The same study found that y = 6 out of n = 87 samples within municipal catchments contained Giardia cysts.

(a) What is the distribution of y, the number of samples containing Giardia cysts?

(b) Let π be the true probability that a one-liter water sample from a site within a municipal catchment contains Giardia cysts. Use a beta (1, 4)

prior for π. Find the posterior distribution of π given y.

(c) Summarize the posterior distribution by its first two moments.

(d) Find the normal approximation to the posterior distribution g(π|y).

(e) Calculate a 95% credible interval for π using the normal approximation in part (c).