Another hierarchical model
Having some trouble with a hierarchical model. Can someone please check my first answer and help me to get on with the b-assignment?
Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and that Y has a Poisson distribution with parameter . Further assume that varies from location to location and has a gamma distribution w. parameters and , where is a positive integer. If we randomly select a location, what is the:
a) Expected number of bacteria per cubic centimeter?
That would mean that we're looking for
since Y given \lambda means that Y also follows the Gamma distribution, we get
since this is a constant we receive
b) standard deviation of the number of bacteria per cubic centimeter?
but how do I calculate this? I get confused by all those parenthesis.
Thanks for your help.