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Refer to Chebyshev’s inequality given in Exercise 44.

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 67E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 67E

Refer to Chebyshev’s inequality given in Exercise 44. Calculate P( | X - ? | ? k?) for k = 2 and k = 3 when X ? Bin (20,. 5) , and compare to the corresponding upper bound. Repeat for X ? Bin (20,. 75) Reference exercise 44 A result called ?Chebyshev’s inequality ?states that for any probability distribution of an rv X and any number k that is at least 1 P(|X – ?| ? k?) ? 1/k2 . In words, the probability that the value of X lies at least k standard deviations from its mean is at most 1/k2. a.? hat is the value of the upper bound for k = 2? K = 3? k = 4 ? k+ 5? K+ 10? b. ?Compute ? and ? for the distribution of Exercise 13. Then evaluate P(| X - ? | ? k? ) for the values of k given in part (a). What does this suggest about the upper bound relative to the corresponding probability? c. ?Let X have possible values -1, 0, and 1, with probabilities 1/18 , 8/9 and 1/ 18, respectively. What is P( |X - ?| ? 3?), and how does it compare to the corresponding bound? d.? ?Give a distribution for which P( |X - ?| ? 5?) = . 04

Step-by-Step Solution:

Answer : Step 1 of 2 : Chebyshev’s inequality states that for any probability distribution of an random variable X and any number k that is at least 1, P(|X – | k) 1 k2 Where, X~B(20, 0.5) The claim is to compare to the corresponding upper bound. Repeat for X Bin (20,. 75) 1 Using Chebyshev’s inequality P(|X – | k) k2 Where, k = 2 and k = 3 For k = 2 P(|X – | k) 1 4 For k = 3 P(|X – | k) 1 9

Step 2 of 2

Chapter 3, Problem 67E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: Bound, distribution, Probability, exercise, Upper. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 67E from 3 chapter was answered, more than 363 students have viewed the full step-by-step answer. The answer to “Refer to Chebyshev’s inequality given in Exercise 44. Calculate P( | X - ? | ? k?) for k = 2 and k = 3 when X ? Bin (20,. 5) , and compare to the corresponding upper bound. Repeat for X ? Bin (20,. 75) Reference exercise 44 A result called ?Chebyshev’s inequality ?states that for any probability distribution of an rv X and any number k that is at least 1 P(|X – ?| ? k?) ? 1/k2 . In words, the probability that the value of X lies at least k standard deviations from its mean is at most 1/k2. a.? hat is the value of the upper bound for k = 2? K = 3? k = 4 ? k+ 5? K+ 10? b. ?Compute ? and ? for the distribution of Exercise 13. Then evaluate P(| X - ? | ? k? ) for the values of k given in part (a). What does this suggest about the upper bound relative to the corresponding probability? c. ?Let X have possible values -1, 0, and 1, with probabilities 1/18 , 8/9 and 1/ 18, respectively. What is P( |X - ?| ? 3?), and how does it compare to the corresponding bound? d.? ?Give a distribution for which P( |X - ?| ? 5?) = . 04” is broken down into a number of easy to follow steps, and 221 words. The full step-by-step solution to problem: 67E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM.

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Refer to Chebyshev’s inequality given in Exercise 44.