An automobile piston manufacturing company has two plants in North America.

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1. An automobile piston manufacturing company has two plants in North America. Plant A produces pistons of which 2% are defective, while plant B produces about 10% defective pistons. An automobile manufacturer receives 60% of the pistons from plant A and 40% from plant B. They inspect the pistons before assembly. Answer the following questions.

1. Postulate Beta prior distributions for the defective rate for the two plants: plant A: p~ Beta (co, Bo) and plant B: p~ Beta (a1, B1). Assume ao + Boα1 + 1 = 100.

2. During inspection of 200 pistons by the automobile manufacturer, 15 pistons are found to be defective. Find the posterior distribution of the defective rate (p).

3. Find the 95% equi-tailed credible interval for p.

4. Find the 95% HPD credible set for p.

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