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2. An engineer plans to build a log cabin in the middle of a forest Where logs of similar size are available. He assumes that the bending capacity M of each log follows Rayleigh distribution fM (m) = g e_(%)(%)2 where the parameter A is the modal value of the distribution. From previous experience with similar logs, he feels that ,1 would be 4 (kip-ft) with probability 0.4 or 5 (kip-ft) with probability 0.6. Not entirely satisfied with these subjective probabilities, he decides to get a better measure of the parameter A. Being pressed for time and with limited supply of logs, he can only afford to test the bending capacity of two logs by a simple load test on the site. The test results yielded 4.5 kip-ft and 5.2 kip-ft for the two tests. (a) Determine the posterior distribution (discrete) for the parameter 2L. (b) Derive the distribution of the bending capacity of the logs M , using the posterior distribution of A. (c) What is the probability that M will be less than 2 kip-ft