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Markov after a shift

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A daily loss $L$ is never below $2$ and has mean $6$ . Apply Markov's inequality to the non-negative variable $L - 2$ . What upper bound does this give on $P (L \geq 18)$ ? Give a fraction in lowest terms.

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Hint

Rewrite the event in terms of $L - 2$ .

Solution

The event $L \geq 18$ is the same as $L - 2 \geq 16$ , and the shifted variable has mean $6 - 2 = 4$ .
Markov gives the bound $\frac{4}{16} = \frac{1}{4}$ .

Answer: $\frac{1}{4}$

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