Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Hypergeometric? No! But how close?
Posted:
Jun 18, 1996 9:01 AM
|
|
"Bingo" lottery. Players chose a=20 numbers from N=75 numbers,
after some rules that are not of consern here. Approx 20% of the
8 10^17 { N \choose a } subsets are legal. There are many players, 10^6.
Numbers are drawn from the N. A "winner" is one player that has all
his a=20 numbers among the drawn ones.
One can consider the hypergeometric probability for x "winners".
hyp(x; s, m, t) = {{m \choose x } { s - m \choose t - x}} \over { s \choose t}
where s = { N \choose a}, m the players, t = {n \choose a}.
In a correct drawing process of hypergeometric sample, every element,
i.e {n \choose a }, in the sample is drawn "random" (with removing).
In the drawing process above one draws n numbers, and consider
the big set of all {n \choose a } subsets. The "randomness" is
limited, compared with a correct hypergeometric sample.
The problem: When is hyp(x; s, m, t) a good approximation to the
probability of x winners? How good? (It is very good when n=N)!
- bjoern
|
|
|
|
