Refer back to Exercise 4.
a. Calculate the Bayes estimate of the probability p.
b. Calculate and interpret a 95% credible interval for p.

Data from in Exercise 4

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At children's party, kids toss ping-pong balls into the swimming pool hoping to land inside a plastic ring (picture a small hula hoop). Let p denote the probability of successfully tossing a ball into the ring, which we will assign a Beta(1, 3) prior distribution. The variable X = number of tosses required to get 5 balls in the ring (at which point the child wins a prize) will be observed for a sample of children.