There is an urn containing 9 balls, which can be either green or red. Let X...

There is an urn containing 9 balls, which can be either green or red. Let X be the number of red balls in the urn, which is unknown. As a prior, assume that all possible values of X from 0 to 9 are equally likely.

(a) One ball is drawn at random from the urn, and it is red. Compute the Bayes box to give the posterior probability distribution of X. Calculate the posterior mean of X.

(b) Suppose that a second ball is drawn from the urn, without replacing the first, and it is green. Use the posterior distribution of X from part a) as the prior distribution for X and compute the Bayes box and to give the posterior probability distribution of X. Calculate the mean of X.

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