Start with Markov's Inequality
[tex]P(x\ \textgreater \ a) \leq \frac{E(x)}{a}[/tex]
Given :
[tex]P(x\ \textgreater \ a) +P(x \leq a) = 1 \\ P(x\ \textgreater \ a) = 1-P(x \leq a)[/tex]
Substitute into Markov's inequality
[tex]1-P(x \leq a) \leq \frac{E(x)}{a} [/tex]
Rearrange:
[tex]P(x \leq a) \geq 1-\frac{E(x)}{a} [/tex]
