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Homework Help: Solve binomial distribution

  1. Jan 10, 2006 #1

    Does someone know how to solve this equation (see the link) if all variables are known without P_U (without using a computer program)?


    Can it be done in some easy way? I have read courses in calculus at the university, altough it was several years ago :(

  2. jcsd
  3. Jan 10, 2006 #2


    Staff: Mentor

    I don't think there is a general closed-form solution. You can easily see that this is a N-th order polynomial in P_U. So there will only be a closed form solution up to N=4. For N=4 (or less) I would recommend simply expanding it and plugging it in to the quadratic equation or its equivalent.

  4. Jan 10, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper

    When N is large, the sum has a maximum at N = p (use Stirling's approximation to see this) and you can approximate the sum with a gaussian function. This will allow you to find approximate solutions.
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