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is selected randomly from a X. Now select an integer Y uniformly at random from f1,... ,X). Find: (a) E(Y) (b) E(Y2); (c) Var(Y); (d) P(X Y 3)

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a) E(Y); Solution: Using the double expectation formula: E(Y)- E(E(Y|X)). Note that Y|X is distributed uniformly on (1 . . .

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