Question: Exercise 3.4 Show that in the binomial case, the posterior mean is a weighted average of the prior mean and the MLE. Exercise 3.5 Show

Exercise 3.4 Show that in the binomial case, the posterior mean is a weighted average of the prior mean and the MLE. Exercise 3.5 Show that in the binomial case, the variance of the posterior distribution might be in some situations larger than that of the prior distribution, see also Pham-Gia (2004) for a general result in this context.

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