If the independent random variables X and Y have the marginal densities f(x) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 1 2 for 0 < x < 2 0 elsewhere π(y) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 1 3 for 0 < y < 3 0 elsewhere find (a) the joint probability density of X and Y; (b) the value of P(X2 + Y2 > 1).

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