- #1
eprparadox
- 138
- 2
Homework Statement
Show that the expected number of successes in n Bernoulli trials w probability p of success is <x> = np
Homework Equations
The Attempt at a Solution
So I get the right answer which is this: [tex]E\left( x\right) =\sum _{x=0}^{n}x\left( \begin{matrix} n\\ x\end{matrix} \right) p^{x}\left( 1-p\right) ^{n-x}[/tex]
I know it's right, though, because I inputted it into wolframalpha and get <x> = np.
My question is how do I try to sum this by hand. I really have no idea where to start and I'm curious as to how this is done. Do I maybe use Stirling's formula to simplify the C(n, x)?