Abstract
The distribution of the number of successes in $n$ independent trials is "bell-shaped". The expected number of successes, $\mu$ say, either determines the most probable number of successes uniquely or restricts it to the pair of integers nearest to $\mu$.
Citation
J. N. Darroch. "On the Distribution of the Number of Successes in Independent Trials." Ann. Math. Statist. 35 (3) 1317 - 1321, September, 1964. https://doi.org/10.1214/aoms/1177703287
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