Moment-generating function of a binomial distribution
= Moment-generating function of a binomial distribution
{title2=$M_X(t)=(1-p+pe^t)^n$}
For a <binomial distribution> with parameters $n$ and $p$, the <binomial theorem> gives the displayed <moment-generating function>, finite for every real $t$. Products of these <moment-generating functions> show that the sum of <independent> <binomial random variables> with the same success <probability> again has a <binomial distribution>, with trial counts added.