Question: (Markovs Inequality) Let X be a real-valued random variable with X 0. Show that, for any t > 0, P{X t} E[X

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

E[X I{X ≥ t}]

t

≤

E(X)

t

;

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

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