设二维随机变量(X,Y)的概率密度为f(x,y)求F(x,y) 设随机变量X-N(0 1)求Y=e^x概率密度?
\u8bbe\u4e8c\u7ef4\u968f\u673a\u53d8\u91cf(X,Y)\u7684\u6982\u7387\u5bc6\u5ea6\u4e3af(x,y)=2,0<=x<=1,0<=y<=x,f(x,y)=0,\u5176\u4ed6\uff0c\u6c42E(X+Y)\u89c1\u56fe
\u76f4\u63a5\u7528\u516c\u5f0f\u6cd5\uff0c\u7b80\u5355\u5feb\u6377\uff0c\u7b54\u6848\u5982\u56fe\u6240\u793a
f(x,y)=Fxy(x,y),就是F(x,y)对x,y求偏导得到的,那么F(x,y)就是 f(x,y)对x积分 从负无穷大积到x,然后再对y积分,从负无穷大积到y
绛旓細P(Z=0)=P(x=0,y=0)=0.25 P(Z=1)=P(x=0,y=1)+P(x=1,y=0)=0.1+0.15=0.25 P(Z=2)=P(x=0,y=2)+P(x=1,y=1)=0.3+0.15=0.45 P(Z=3)=P(x=1,y=2)=0.05
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绛旓細鏍规嵁姒傜巼瀵嗗害鍑芥暟鐨勭Н鍒=1锛屽彲浠ョ畻鍑篈鐨勫笺傚嵆锛氣埆 鈭 f(x,y) dx dy = 1 锛堚埆 鍧囦粠-鈭炵Н鍒嗗埌+鈭烇級銆傚垯浠庨涓凡鐭ユ潯浠跺彲寰楋紝+鈭 蟺/2 鈭 鈭 f(x,y) dx dy = 鈭 鈭 A sin(x+y) dx dy (x,y 鍧囦粠0鍒跋/2绉垎)-鈭 0 蟺/2 = A 鈭 -[cos(蟺/2+y) - co...