## Upper Bound of the Variance When a Random Variable is Bounded

## Problem 753

Let $c$ be a fixed positive number. Let $X$ be a random variable that takes values only between $0$ and $c$. This implies the probability $P(0 \leq X \leq c) = 1$. Then prove the next inequality about the variance $V(X)$.

\[V(X) \leq \frac{c^2}{4}.\]