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.

Let $P,R,T$ be integer constants with $PR$ much greater than $T$.

Suppose I flip a coin $PR$ times, each time (independent of other times) getting heads with probability $1/P$. The probability that I get at most $T$ heads is

$$\left(1-\dfrac1P\right)^{PR}+\binom{PR}{1}\left(1-\dfrac1P\right)^{PR-1}\left(\dfrac1P\right)+\ldots+\binom{PR}{T}\left(1-\dfrac1P\right)^{PR-T}\left(\dfrac1P\right)^T$$

What upper bound can we find for this?

In particular, it would be nice to get an upper bound that is independent of $P$, something like $$\binom{aT+R}{R}e^{bR+cT}$$ for some constants $a,b,c$.

share|improve this question
    
cs.anu.edu.au/~bdm/papers/littlewood2.pdf might be useful. –  Stephen Montgomery-Smith Nov 20 '13 at 20:49
    
@StephenMontgomery-Smith I don't see how anything there might be useful. Could you be more specific? –  Kunal Nov 20 '13 at 21:03
    
No, it was just a passing comment. –  Stephen Montgomery-Smith Nov 20 '13 at 21:37

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.