Problem 26. A bank granted a credit to 62 firms in the construction business and to 45 firms in the waste management business. Among these firms, 5 firms in the construction business and 6 firms in the waste management business defaulted.
1. Formulate a suitable probability model for these data and derive the joint posterior distribution for the risk of default in each business area.
2. Is the risk of default the same for both business areas or is it different? Use a simulation-based approach to determine the posterior density of the relative difference δ in the default risk in both sectors. Estimate the posterior mean and determine a 95%-credibility interval for δ from the posterior draws.
