12.4 Reconsider Example 12.2.3 on overdoses among released prisoners. You may find the First Bayes software useful for answering these questions.

a. Use an argument based on α −1 previous successes and β −1 previous failures to calculate a heuristic Beta prior. Combine this prior with the data to give a Beta posterior.

b. Calculate the mean of the posterior. Compare this mean to the investigator’s prior opinion of 1 overdose in 200 subjects (0.005). Considering that there were no overdoses in the data, what is wrong with this posterior?