1. A11 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 N Betamo, 5'30) and plant B: p N Betaloq, 3:31). Assume a0 + 3130 : 041 + 531 : 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% equitailed credible interval for p. 4. Find the 95% HPD credible set for p