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

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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 \(G i\) ardia cysts?

(b) Let 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 . Find the posterior distribution of given \(y\).

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

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

(e) Calculate a \(95 \%\) credible interval for using the normal approximation found in part (d).

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