Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1 for 0 < x < 1, x < y < x + 1.

A. What is the marginal density of X and Y ? Use this to compute Var(X) and Var(Y).

B. Compute the expectation E[XY]

C. Use the previous results to compute the correlation Corr(Y, X).

D. Compute the third moment of Y , i.e., E[Y³].

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