Applied Bayesian Statistics Cowles

5.4 A new employee of the trucking firm wishes to learn about the breakdown rate. She does not have the previous information available to the president, so she wishes to assign a noninformative prior density.

1. Derive the Jeffreys prior that goes with the Poisson likelihood.

2. Compute the resulting posterior distribution using this prior and the data given earlier for the 5 days.

3. Find the posterior mean and 95% central credible set for this posterior.