- #1

- 1,015

- 1

## Main Question or Discussion Point

Hello!

Is there a closed form expression or a good estimate for the probability that a binomial distribution yield the average np or less. Basically I'm asking for a good way to evaluate

[tex]

P=\sum_{k=0}^{np} \begin{pmatrix} n\\ k

\end{pmatrix} p^k(1-p)^{n-k}

[/tex]

I just figured that for the simplified case [itex]p=\frac{1}{n}[/itex] this probability converges to 63% for large n. What about more general cases?

Is there a closed form expression or a good estimate for the probability that a binomial distribution yield the average np or less. Basically I'm asking for a good way to evaluate

[tex]

P=\sum_{k=0}^{np} \begin{pmatrix} n\\ k

\end{pmatrix} p^k(1-p)^{n-k}

[/tex]

I just figured that for the simplified case [itex]p=\frac{1}{n}[/itex] this probability converges to 63% for large n. What about more general cases?

Last edited: