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**Problem 14A**

Suppose and are independent random variables such that is exponentially distributed with mean 10 and has the following density function:

where

Find the pdf of .

**Problem 14B**

Suppose and are independent random variables such that is exponentially distributed with mean 20 and has the following density function:

where

Find the pdf of .

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The two problems here provide more practice for using convolution method to find the pdf of an independent sum. An actual Exam P question may not be this straightforward. But using convolution to find the pdf of a sum is a good skill to have. The problems here can help solidify the thought process behind the method of convolution.

For a discussion of the convolution technique, see the blog post Examples of convolution (continuous case).

For additional practice, see Exam P Practice Problem 13 – Convolution Technique.

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