Past exam of the probability, statistics and options I course of the University of Oxford / 2010 / M / 3 / b

Pointwise, $X\ge a{1}_{\{X\ge a\}}$, since $X$ is nonnegative. Taking expectations and dividing by $a>0$ proves the Markov inequalityIf the expectation is infinite, the inequality remains true in the extended-real sense.