  Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$.
Chv\'{a}tal's theorem says that for any fixed $n\geq 2$, as $m$ ranges over
$\{0,\ldots,n\}$, the probability $q_m:=P(B(n,m/n)\leq m)$ is the smallest when
$m$ is closest to $\frac{2n}{3}$. Motivated by this theorem, we consider the
minimum value problem on the probability that a random variable is at most its
expectation, when its distribution is the Weibull distribution or the Pareto
distribution in this note.
