My Math Forum Suppose again that Z = X +Y. Find fz(Z)

July 24th, 2017, 01:06 PM   #1
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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 $$\int_{-∞}^{+∞}((z-y)/2)*(y/2)\,dx,$$, then I got $$\int_{-∞}^{+∞}((zy)/4)-(y^2/4)\,dx,$$, unfortunately I was unable to figure this out
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Last edited by poopeyey2; July 24th, 2017 at 01:25 PM.

 July 24th, 2017, 02:05 PM #2 Senior Member   Joined: Oct 2009 Posts: 428 Thanks: 144 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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