Probability MT22, Chebyshev's inequality
Flashcards
@State Chebyshev’s inequality for a random variable $Z$ with finite variance.
\[\forall c>0, \quad \mathbb{P}( \vert Z - \mathbb{E}[Z] \vert \ge c) \le \frac{\mathrm{Var}(Z)}{c^2}\]
@Prove Chebyshev’s inequality (∆chebyshevs-inequality): for a random variable $X$ with mean $\mu$ and variance $\sigma^2$, and any $t > 0$,
\[\mathbb{P}( \vert X-\mu \vert \ge t) \le \frac{\sigma^2}{t^2}\]
@todo?