^2\u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u6c42\u8fb9\u7f18\u6982\u7387\u5bc6\u5ea6 \u4e0a\u4e0b\u9650\u600e\u4e48\u628a\u63e1

\u753b\u51fa\u56fe\u5f62\uff0c\u5bf9x\u79ef\u5206\u5f97\u5230fY(y),\u753b\u4e00\u6761\u6c34\u5e73\u7ebf\u4ea4\u5706\u4e8e2\u70b9\uff0c\u5176\u6a2a\u5750\u6807\u5206\u522b\u662f-\u221aR^2-y^2,\u221aR^2-y^2,\u4e5f\u5c31\u662f\u79ef\u5206\u4e0a\u4e0b\u9650\u3002
\u5bf9y\u79ef\u5206\u53ef\u5f97\u5230fX(x).\u540c\u7406\u753b\u4e00\u6761\u5782\u76f4\u7ebf\u4ea4\u5706\u4e8e2\u70b9\uff0c\u7eb5\u5750\u6807\u5206\u522b\u662f-\u221aR^2-x^2,\u221aR^2-x^2,\u5f97\u5230\u79ef\u5206\u4e0a\u4e0b\u9650\u3002
\u7531\u9898\u76ee\u53ef\u77e5\uff1af(x,y)=1/\u03c0R^2
\u800c\u8fb9\u7f18\u6982\u7387\u5bc6\u5ea6fY(y)=\u222bf(x,y)dx ,\uff08\u4ece-\u221aR^2-y^2\u5230\u221aR^2-y^2\uff09
=\u222b1/\u03c0R^2dx,\uff08\u4ece-\u221aR^2-y^2\u5230\u221aR^2-y^2\uff09
=2(\u221aR^2-y^2)/\u03c0R^2
\u540c\u7406\uff1afX(x)=2(\u221aR^2-x^2)/\u03c0R^2

\uff081\uff09\u5f53-1\uff1cx\uff1c0\uff0cf\uff08x\uff09\u221ef\uff08x\uff0cy\uff09dy=2\u222bˣ⁺¹₀\uff081/2\uff09dy=x+1
\u540c\u7406\u5f530\uff1cx\uff1c1\uff0cf\uff08x\uff09=-x+1\uff0c\u6240\u4ee5f\uff08x\uff09=x+1\uff0c-1\uff1cx\uff1c0\uff1bf\uff08x\uff09=-x+1\uff0c0\uff1cx\uff1c1\uff1bf\uff08x\uff09=0\u3002
\u540c\u7406\uff1af\uff08y\uff09=y+1\uff0c-1\uff1cy\uff1c0\uff1bf\uff08y\uff09=-y+1\uff0c0\uff1cy\uff1c1\uff1bf\uff08y\uff09=0\u3002
\uff082\uff09P\uff08|x|\uff1cy\uff09=1/4\u3002
\uff083\uff09f\uff08x\uff0cy\uff09\u2260f\uff08x\uff09f\uff08y\uff09\uff0c\u6240\u4ee5x\uff0cy\u4e0d\u72ec\u7acb\u3002

\u6269\u5c55\u8d44\u6599\uff1a
\u76f8\u540c\u7684\u8fb9\u7f18\u5206\u5e03\u53ef\u6784\u6210\u4e0d\u540c\u7684\u8054\u5408\u5206\u5e03\uff0c\u8fd9\u53cd\u6620\u51fa\u4e24\u4e2a\u5206\u91cf\u7684\u7ed3\u5408\u65b9\u5f0f\u4e0d\u540c\uff0c\u76f8\u4f9d\u7a0b\u5ea6\u4e0d\u540c\u3002\u8fd9\u79cd\u5dee\u5f02\u5728\u5404\u81ea\u7684\u8fb9\u7f18\u5206\u5e03\u4e2d\u6ca1\u6709\u8868\u73b0\uff0c\u56e0\u800c\u5fc5\u987b\u8003\u5bdf\u5176\u8054\u5408\u5206\u5e03\u3002
\u5982\u679c\u4e24\u968f\u673a\u53d8\u91cf\u76f8\u4e92\u72ec\u7acb\uff0c\u5219\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\u7b49\u4e8e\u8fb9\u7f18\u5bc6\u5ea6\u51fd\u6570\u7684\u4e58\u79ef\uff0c\u5373f(x,y)=f(x)f(y)\u3002\u5982\u679c\u4e24\u968f\u673a\u53d8\u91cf\u662f\u4e0d\u72ec\u7acb\u7684\uff0c\u90a3\u662f\u65e0\u6cd5\u6c42\u7684\u3002

这是个面积为πR^2的圆形，均布在圆内(dx dy)的概率值为1/πR^2。 如果求边缘分布的话，也就是求f(x)和f(y)，由对称性可看出它俩形式一样 f(x) 的值域是-1到1, 而对应一个确定x的y的值域是(-sqrt(1-x^2),sqrt(1-x^2)) 所以f(x) = 2sqrt(1-x^2)

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鍑芥暟f(x)鐨勫畾涔夊煙涓篟,f(-1)=2,瀵逛换鎰弜灞炰簬R,f(x)瀵煎ぇ浜2,鍒檉(x)澶 ...
绛旓細鈥滃師涓嶇瓑寮忓彲鍖栦负g锛坸锛澶т簬g锛-1锛夆濊繖姝ユ庝箞鏉ョ殑 ANS:濡傛灉灏辫繖涓姝ヤ笉鎳傝鏄庝綘涓嶅瓨鍦 浠涔闂锛沢(-1)=f(-1)-2*(-1)-4 =2+2-4=0 鍗0=g(-1)f锛坸锛>2x+4,<==>f(x)-2x-4>0 <==>g(x)>g(-1) (杩欎竴姝ユ槸鎶0鎹㈡垚g(-1))...

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