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.

In the classic Coupon Collector's problem, it is well known that the time $T$ necessary to complete a set of $n$ randomly-picked coupons satisfies $E[T] \sim n \ln n $,$Var(T) \sim n^2$, and $\Pr(T > n \ln n + cn) < e^{-c}$.

This upper bound is better than the one given by the Chebyshev inequality, which would be roughly $1/c^2$.

My question is: is there a corresponding better-than-Chebyshev lower bound for $T$? (e.g., something like $\Pr(T < n \ln n - cn) < e^{-c}$ ) ?

share|improve this question
    
David, this might be an appropriate question for Math Overflow. If you don't get an answer here in a day or two, you might want to try there. –  Mike Spivey Mar 2 '11 at 16:16
    

1 Answer 1

The question was asked and answered at stats.SE: see http://stats.stackexchange.com/q/7774/. I am posting this just so that the question does not remain unanswered.

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.