If $$P(|X-M|) >t ) \leq a\exp(\frac{-t^2}{b})$$ how can I show that absolute value of the median and expectation is bounded by
$$|M – EX| \leq \min \Big(\sqrt(ab), \frac{a\sqrt(b\pi)}{2}\Big)$$ where $M$ is the median and $t > 0$ and $a,b$ are positive constants.