Question

已知二维随机变量(X,Y)的联合概率密度函数为 f(x,y)=2e^(-2x-y),x>0,y>0; f(x,y)=0(

Answer 1

P=∫(0-->1)e^(-y)dy∫(0-->1-y)2e^(-2x)dx

=∫(0-->1)e^(-y)(1-e^(2(1-y))dy

=∫(0-->1)(e^(-y)-e^2e^y)dy=(1-e)(1+e^2)