Bayesian Genetic Mutant Cdc-
1. Assume that in the context of problem
2. Genetic Mutant Cdc-1, researchers postulated Poi(λ) distribution for X2 - the count of cell colonies containing cdc-1 mutants. Experts suggest a gamma prior on λ with the expectation equal to 55 and variance of 220.
(a) Specify fully this gamma prior, that is, find its parameters.
(b) An experiment yielded X2 = 60. Find the posterior distribution for λ using the prior from (a). What is the Bayes' estimator of λ?
(c) Run a WinBUGS program for (b) and check the output. Do you get an estimator for λ close to that in (b)? What is a 95% credible set for λ that WinBUGS outputs?