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Math Help - Cumulative distribution function of binomial distribution

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Tornam View Post
    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.
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  3. #3
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    Fantastic thank you!
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