EXERCISE 8 Suppose X, Y have the joint probability density function given by f(x, y; 0) = ex- , x > 0, y > 0. Consider the i.i.d sample (x1, y₁), (2, Y2),..., (Xn, Yn). Find the marginal pdfs of X and Y and show that X and Y are independent. Find E[X2Y2]. Which theorem from lecture notes do we use for the last question?

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