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Let (X, Y) be a random vector (or a random variable) with joint density f (X,...

Let (X, Y) be a random vector (or a random variable) with joint density f (X, Y) (x, y) = 3 (x + y)1(0,1) (x + y)1(0,1) (x)1(0.1) (y), with 1 (0,1) = indicator function.

a) Calculate the marginal density functions of X and Y, respectively.
b) Calculate the conditional density functions of X given Y = y, and of Y given X = x.
c) Are X and Y independent?

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