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?



Answer :
The posterior density is 3θ^2

b)The posterior mean is 3/4

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