You are going to take a random sample of voters in a city in order to estimate the proportion who support stopping the uoridation of the municipal water supply. Before you analyze the data, you need a prior distribution for . 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 \(\mathrm{u}-\) oridation from the municipal water supply. Determine your posterior distribution.