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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