You are going to take a random sample of voters in a city in order to estimate the proportion π who support stopping the fluoridation of the municipal water supply. Before you analyze the data, you need a prior distribution for π. You decide that your prior mean is .4, and your prior standard deviation is .1.

(a) Determine the beta

(a,

b) prior that matches your prior belief.

(b) What is the equivalent sample size of your prior?

(c) Out of the 100 city voters polled, y = 21 support the removal of fluoridation from the municipal water supply. Determine your posterior distribution.