A large shipment of parts is received, out of which five are tested for defects. Past experience with the supplier leads you to place a beta(1,9) prior on the part defect rate. Suppose no defects are...

Extracted text: A large shipment of parts is received, out of which five are tested for defects. Past experience with the supplier leads you to place a beta(1,9) prior on the part defect rate. Suppose no defects are observed in the five tested from the shipment. Give the posterior distribution on the defect rate, the MAP estimate of the defect rate, the Bayes estimate (LMS) of the defect rate, and the 95% HDI.