Question

A seizure of 348 packets of suspected cocaine have been taken from the bag of a suspect. The drugs examiner has tested ten for cocaine and found it present in nine of the packages.

a.What is the distribution of y, the number of packets testing positive for cocaine? Provide name, formula, and parameters of distribution, explicitly.

b.Let π be the true proportion of packets that are positive for cocaine from the bag. Use a Beta(α = 4, β = 2) prior for π. Find the posterior distribution of π given y. Provide its parameters, explicitly.

c.Summarize the posterior distribution by its first two moments (i.e. mean and variance).

Answer 1