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$\begingroup$

I saw some result that some article used, (without proving) that stated:$$\int_0^1 p^k (1-p)^{n-k} \mathrm{d}p = \frac{k!(n-k)!}{(n+1)!}$$

But I was wondering, how would you integrate it? How did this integral come about? Is it something to do with the binomial distribution?

  • 3
    [Beta function](http://en.wikipedia.org/wiki/Beta_function)2012-03-19
  • 1
    see too [Weisstein's derivation](http://mathworld.wolfram.com/BetaFunction.html)2012-03-19
  • 0
    Ahh okay, thanks for the heads up! :)2012-03-20

4 Answers 4