Question: Question 4 [20 marks] (a) Given that X and Y are continuous random variables, show that (i) E[E[XIY]] = E(X) (ii) E[Var (X|Y)] + Var

Question 4 [20 marks] (a) Given that X and Y are continuous random variables, show that (i) E[E[XIY]] = E(X) (ii) E[Var (X|Y)] + Var [E(X|Y)] = Var(X) [10 marks] (b) Given: X - N ( 1, 0' ) and Mx (t ) = ett+=0212 X = logY Find expressions for E(Y) and Var(Y). [10 marks]

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