For a binomial random variable $\xi$ with parameters $n$ and $b∕n$, it is well known that the median equals $b$ when $b$ is an integer. In 1968, Jogdeo and Samuels studied the behaviour of the relative difference between $\mathsf{P}(\xi =b)$ and $1∕2-\mathsf{P}(\xi <b)$. They proved its monotonicity in $n$ and posed a question about its monotonicity in $b$. This question is motivated by the solved problem proposed by Ramanujan in 1911 on the monotonicity of the same quantity but for a Poisson random variable with an integer parameter $b$. In the paper, we answer this question and introduce a simple way to analyse the monotonicity of similar functions.

对于二项式随机变量 $\xi$ 带参数 $ñ$ 和 $b∕ñ$，众所周知，中位数等于 $b$ 什么时候 $b$是一个整数。1968年，Jogdeo和Samuels研究了行为之间的相对差异$\mathsf{P}（\xi =b）$ 和 $\mathrm{1个}∕\mathrm{2个}-\mathsf{P}（\xi <b）$。他们证明了它的单调性$ñ$ 并提出了一个关于它的单调性的问题 $b$。这个问题是由Ramanujan在1911年提出的关于相同数量的单调性但具有整数参数的Poisson随机变量的已解决问题引起的$b$。在本文中，我们回答了这个问题，并介绍了一种简单的方法来分析相似函数的单调性。