## find the expected number

Assume that Y denotes the number of bacteria per cubic centimetre in a particular liquid and that Y has a Poisson distribution with parameter $\lambda$ . Further assume that $\lambda$ varies from location to location according to a gamma distribution with parameters $\alpha$ and $\beta$ , where $\alpha$ 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?