C, D, and E Suppose that the random variables X and Y have a joint probability density functionf(x, y) = c(x + y)²for 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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Answered: (c) Find the marginal distribution of X…

A First Course in Probability (10th Edition)

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(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.