random positions of fixed length

[Jewel Bright <jwlbright@yahoo.com>]

Folks:

 

Sorry for a sort of dumb question. Suppose I have a sequence of random vectors A[N,n] each of length N (say, N=10000). Suppose that n<<N (say, n=100) are ones, and the rest (N-n) are zeros. Positions of "ones" in each of these vectors are random. I want to represent the vectors A[N,n]  as if they are drawn (independently, for simplicity) from some probabilistic distribution. Which distribution is it? Some people say it is binomial. I say that it is not. In binomial, the probability , p, is fixed whereas the number of "successes", n, is not fixed. In my case, n is fixed and known a priori. What is random are the positions of "ones" amongst zeros.

 

So, what is the correct way to present this kind of randomness?

It is probably a statistical textbook question. But I am not a professional statistician, more closer to mathematical biophysics, so simple statistical questions are sometimes difficult to resolve.

 

thanks

 

Jewel   

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