How Can Binomial Distribution Be Solved Without Using a Computer Program?

[swede]

Hi!

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

http://www.itl.nist.gov/div898/handbook/prc/section2/gifs/pueq.gif

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

regards
swede

 

[Dale]

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 into the quadratic equation or its equivalent.

-Dale

 

[Tide]

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.