A median of a random variable $X$ is defined as a number $m \in \mathbb{R}$ such that $P(X \leq m) \geq \frac{1}{2}$ and $P(X \geq m) \geq \frac{1}{2}$.
Is it equivalent to say: $m$ is a median of $X$ iff $P(X < m) = P(X > m)$?
Is it true that $m$ is a median of $X$ iff $P(X
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