Question

The random variables X and Y are independent. X has a Uniform distribution on [0, 5],...

The random variables X and Y are independent. X has a Uniform distribution on [0, 5], while Y has an Exponential distribution with parameter λ = 2. Define W = X + Y.

A.    What is the expected value of W?

B.    What is the standard deviation of W?

C.    Determine the pdf of W.  For full credit, you need to write out the integral(s) with the correct limits of integration. Do not bother to calculate the integrals.

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