Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If I uniformly sample-without-replacement a small bunch of multicolored balls (say, five colors) from one urn into a "smaller" urn, will the distribution of ball colors in the smaller urn be the same as the true distribution of ball colors in the larger urn, within some interval?

share|improve this question
2  
For certain? Only if the interval is large enough to include every possible sample, no matter how unrepresentative. The sample size $n$ is also relevant: you can’t get a very representative sample if $n$ is just $1$ or $2$, say. –  Brian M. Scott Oct 28 '11 at 23:29
    
Let's say I have a population of 10M balls. I close my eyes and pull out 5% of them from this very large urn, which is 500K balls. Can I expect that the 5% subset I pulled out has roughly the same distribution of colors as the larger population? –  Alex Reynolds Oct 28 '11 at 23:33
    
Yes; you just can’t guarantee it. –  Brian M. Scott Oct 28 '11 at 23:56
1  
Yes, for appropriate definitions of "expect" and "roughly the same". –  mhum Oct 29 '11 at 0:31
    
Which would be...? –  Alex Reynolds Oct 29 '11 at 1:49

1 Answer 1

Taking your example "I have a population of 10M balls. I close my eyes and pull out 5% of them from this very large urn, which is 500K balls" then for any colour which has a fraction $k$ of the balls in the big urn will with probability greater than 99.5% have a fraction in the small urn in the range $[k-0.001,k+0.001]$.

If $k$ is very small or very large then the range can be narrowed or the probability increased, but any answer will be of this type.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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