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Summation with combinations

  • #1
210
1

Homework Statement



I'm trying to derive the PGF for the Binomial.


The Attempt at a Solution



I have it whittled down to [itex]\sum^{n}_{x=0}(nCx)(\frac{sp}{1-p})^x[/itex]

I just don't know how to simplify this further. Any help is most appreciated.
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
I think you lost some ##(1 - p)##s there, are you sure you didn't mean ##\sum_{x = 0}^n \binom{n}{x} (sp)^x (1 - p)^{n - x}##?

The result should follow from the binomial theorem,
$$ (x + y )^n = \sum_{k = 0}^n \binom{n}{k} x^{n-k} y^k. $$
 

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