Suppose n, cities were sampled and for each cit}:r i the number 95: of deaths from ALS were recorded for a period of one year. We expect the numbers to be Poisson distributed, but the size of the city is a factor. Let Mi be the known population for cit},F z' (in thousands of people] and let yg I 3 lid Pois(0M;-_), 1': 1,... ,n, where I9 2: 0 is an unknown parameter measuring the common death rate per 1000 people for all cities. Given 9, the expected number of ALS deaths for city 2' is 9311;, so 3 is ex pected to be small. Assume that independent scientic information can be obtained about 9 in the form of a gamma distribution, say Gamma (oz, ,8). Show that the posterior distribu tion for 9 I m, ..., y\" is a Gamma distribution in this case, and nd the value of its parameters