Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: Hypergeometric? No! But how close?
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Bj|rn Elstad

Posts: 2
Registered: 12/12/04
Hypergeometric? No! But how close?
Posted: Jun 18, 1996 9:01 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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











Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.