2
$\begingroup$

After some heavy reordering and canceling of factorials, I discovered that the following experiment is approximately equivalent for $m \ll n < N$ if conducted with or without replacement:

In $n$ turns, draw marbles (with/without replacement) from an urn containing $m$ white and $N-m$ black marbles. Count the white marbles.

Now, the "with replacement" part is a Bernoulli trial:

Throw $m$ times an unfair coin with success probability $n/N$. Count the number of successes.

Are there any pitfalls in this approximation?

I am pretty sure that this is textbook knowledge. Can you recommend a good book where this approximation is derived?

I did the exercise in order to Derive househould weights from a uniformly distributed person sample.

$\endgroup$
  • 1
    $\begingroup$ Your first example us the hypergeometric distribution, while the second one is the binomial distribution. This approximation is quite common and works well for large N. $\endgroup$ – MånsT Apr 10 '12 at 14:01
1
$\begingroup$

Partially answered in comments:

Your first example us the hypergeometric distribution, while the second one is the binomial distribution. This approximation is quite common and works well for large N. – MånsT See also Binomial Approximation to Hypergeometric Probability

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.