conjugate distributions

The percentage p ofdel'ective items in a large from the lot and are tested. defective ( lot is to be estimated. Items are randomly selected The outcome from the test is an indication of whether the item is . when it fails the 1951) or not (when it passes the test). However, the test proceduc'ii'eg'hs;e imperfect such that there is 0.06 probability that a truly defective item Will pass the test an is 0'04 probability that a truly non-defective item will fail the test. - - - . E ress this a) Determine the probability that a randomly selected item Will fail the test xp probability as a function ofp. - ' ssumin no pt'iOr b) Suppose three items are tested of which two pass and one fails. A g - - - ' its mean and information is available, determine the posterior distribution of]? and standard deviation. ' ' ' xt item to be c) Using the posterior distribution ofp, determme the probability that the nc tested will fail. Fully account for the uncertainty in p