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3) Let X and Y be independent uniform [0, 1] random variables. a) Find the joint pdf of X and XY and also the conditional

3) Let X and Y be independent uniform [0, 1] random variables. a) Find the joint pdf of X and XY and also the conditional pdf of X given XY. [7 points] b) Compute E[X |XY]. [3 points] [Note: Please do not use 'approximation' type definitions P(x

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