Kindly help in answering the questions.

A 0.5 1.0 1.5 (AX) 0.12 0.41 0.17 11.5. In a lot of a bolts produced by a machine, an unknown number p are defective. Assume that p has a prior binomial distribution with parameterp. Find the posterior distribution of p if a bolt chosen at random from the lot is (a) defective; (b) not defective.402 CHAPTER 11 Bayesian Methods 11.87. X is a Poisson random variable with parameter A. An initial sample of size n gives A a gamma posterior distribution with parameters nut + a and p/(1 + np). It is planned to make one further observation on the original population. (a) Find the predictive distribution of this observation. (b) Show that the predict tive mean is the same as the posterior mean.(@), (d), (e). (g). (1): subjective; (b), (J). (K): classical; (c). (f), (h): frequency Prior and posterior distributions 11.2. A box contains two fair coins and two biased coins (each with P("heads") = 0.3). A coin is chosen at ran- dom from the box and tossed four times. If two heads and two tails are obtained, find the posterior prob- abilities of the event F that the chosen coin is fair and the event B that the coin is biased.\fQuestion 2B.51 Explain the transactions costs approach to explaining the external growth of the firm via a merger or strategic alliance. 131