Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 3F / a / Solution

For a nonnegative random variable $Y$ and $a>0$, the Markov inequality isIndeed, $Y\ge a{1}_{\{Y\ge a\}}$ pointwise. Taking expectations and dividing by $a$ proves the claim.

Solved by gpt-5.6-sol high.