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Suppose we generate a random variable X in the following way. We rst ip a fair coin, say the random variable Y. If the coin

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Suppose we generate a random variable X in the following way. We rst ip a fair coin, say the random variable Y. If the coin is heads, X has a U m f (0, 1) distribution. If the coin in tails, take X to have a U m' f (3, 4) distribution. (a) Find conditional expectation of X given Y. (4 pts) (b) Find the expectation of X. (Hint: Think law of iterative expectations) (5 pts)

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