论文信息 - An Elementary Analysis of the Probability That a Binomial Random Variable Exceeds Its Expectation

An Elementary Analysis of the Probability That a Binomial Random Variable Exceeds Its Expectation

Abstract We give an elementary proof of the fact that a binomial random variable X with parameters n and 0 . 29 ∕ n ≤ p 1 with probability at least 1 ∕ 4 strictly exceeds its expectation. We also show that for 1 ∕ n ≤ p 1 − 1 ∕ n , X exceeds its expectation by more than one with probability at least 0.0370. Both probabilities approach 1 ∕ 2 when n p and n ( 1 − p ) tend to infinity.

Benjamin Doerr | Benjamin Doerr

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