How Do You Find the PDF of Z=X+Y When X and Y Are Not Independent?

[joserse46]

f(x,y) = (1/x) for 0≤y≤x≤1

A new rv Z=X+Y where X,Y not independent find the pdf of z

My approach

F(z) = P(Z≤z) = ∫∫fXY(x,y) dx dy x= -∞ to ∞ y= 0 to z-y

f(z) = d/dz(F(z)) = ∫fXY(z-y,y) dy y= -∞ to ∞ (using Leibnitz)

where i am stuck is this doesn't converge

 

[bpet]

(this thread belongs in the homework forums)

f(x,y) might not be a valid pdf