1. Find and plot the posterior distribution for a binomial likelihood with x = 5 successes out of n = 10 trials using at least three different beta prior distributions. Does the prior make a large difference in the outcome— when?
5. Find and plot the posterior distribution for a normal distribution likelihood with a sample mean ¯x = 100 and variance var(x) = 144 (assume n = 169) using at least three different normal priors for the mean. When does the prior make the largest difference in the outcome—when the prior mean varies substantially from the sample mean, or when the prior variance is small or large?