A radioactive device gives hourly counts which are assumed to have a Poisson distribution with mean A. In ten hours the total count was 23. (a) A scientist chocses a Gamma prior with mean 2.0 and...

Extracted text: A radioactive device gives hourly counts which are assumed to have a Poisson distribution with mean A. In ten hours the total count was 23. (a) A scientist chocses a Gamma prior with mean 2.0 and variance 0.5. Find this prior and show that the resulting posterior has a mean which is a weighted average of the prior mean and the data Imean. (b) Using the loss function 1(t, X) = exp(c(t – )] – c(t – X) – 1 show that the Bayes estimator is i =- - log, Elexp(-cA)] (c) Calculate the Bayes estimate for the scientist's posterior.