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## Homework Statement

X is a discrete random variable that has a Poisson Distribution with parameter L. Hence, the discrete mass function is [tex]f(x)[/tex] = [tex]L^{x} e^{-L} / x![/tex].

Where L is a real constant, e is the exponential symbol and x! is x factorial.

Without using generating functions, what is [tex]E(X^{3})[/tex]? (the 3rd moment)

## Homework Equations

N.A.

## The Attempt at a Solution

[tex]E(X^{3})[/tex] = [tex]\Sigma x^{3} L^{x} e^{-L} / x![/tex] from the definition of Expectation. Sigma is summation over all x values.

I think I am suppose to rearrange all the terms in order to get something of the form "{summation that sums to 1} times {answer}" but I totally lost regarding what I should be manipulating the terms into. Or maybe this is the wrong approach?

A little nudging would go a long way...and please don't give me the answer outright! Thanks in advance! :)