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LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤1,...

LetX1 andX2 have joint density function f(x1,x2) =( 30x1x2^2, x1 −1≤ x2 ≤1−x1, 0≤ x1 ≤1, 0 otherwise.

(a) Find the marginal density of X1.

(b) Find the marginal density of X2.

(c) Are X1 and X2 independent?(why/why not)

(d) Find the conditional density of X2 given X1 = x1

(e) Compute Cov(X1,X2)

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