# Characteristic equation of binomial random variable

## Homework Statement

find the characteristic equation of a binomial variable with pmf p(x) =$$\frac{n!}{(n-k)!k!}$$*p$$^{k}$$*(1-p)$$^{n-k}$$

## Homework Equations

characteristic equation
I(t) = $$\sum$$p(x)*e$$^{tk}$$

## The Attempt at a Solution

I(t) = $$\sum$$$$\frac{n!}{(n-k)!k!}$$*(p$$^{k}$$*(1-p)$$^{-k}$$*e$$^{tk}$$)*(1-p)$$^{n}$$

i am stuck on this series because i dont know what to do with the combination term.

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LCKurtz
$$E(tX) = \sum_{k-0}^{n}\binom n k e^{tk}p^k(1-p)^{n-k}$$