題組內容

Suppose that X and Y are two independent random variables which are exponentially distributed with parameter λ = 1. That is, X and y both have Exponential   (1)   -distribution, with cazresponding density functions being fx and fy deined as 627cb0ce4cb80.jpg . 627cb0e7e372b.jpgand 627cb1034c494.jpg. 627cb11b02e61.jpg respectively. 
Let T = X+Y. 

(a)  Find the joint density of the random vector (X,Y).