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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


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|cite|improve this question 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

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