设二维随机变量（X,Y）的联合分布函数为F(X,Y)=A(B+arctanX)(C+arcY).求

题目

设二维随机变量（X,Y）的联合分布函数为F(X,Y)=A(B+arctanX)(C+arcY).求
（1）常数A,B,C
(2)关于X,Y的边缘分布函数
是arctanY

答案

F(-∞,-∞)=A(B-π/2)(C-π/2)=0F(-∞,+∞)=A(B-π/2)(C+π/2)=0F(+∞,-∞)=A(B+π/2)(C-π/2)=0F(+∞,+∞)=A(B+π/2)(C+π/2)=1解得：A=1/π^2,B=π/2,C=π/2f(x,y)=dF(x,y)/dxdy=1/[π^2 (1+x^2)(1+y^2)]边缘函数f...