概率论，由条件概率密度函数，求边缘密度函数。具体题目请点开看图片 概率论联合密度函数如果y的绝对值小于x怎么求边缘
\u6982\u7387\u8bba\u6c42(1)\u8fb9\u7f18\u6982\u7387\u5bc6\u5ea6\u51fd\u6570 (2)\u6761\u4ef6\u6982\u7387\u5bc6\u5ea6\u51fd\u6570(1)\uff0c\u6309\u7167\u5b9a\u4e49\uff0cX\u7684\u8fb9\u7f18\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570fX(x)=\u222b(-\u221e,\u221e)f(x,y)dy=\u222b(0,x)3xdy=3x²\uff0c0<x<1\u3001fX(x)=0\uff0cx\u5176\u5b83\u3002
\u540c\u7406\uff0cY\u7684\u8fb9\u7f18\u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570fY(y)=\u222b(-\u221e,\u221e)f(x,y)dx=\u222b(y,1)3xdx=(3/2)(1-y²)\uff0c0<y<1\u3001fX(x)=0\uff0cy\u5176\u5b83\u3002
(2)\uff0c\u6309\u7167\u5b9a\u4e49\uff0cX\u5bf9Y\u5373(X\u4e28Y)\u65f6\u7684\u7684\u5bc6\u5ea6\u51fd\u6570fX\u4e28Y(x\u4e28y)=f(x,y)/fY(y)=2x/(1-y²)\uff0c0<x<1\u30010<y<x\uff1bfX\u4e28Y(x\u4e28y)=0\uff0c(x,y)\u5176\u5b83\u3002
\u540c\u7406\uff0cY\u5bf9X\u5373(Y\u4e28X)\u65f6\u7684\u7684\u5bc6\u5ea6\u51fd\u6570fY\u4e28X(y\u4e28x)=f(x,y)/fX(x)=1/x\uff0c0<x<1\u30010<y<x\uff1bfY\u4e28X(y\u4e28x)=0\uff0c(x,y)\u5176\u5b83\u3002
\u4f9b\u53c2\u8003\u3002
\u8981\u4ece\u8054\u5408\u5bc6\u5ea6\u51fd\u6570\u6c42\u51faX\u7684\u8fb9\u7f18\u5bc6\u5ea6\u51fd\u6570\uff0c\u90a3\u4e48\u5c31\u8981\u6d88\u6389\u539f\u8868\u8fbe\u5f0f\u4e2d\u7684y\uff0c\u56e0\u6b64\u662f\u5bf9y\u8fdb\u884c\u79ef\u5206\uff0c\u79ef\u5206\u7684\u4e0a\u4e0b\u9650\u5f53\u7136\u662fy\u7684\u53d6\u503c\u8303\u56f4\u4e86\uff0c\u4f46\u662f\u8981\u628ay\u7684\u53d6\u503c\u8303\u56f4\u7528\u542bx\u7684\u8868\u8fbe\u5f0f\u5199\u51fa\u6765\uff0c\u8fd9\u6837\u79ef\u5206\u4e4b\u540e\u5c31\u53ea\u5269\u4e0bx\uff0c\u5f53\u7136\u5c31\u5f97\u51fa\u4e86X\u7684\u8fb9\u7f18\u5bc6\u5ea6\u51fd\u6570\u3002
\u6839\u636e\u968f\u673a\u53d8\u91cf\u7684\u4e0d\u540c\uff0c\u8054\u5408\u6982\u7387\u5206\u5e03\u7684\u8868\u793a\u5f62\u5f0f\u4e5f\u4e0d\u540c\u3002\u5bf9\u4e8e\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\uff0c\u8054\u5408\u6982\u7387\u5206\u5e03\u53ef\u4ee5\u4ee5\u5217\u8868\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u4e5f\u53ef\u4ee5\u4ee5\u51fd\u6570\u7684\u5f62\u5f0f\u8868\u793a\uff1b\u5bf9\u4e8e\u8fde\u7eed\u578b\u968f\u673a\u53d8\u91cf\uff0c\u8054\u5408\u6982\u7387\u5206\u5e03\u901a\u8fc7\u975e\u8d1f\u51fd\u6570\u7684\u79ef\u5206\u8868\u793a\u3002
见图。
绛旓細鍥炵瓟锛氬叏鍖洪棿绉垎,绛変簬1銆傚彲浠ョ畻鍑簁绛変簬0.5
绛旓細7棰橈紝(1)鏍规嵁姒傜巼瀵嗗害鍑芥暟鐨勬ц川锛屾湁鈭(-鈭,鈭)dx鈭(-鈭,鈭)f(x,y)dy=1銆傗埓c鈭(0,鈭)dx鈭(0,鈭)e^(-x-2y)dy=c鈭(0,鈭)e^(-x)dx鈭(0,鈭)e^(-2y)dy=c/2=1銆傗埓c=2銆(2)锛孭(X<1,Y>2)=鈭(0,1)dx鈭(2,鈭)f(x,y)dy=2鈭(0,1)e^(-x)dx鈭(2,鈭)e^(...
绛旓細鎵浠=1/8 2)鍒╃敤杈圭紭姒傜巼瀵嗗害鍏紡fx(x)=鈭(-鈭,+鈭)f(x,y)dy=x/2,0<x<2锛0鍏朵粬 fy(y)=鈭(-鈭,+鈭)f(x,y)dx=(4-y)/16锛0鈮<4锛(4+y)/16锛-4<y<0锛0鍏朵粬 3)鏉′欢姒傜巼瀵嗗害鏄鑱斿悎瀵嗗害/杈圭紭瀵嗗害锛fY/X(y|x)=f(x,y)/fx(x)=1/4x,0<x<2锛0鍏朵粬 ...
绛旓細濡傛灉娌℃湁鍏跺畠鏉′欢锛屽彧鐭ラ亾涓や釜杈圭紭姒傜巼瀵嗗害fx(x),fy(y)锛屾槸鏃犳硶姹傚嚭鑱斿悎姒傜巼瀵嗗害f(x,y)鐨勩傚鏋滀袱涓彉閲忕嫭绔嬶紝鍒檉(x,y)=fx(x),fy(y)銆俧(y) = f(x)/|g'(x)|= f{(y-1)/(-2)}/2= f{(1-y)/2}/2锛
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绛旓細36/锛4+5锛=4 姝ｆ柟褰㈠懆闀垮垎鍒负锛4*4=16锛4*5=20 姝ｆ柟褰㈣竟闀夸负4锛5 闈㈢Н鍜4^2+5^2=41
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