设(X,Y)的联合分布函数为F(x,y)=则P{max(X,Y)>1}=______.

admin2018-01-23  57

问题 设(X,Y)的联合分布函数为F(x,y)=则P{max(X,Y)>1}=______.

选项

答案e-2+e-3-e-5

解析 由FX(x)=F(x,+∞)=得X~E(2),同理Y~E(3),且X,Y独立.
P{max(X,Y)>1}=P(X>1或Y>1)=1-P(X≤1,Y≤1)=1-P(X≤1)P(Y≤1)
=1-FX(1)FY(1)=1-(1-e-2)(1-e-3)=e-2+e-3-e-5
转载请注明原文地址:https://jikaoti.com/ti/oAKRFFFM
0

最新回复(0)