Question: Exercise 2.11 (Markovs Inequality) Let X be any random variable. For any smooth function h(x), show that provided that the expectation exists. Hint: Take A

Exercise 2.11 (Markov’s Inequality) Let X be any random variable. For any smooth function h(x), show that

P{|h(X)|> a} < E[|h(X)|] a > 0, a

provided that the expectation exists. Hint: Take A = {x : |h(x)| > a} and apply Proposition 2.2.

P{|h(X)|> a} < E[|h(X)|] a > 0, a

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