Suppose that the number of defects in a 1200-foot roll of magnetic recording tape has a Poisson distribution for which the value of the mean 0 is unknown, and that the prior distribution of 0 is a gamma distribution with parameters ex = 3 and f3 = 1. When five rolls of this tape are selected at random and inspected, the numbers of defects found on the col1s are 2, 2, 6, 0, and 3. If the squared error loss function is used, what is the Bayes estimate of 8? (See Exercise 4 of Sec. 6.3.)