Probability MT22, Chebyshev's inequality
Flashcards
What does Chebyshev’s inequality state about a r.v. $Z$ with finite variance?
\[\forall c>0, \text{ } \mathbb{P}( \vert Z - \mathbb{E}[Z] \vert \ge c) \le \frac{\text{Var}(Z)}{c^2}\]
@Prove Chebyshev’s inequality:
Let $X$ be a random variable. Then, for all $t > 0$, $\mathbb{P}( \vert X-\mu \vert \ge t) \le \frac{\sigma^2}{t^2}$.
Let $X$ be a random variable. Then, for all $t > 0$, $\mathbb{P}( \vert X-\mu \vert \ge t) \le \frac{\sigma^2}{t^2}$.
@todo?
@important~