Suppose X and Y are jointly continuous with joint density
f(x,y)= (exp(-x/y)*exp(-y))/y for 0<x<oo and 0<y<oo
f(x,y)= 0 otherwise
I first find the density functions of X and Y respectively.
But I am in difficulty in integrating (exp(-x/y)*exp(-y))/y with respect to y. Can someoneone provides some hints?
Also P(X>1|Y=y)=P(X>1 and Y=y)/P(Y=y)
But for continuous random variable Y, P(Y=y)=0?