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Let the unknown probability that a basketball player makes

Question: Let the unknown probability that a basketball player makes a shot successfully be θ. Suppose your prior on θ is uniform on [0, 1] and that she then makes two shots in a row. Assume that the outcomes of the two shots are independent.

a. What is the posterior density of θ?

b. What would you estimate the probability that she makes a third shot to be?

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