Construct another (discrete) prior distribution for the proportion of brown or orange M& Ms, . Use the same values of given in Table 11.8

Construct another (discrete) prior distribution for the proportion of brown or orange M& M’s, π. Use the same values of π given in Table 11.8 but use different probabilities, p(π), so that the mean is the same but the variance is larger. Then based on this new prior and using your M&M’s data or the MyMMs data, answer the following:
a. Compute the posterior distribution for π, as well as its mean and variance.
b. Compare the values of the posterior mean and variance to those calculated in Exercise 1. Is the change between the prior and posterior estimate of π more or less than the change between the prior and posterior estimate of π that you observed in Exercise 1? How did changing the variance of the prior distribution, but not the mean, affect the posterior mean and variance?