Proof that binomial function is a probability function?

**Marmy** · December 28th 2011, 12:42 PM

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!

**Plato** · December 28th 2011, 01:06 PM

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, $1 = \left( {p + q} \right)^N = \sum\limits_{k = 0}^N {\binom{N}{k}p^k q^{N - k} }$

**Marmy** · December 28th 2011, 02:26 PM

Thanks!

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