论文标题
关于二项式变量的可能性最多是其期望
On the probability that a binomial variable is at most its expectation
论文作者
论文摘要
考虑到具有整数期望$ m $的二项式随机变量bi $（n，m/n）$的可能性最多是其期望的。 Chvátal推测，对于任何给定的$ N $，当$ M $是最接近$ 2N/3 $的整数时，此概率是最小的。我们表明，当$ n $很大时，这会成立。
Consider the probability that a binomial random variable Bi$(n,m/n)$ with integer expectation $m$ is at most its expectation. Chvátal conjectured that for any given $n$, this probability is smallest when $m$ is the integer closest to $2n/3$. We show that this holds when $n$ is large.
