An engineer plans to build a log cabin in the middle of a forest where logs of similar size are available. He assumes th

[answerhappygod]

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)= (𝑚/𝜆^2)*𝑒^[−(1/2)*(𝑚/𝜆)^2]

where the parameter 𝜆 is the modal value of the distribution.
From previous experience with similar logs, he feels that 𝜆 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 𝜆. 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 𝜆. (b) Derive the distribution of the bending capacity of
the logs 𝑀, using the posterior distribution of 𝜆. (c) What is the
probability that 𝑀 will be less than 2 kip-ft?