(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Poisson distribution questions

**Physics Forums | Science Articles, Homework Help, Discussion**