1. The problem statement, all variables and given/known data Suppose x has a Poisson [itex]\lambda[/itex] distribution Find the probability generating function and range it is well defined. Then evaluate E[x(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)(x-7)(x-7)(X-8)(x-9)(x-10)(x-11)] 2. Relevant equations f_x (x) = exp(-lamda) (lamda)^x/x! for x=0,1,2,3.... 3. The attempt at a solution The probability generating function I got easily by using the exponential power series and got p_x (s) = exp(lamda(s-1)) . It is well defined for s real. I do not know how to approach the expected value.