Question: 20. Let X be a continuous random variable. Prove that These important inequalities show that if and only if the series Hint: By Exercise 19,

20. Let X be a continuous random variable. Prove that

n=1 P(Xn) E(|X|) 1+ P(|X| n). =1

These important inequalities show that image text in transcribed if and only if the series

image text in transcribed

Hint: By Exercise 19,

image text in transcribed

Note that on the interval [n, n + 1),

image text in transcribed

n=1 P(Xn) E(|X|) 1+ P(|X| n). =1

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