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Dec 3, 2016 at 21:01 vote accept marcella
Dec 3, 2016 at 21:01 comment added Pat Devlin Well $2n p_0$ is simply the expected number of symbols of type corresponding to $p_0$. The other calculation you could find in a lot of probability books. You want to assume say the thing is uniform over $R$ and see what the answer is (bound each tail probability by something like Chernoff and see what a union bound says). [could have a typo in that second bound; didn't think too hard] If you want tighter control, try a second moment calculation. If you want even tighter control, you have options.
Dec 3, 2016 at 20:57 comment added marcella Is there a proof?
Dec 3, 2016 at 20:53 history answered Pat Devlin CC BY-SA 3.0