I think you can justify it by approximating each category as an independent Poisson distribution. Then for each such processes the variance equals the mean. So once you have 10 successes in a bin, you have evidence of a probably good estimate for the arrival rate of that category. The book "The Probabilistic Method" calls a related idea "the Poisson paradigm."
(10 a nice round number where the standard deviation is below the mean)
I think you can justify it by approximating each category as an independent Poisson distribution. Then for each such processes the variance equals the mean. So once you have 10 successes in a bin, you have evidence of a probably good estimate for the arrival rate of that category. The book "The Probabilistic Method" calls a related idea "the Poisson paradigm."
(10 a nice round number where the standard deviation is below the mean)