Consider a binomial random variable x given by (2.9), with prior distribution for u given by the beta distribution (2.13), and suppose we have observed m occurrences of x = 1 and l occurrences of x = 0. show that the posterior mean value of x lies between the prior mean and the maximum likelihood estimate for u. to do this, show that the posterior mean can be written as lambda times the prior mean plus (1 - lambda) times the maximum likelihood estimate, where 0 < = lambda < = 1. this illustrates the concept of the posterior distribution being a compromise between the prior distribution and the maximum likelihood solution