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7. (8 points) Suppose that the time in minutes required to serve a customer has an exponential distribution for which the value of the parameter

7. (8 points) Suppose that the time in minutes required to serve a customer has an exponential distribution for which the value of the parameter 6 is unknown and that the prior distribution of 6 is a gamma distribution with mean 0.2 and the variance 1. If the average time required to serve a random sample of 20 customers is observed to be 2 minutes, what is the posterior distribution of 0

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