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Probability

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Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$

\begin{align*}
&P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right )  - P(a \leq X < b)\cdot \left ( \frac{a}{b} \right ) \right ] \\
\end{align*}
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