 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2011/m/m4/b/iii/solution

Z

and

a > 0

Pr (Z \geq a) \leq \frac{E Z}{a} .

It follows immediately from

Z \geq a 1_{{Z \geq a}}

and monotonicity of expectation. A finite expectation makes the bound informative.

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