# Exam P Practice Problem 13 – Convolution Technique

Problem 13A
Suppose that $X$ and $Y$ are independent random variables where their probability density functions are $f(x)=0.1 \ e^{-0.1 \ x}$ and $g(y)=0.05 \ e^{-0.05 \ y}$, respectively. Find the pdf of $W$ where $W=X+Y$.

Problem 13B
Suppose that $X$ and $Y$ are independent random variables where their probability density functions are $f(x)=0.2 \ e^{-0.2 \ x}$ and $g(y)=0.25 \ e^{-0.25 \ y}$, respectively. Find the pdf of $W$ where $W=X+Y$.

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These are two practice problems on finding the density function of an independent sum using the convolution approach. For a discussion of the convolution technique, see the blog post Examples of convolution (continuous case).

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