# Proof that binomial function is a probability function?

• December 28th 2011, 01:42 PM
Marmy
Proof that binomial function is a probability function?
How can I prove that the binomial function is a probability function?

I attached the solution I got from my slides...but I dont understand the 2nd part!

Thanks for your help!
• December 28th 2011, 02:06 PM
Plato
Re: Proof that binomial function is a probability function?
Quote:

Originally Posted by Marmy
How can I prove that the binomial function is a probability function?
I attached the solution I got from my slides...but I dont understand the 2nd part!

The binomial probability is $P(X=k)=\binom{N}{k}p^kq^{N-k}$ where $q=1-p$

Thus, $1 = \left( {p + q} \right)^N = \sum\limits_{k = 0}^N {\binom{N}{k}p^k q^{N - k} }$
• December 28th 2011, 03:26 PM
Marmy
Re: Proof that binomial function is a probability function?
Thanks!