Assume that Y denotes the number of bacteria per cubic centimetre in a particular liquid and that Y has a Poisson distribution with parameter $\displaystyle \lambda$ . Further assume that $\displaystyle \lambda$ varies from location to location according to a gamma distribution with parameters $\displaystyle \alpha$ and $\displaystyle \beta$ , where $\displaystyle \alpha $ is a positive integer. If we randomly select a location, what is the

(A) expected number of bacteria per cubic centimetre?

(B) standard deviation of the number of bacteria per cubic centimetre?