关于求边缘密度函数的公式应用 关于联合密度函数求边缘密度函数的题？
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绛旓細鐢遍璁炬潯浠讹紝y=x²涓巠=x鐨勪氦鐐逛负(0,0)銆(1,1)銆傗埓鎸夌収杈圭紭瀵嗗害鍑芥暟鐨瀹氫箟锛屾湁fX(x)=鈭(x²,x)f(x,y)dy=6x-6x²锛寈鈭(0,1)锛沠X(x)=0锛寈涓哄叾瀹冦傚悓鐞嗭紝fY(y)=鈭(y,鈭歽)f(x,y)dx=4y^(3/2)-3y²锛寉鈭(0,1)锛沠Y(y)=0锛寉涓哄叾瀹冦
绛旓細杈圭紭瀵嗗害鍑芥暟fx绛変簬f(x,y)瀵箉杩涜绉垎寰楀埌鐨勭粨鏋溿傝屾潯浠舵鐜囧瘑搴︽槸鍦ㄨ绠楀嚭杈圭紭瀵嗗害鍑芥暟鐨鍩虹涓娿傚惈涔 鍒橷涓鸿繛缁瀷闅忔満鍙橀噺锛岀Оf(x)涓篨鐨勬鐜囧瘑搴﹀嚱鏁帮紝绠绉颁负姒傜巼瀵嗗害銆傚崟绾殑璁叉鐜囧瘑搴︽病鏈夊疄闄呯殑鎰忎箟锛屽畠蹇呴』鏈夌‘瀹氱殑鏈夌晫鍖洪棿涓哄墠鎻愩傚彲浠ユ妸姒傜巼瀵嗗害鐪嬫垚鏄旱鍧愭爣锛屽尯闂寸湅鎴愭槸妯潗鏍囷紝姒傜巼瀵嗗害瀵...
绛旓細p(x) = 鈭 [-x,x] 1dy = 2x, 0<x<1; 0, 鍏朵粬銆俻(y) = 鈭 [|y|,1] 1dx = 1-|y|, -1<y<1; 0, 鍏朵粬銆俻(x,y) 涓嶇瓑浜 p(x)p(y)銆 鏁匵锛孻 涓嶇嫭绔嬨
绛旓細X鐨杈圭紭鍒嗗竷鐨瀵嗗害鍑芥暟fX(x)=鈭(-鈭,鈭)f(x,y)dy=鈭(0,x)3xdy=3x²锛0<x<1銆乫X(x)=0锛寈鍏跺畠銆俌鐨勮竟缂樺垎甯冪殑瀵嗗害鍑芥暟fY(y)=鈭(-鈭瀞hu,鈭)f(x,y)dx=鈭(y,1)3xdx=(3/2)(1-y²)锛0<y<1銆乫X(x)=0锛寉鍏跺畠銆俋瀵筜鍗(X涓╕)鏃剁殑鐨勫瘑搴﹀嚱鏁癴X涓╕(x涓▂)=...
绛旓細鏍规嵁鍙橀噺鐨勫彇鍊艰寖鍥达紝瀵硅仈鍚堟鐜瀵嗗害鍑芥暟绉垎锛屽y绉垎寰楀埌X鐨杈圭紭姒傜巼瀵嗗害锛屽x绉垎寰楀埌Y鐨勮竟缂樻鐜囧瘑搴﹁繃绋嬪涓嬶細
绛旓細瑙ｇ瓟杩囩▼濡備笅锛氳棰樺垎涓轰笁灏忛銆傜涓灏忛姹傛鐜囧瘑搴﹀嚱鏁帮紝鍗冲鍒嗗竷瀵嗗害鍑芥暟姹傚鍗冲彲锛屾敞鎰忚繖閲屽洜涓烘槸鍚湁x鍜寉锛屾墍浠ヨ瀵箈鍜寉閮芥眰鍋忓銆傜浜屽皬棰樻槸姹傝竟缂樺瘑搴﹀嚱鏁锛屽嵆鍦ㄧ涓棰樼殑鎵寰楀埌鐨勬鐜囧瘑搴﹀嚱鏁板熀纭涓婏紝鍒嗗埆瀵箈鍜寉姹傜Н鍒嗭紝寰楀埌杈圭紭瀵嗗害鍑芥暟銆傜涓夊皬棰樻牴鎹墍寰楀埌鐨勬鐜囧瘑搴﹀嚱鏁颁唬鍏ョН鍒嗗嵆鍙
绛旓細鍒嗗埆姹傚叾杈圭紭姒傜巼瀵嗗害,f(x) = 2x锛宖(y) = 2y锛孹鍜孻鐙珛鐨勫厖鍒嗗繀瑕佹潯浠舵槸f(x,y) = f(x)f(y)鎴愮珛锛屾鏃跺彲鐭(x,y) = 4xy = f(x)f(y),鍒欑嫭绔嬫垚绔嬨傞殢鏈哄彉閲忔槸鍙栧兼湁澶氱鍙兘骞朵笖鍙栨瘡涓奸兘鏈変竴涓鐜囩殑鍙橀噺锛屽垎涓虹鏁ｅ瀷鍜岃繛缁瀷涓ょ锛岀鏁ｅ瀷闅忔満鍙橀噺鐨勫彇鍊间负鏈夐檺涓垨鑰呮棤闄愬彲鍒椾釜...
绛旓細姹傝竟缂樺瘑搴﹀嚱鏁锛屾牴鎹畑,y鐨勫绉版э紝涓や釜杈圭紭瀵嗗害鍑芥暟鏄悓鍒嗗竷鐨勶紝渚嬪瀵1>x>0, 瀵嗗害鍑芥暟鏄 2sqrt(1-x^2)/PI,鍒嗗竷鍑芥暟涓 1/2+arcsinx/PI +sin(2arcsinx)/(2PI),瀵逛簬1>y>0, Y鐨勮竟缂樻鐜囧瘑搴﹀嚱鏁颁负 2sqrt(1-y^2),鍚屽垎甯冿紝浣嗘槸涓嶇嫭绔嬶紝
绛旓細鐪嬪浘
绛旓細鏍规嵁鍙橀噺鐨勫彇鍊艰寖鍥达紝瀵硅仈鍚堟鐜瀵嗗害鍑芥暟绉垎锛屽y绉垎寰楀埌X鐨杈圭紭姒傜巼瀵嗗害锛屽x绉垎寰楀埌Y鐨勮竟缂樻鐜囧瘑搴﹁繃绋嬪涓嬶細
