Chebyshev 's inequality, (Exercise 44, Chapter 3), is valid for continuous as well as discrete distributions It states that for any number k satisfying k 1, P( X k) 1 k2 (see Exercise 44 in Chapter 3 for an interpretation) Obtain this probability in the case of a normal distribution for k 1, 2, and 3, and compare to the upper bound

Question: Chebyshev's inequality, (Exercise 44, Chapter 3), is valid for continuous as well as discrete distributions. It states that for any number k satisfying k

Chebyshev's inequality, (Exercise 44, Chapter 3), is valid for continuous as well as discrete distributions. It states that for any number k satisfying k ≥ 1, P(|X - μ| ≥ kσ) ≤ 1/k2 (see Exercise 44 in Chapter 3 for an interpretation). Obtain this probability in the case of a normal for k = 1, 2, and 3, and compare to the upper bound.

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