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Let X and Y have the joint p.d.f. f(x, y) = 1I(|x^2−y^2|<1). Then, (a) Find the...

Let X and Y have the joint p.d.f. f(x, y) = 1I(|x^2−y^2|<1). Then,

(a) Find the marginal distributions of X and Y respectively.

(b) Obtain the conditional distribution of Y given X=x,for 0< x <1.

(c) Find the mean and variance of X only.

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