Theorem (Markov’s inequality): Let $X$ be a nonnegative random variable. For any $\eps > 0$,
\[\Pr(X \ge \eps) \le \frac{\Ex(X)}{\eps}.\]Proof: Probability and Measure (1995), Billingsley P. Wiley.
Theorem (Markov’s inequality): Let $X$ be a nonnegative random variable. For any $\eps > 0$,
\[\Pr(X \ge \eps) \le \frac{\Ex(X)}{\eps}.\]Proof: Probability and Measure (1995), Billingsley P. Wiley.