(Markov’s Inequality) Let X be a real-valued random variable with X ≥ 0. Show that, for any t > 0, P{X ≥ t} ≤ E[XI{X ≥ t}]

t ≤ E(X)

t ;

here I(X ≥ t) is the indicator variable that is 1 if X ≥ t and is 0 otherwise.