 Solution

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

Z

and

u > 0

P (Z \geq u) \leq \frac{E Z}{u} .

It follows by taking expectations in

Z \geq u 1_{{Z \geq u}}

. A finite expectation makes the bound informative.

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