# Math Help - Cumulative distribution function of binomial distribution

1. ## Cumulative distribution function of binomial distribution

Hello,

Looking to find the following analytically:

$P(p \le 0.5) = \frac{\int_{0}^{0.5}p^{550}(1-p)^{450}\, dp}{\int_{0}^{1}p^{550}(1-p)^{450}\, dp}$

Note that I've taken away the binomial coefficients on both numerator and denominator because they are the same and cancel out.

Anyone?

Thanks

2. Originally Posted by Tornam
Hello,

Looking to find the following analytically:

$P(p \le 0.5) = \frac{\int_{0}^{0.5}p^{550}(1-p)^{450}\, dp}{\int_{0}^{1}p^{550}(1-p)^{450}\, dp}$

Note that I've taken away the binomial coefficients on both numerator and denominator because they are the same and cancel out.

Anyone?

Thanks
Read this: Beta Integral -- from Wolfram MathWorld

To recognise the top integral in this way you should first make the substitution t = 2p.

3. Fantastic thank you!