Probability MT22, Markov's inequality
Flashcards
What does Markov’s inequality state about a non-negative r.v. $Y$ with finite expectation?
\[\forall t> 0, \text{ } \mathbb{P}(Y \ge t) \le \frac{\mathbb{E}[Y]}{t}\]
What random variable do you consider in the proof of Markov’s inequality?
\[\tilde{Y _ t} = \begin{cases}0 \text{ if } Y < t \\\\t \text{ if } Y \ge t\end{cases}\]
@Prove Markov’s inequality:
Let $X$ be a random variable. Then, for all $t > 0$, $\mathbb{P}(X > t) < \frac{\mathbb{E}[X]}{t}$.
Let $X$ be a random variable. Then, for all $t > 0$, $\mathbb{P}(X > t) < \frac{\mathbb{E}[X]}{t}$.
@todo, (probability, page 64)
@important~