Joint probability,-limit values

[aruna1]

hello
i have given this problem to find pdf of function z.i have solved most of it and stuck at the end.
i have attached problem and my solution so far as pdf here.
what i want to know what are the integral limits for finding f(z) using marginal density (see the end the end of attached solution is it [0 to z] or [z to 1] ?)

thanks.

 

[zli034]

start with
P(Z<=z)
=P(XY<=z)
=P(Y<=z/x), x not equals 0
from here we do double integration on pxy(x,y) to obtain area of Fxy(Y<=z/x)=1-P(Y>z/x)=Fz
The limit of x is from z to 1, limit of y is z/x to 1

Fz(z) my calculation z^2-2zlnz