Suppose that the random variables X and Y have a joint probability density function f(x, y) = c(x + y)² for 0≤x≤ 1 and 0 ≤ y ≤ 1. (a) Find c. (b) Let Z = (X+Y)−¹, find E[Z]. (c) Find the marginal distribution of X and Y. (d) What is Cov(X,Y)? (e) Find the probability density function of X conditional on Y = 1.5.

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