Let $X$ be a random variable which follows normal distribution. Is True that
$Pr[|X|\leq \epsilon] \leq \epsilon$ for all $\epsilon \geq 0$.
2026-05-05 16:40:01.1777999201
Normal distribution bound
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For the case $\epsilon\geq 0.5$ it's obvious that the strict inequality will hold (if X is standard normal). So you should actually show $P \Big[|X|\leq\epsilon\Big]\leq \epsilon$, for all $\epsilon<0.5$ .