Question: Fix a constant x in R. Let U be an exponential random variable with rate 2. Also let V be a random variable satisfying P(V

Fix a constant x in R. Let U be an exponential random variable with rate 2. Also let V be a random variable satisfying P(V = 1) = P(V = -1) = 1/2. Suppose U and V are independent, and define Z = x + UV. find the distribution of z.

Z should be some form of ce^(-2|y-x|).

Hint: Derive the cumulative distribution function of Z and then differentiate to see that the probability function is in the form ce^(-2|y-x|). Note that Z.x only if V = 1 and Z < x only if V = -1

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