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July 24th, 2017, 02:06 PM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Suppose again that Z = X +Y. Find fz(Z)
Let X and Y be independent random variables deﬁned on the space Ω, with density functions fx(x)nd fy(y), respectively. Suppose Z = X + Y. Find the density fz(Z) if fx(x)=fy(z)= \begin{cases} X/2, & \text{if 0<$x$<2,} \\ 0, & \text{otherwise.} \end{cases} attempt: I tried to take the integral $$\int_{∞}^{+∞}((zy)/2)*(y/2)\,dx,$$, then I got $$\int_{∞}^{+∞}((zy)/4)(y^2/4)\,dx,$$, unfortunately I was unable to figure this out Last edited by poopeyey2; July 24th, 2017 at 02:25 PM. 
July 24th, 2017, 03:05 PM  #2 
Senior Member Joined: Oct 2009 Posts: 142 Thanks: 60 
Your integral limits should not be infinite. What should your limits be? If $f_Y(y)$ is 0 outside $(0,2)$, what does this mean for your limits?


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