Question

设随机变量X服从区间[0,1]上的均匀分布,Y服从参数为1的指数分布,且X,Y相互独立.求,(1)X,Y的概率密度(2)

Answer 1

fx(x)=1,fy(y)=e^-y

fx,y(x,y)=fx(x)fy(y)=e^-y

P(x>y)=P(x>y|Y=y)=1-P(x