Suppose another 5 independent trials of the experiment are performed and \(Y_{2}=2\) successes are observed. Use the posterior distribution for from Exercise 6.4 as the prior distribution for . Find the new posterior distribution by filling in the simplified table.

Data From Exercise 6.4

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Let Y be the number of successes in n = 10 independent trials where each trial results in a success or failure, and, the probability of success, remains constant over all trials. Suppose the 4 possible values of are .20, .40, .60, and .80. We do not wish to favor any value over the others so we make them equally likely. We observe Y = 7. Find the posterior distribution by lling in the simpli ed table. prior likelihood prior likelihood posterior marginal P(Y = 7)