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## Homework Statement

Hey guys, I'm self studying some probability theory and I'm stuck with the basics.

I must find the characteristic function (also the moments and the cumulants) of the binomial "variable" with parameters n and p.

I checked out wikipedia's article http://en.wikipedia.org/wiki/Characteristic_function_(probability_theory), apparently the solution is [itex](1-p+pe^{it})^n[/itex] though I didn't really understand what t stand for (number of successes?).

## Homework Equations

Characteristic function: [itex]\int e^{ikX} P(x)dx[/itex].

## The Attempt at a Solution

I'm guessing that I must simply apply the given formula. The k would be wikipedia's t variable. I'm stuck at finding P(x) and X. I've searched and found out the binomial distribution's article in wikipedia and [itex]P(K=k)=\frac{n!p^k (1-p)^{n-k}}{k!(n-k)!}[/itex] which is called the probability mass function. I don't know how how I could "plug" this into the given formula.

Thanks for any tip.