Let Y have a discrete uniform distribution on the integers 1, 2, 3. That is 1 P(Y= 1) = P(Y = 2) = P(Y = 3) : 3 Given Y = y, the random variable X has conditional pdf f(x) = (y + 1)r", where 0 < x < 1. Compute the conditional expectation E(XY = y). Use the double expectation formula to show that E(X) = )= HINT: The double expectaton formula is E[E(XY)] = E(X). 133 180

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