In a toy manufacturing company, parts of the toys are produced by a plastic molding machine...

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In a toy manufacturing company, parts of the toys are produced by a plastic molding machine with a success rate of 0. After a batch of molding of size K, L many parts are faulty, and the remaining K - L many parts are successfully produced. (a) We believe that there are two types of molding machines and put our prior knowledge as follows: (0.5, 0 = 0.4 (0.5, 0=0.6 p(0) = Given the prior, find the MAP estimate of the parameter in terms of K and L. (b) We can model the prior knowledge with Beta distribution p(0) = Beta(0; a, 3). Find the MAP estimator Ô with this prior. (c) Explain why we consider Beta distribution as conjugate prior for the likelihood function in this problem. In a toy manufacturing company, parts of the toys are produced by a plastic molding machine with a success rate of 0. After a batch of molding of size K, L many parts are faulty, and the remaining K - L many parts are successfully produced. (a) We believe that there are two types of molding machines and put our prior knowledge as follows: (0.5, 0 = 0.4 (0.5, 0=0.6 p(0) = Given the prior, find the MAP estimate of the parameter in terms of K and L. (b) We can model the prior knowledge with Beta distribution p(0) = Beta(0; a, 3). Find the MAP estimator Ô with this prior. (c) Explain why we consider Beta distribution as conjugate prior for the likelihood function in this problem.