Suppose X and Yare both independent and uniformly distributed on [0, 1] (i.e., f(x) = g(x) = 1 for x = [0, 1] and 0 otherwise). Define has the density of the random variable Z = X + Y. Please answer the following questions. a). What is h? b). What is Pr(X ≤ 1/2|X + Y≥ 5/4)?

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