The number of patients, x, arriving at a hospitals emergency room in a night has a Poisson distribution with expected value . Over the last

The number of patients, x, arriving at a hospital’s emergency room in a night has a Poisson distribution with expected value λ. Over the last three
nights there were 20, 26, 25 patients. A log-uniform prior is assumed for λ.
(a) Find the posterior density for λ.

(b) Write the R-code computing the posterior probability that there are more than 27 patients on average.

(c) How many patients are expected in a night for the next two days given data?

(d) Over the next two nights, total 52 patients came and now five records are available. Update the density for λ given the record of five nights.