5. For independent random variables X ~ Exp(A1) and Y ~ Exp(\2), find the density function for the convolution of these two random variables.

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5. For independent random variables X ~ Exp(A1) and Y ~ Exp(\2), find
the density function for the convolution of these two random variables.
Transcribed Image Text:5. For independent random variables X ~ Exp(A1) and Y ~ Exp(\2), find the density function for the convolution of these two random variables.
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Step 1

Introduction:

For the exponentially distributed random variables X and Y, with respective parameters λ1 and λ2, the probability density functions or pdf’s, f (x) and f (y) are given below:

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