- #1
silentone
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Homework Statement
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)]
Homework Equations
f_x (x) = exp(-lamda) (lamda)^x/x! for x=0,1,2,3...
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.