Overview
(a) ) Derive the form of the NORMALIZED likelihood under this model with respect to ?^2.
(b) The parameter of the Raleigh distribution, ?, represents the scale and is also the mode. From 10 previous replacement measurements, we believe apriori that most engines will required a valve replacement around 6 months (or 24 weeks). The prior mean of the Inverse Gamma distribution and the fact that a0 + 1 is the prior effective sample size to specify values for a0 and b0. Overlay the prior, likelihood, and posterior densities of ?^2 in one figure. Discuss your findings. In particular, discuss how informative the prior appears to be compared to the data. Is the posterior mode closer to the prior mode or the MLE?