Let $X$ be a random variable. Is there a way to bound the probability that $|X|$ is large in terms of $\Bbb{E}(X^{4})$?
2026-04-12 22:46:26.1776033986
Bounding a random variable $X$ by $\Bbb{E}(X^4)$
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According to Markov's inequality (extended version), for any $a > 0$ we have:
$$\Bbb{P}(|X| \ge a) \le \dfrac{\Bbb{E}(X^4)}{a^4}$$
Hope it helps.