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5. (Casella & Berger, 2nd ed.) A p.d.f. is defined by f(x, y) = C(x +...

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Basic Math

5. (Casella & Berger, 2nd ed.) A p.d.f. is defined by f(x,y) = C(x + 2y) for 0 < y < 1 and 0 < x < 2, and is zerootherwise. a) Find the value of C. b) Are X and Y independent? c)Find the marginal p.d.f of X. d. Find the conditional p.d.ffy|x(y|x). e) Find E[Y |x = 1].

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