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Sample without replacement from finite population?
Suppose we sample without replacement from an urn with 8 marbles, one of which is marked. What is the expected number of trials to draw the marked marble?
This seems to come from the negative hypergeometric distribution with N=8, M=1, and m=1. So the expected value would be m(N-M)/(M+1) = 7/2, but this seems a little counter-intuitive. I would have expected the answer to be 4.
1 Answer
- Awms ALv 710 years agoFavorite Answer
It's 9/2.
You don't need the hypergeometric, nor do you even need the geometric. I believe both of these require the sampling to be done with replacement, anyway. Instead, you just need basic counting.
Draw all 8 marbles and write down the position (1-8) of the marked marble. By symmetry, each position is equally likely, so we're actually dealing with a uniform distribution. That is, the expected value is the average of the numbers 1-8.
Therefore 9/2.
