The number of customers arriving during a one-hour period at an ice cream shop is modeled by a Poisson distribution with unknown parameter μ. Based on past experience, the owner believes that the average number of customers in one hour is about 15.
a. Assign a prior to μ from the gamma family of distributions, such that the mean of the prior is 15 and the standard deviation is 5 (reflecting moderate uncertainty). 15.1 Prior and Posterior Distributions 895 

b. The number of customers in ten randomly selected one-hour intervals is recorded:

Determine the posterior distribution of μ.

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