# Cumulative distribution function of binomial distribution

• Oct 31st 2008, 07:13 AM
Tornam
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 :)
• Oct 31st 2008, 02:08 PM
mr fantastic
Quote:

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.
• Oct 31st 2008, 04:34 PM
Tornam
Fantastic thank you!