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Consider a deck consisting of seven cards, marked 1, 2, .

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 94E 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 94E

Consider a deck consisting of seven cards, marked 1, 2, . . . , 7. Three of these cards are selected at random. Define an rv W by W = the sum of the resulting numbers, and compute the pmf of W. Then compute m and s2. [Hint: Consider outcomes as unordered, so that (1, 3, 7) and (3, 1, 7) are not different outcomes. Then there are 35 outcomes, and they can be listed. (This type of rv actually arises in connection with a statistical procedure called Wilcoxon’s rank-sum test, in which there is an x sample and a y sample and W is the sum of the ranks of the x’s in the combined sample; see Section 15.2.)

Step-by-Step Solution:
Step 1 of 3

Answer: Step1: Consider a deck consisting of seven cards, marked 1,2,3,4,5,6,7. Three of these cards are selected at random. c = 35 ways. 3 Thus the total number of outcomes is 35. i.e, (1,2,3),(1,2,4),(1,2,5),(1,2,6),(1,2,7),.......,(5,6,7). Then, P(each outcome) = 35 Here, W = sum of the resulting numbers. i.e, (1+2+3 = 6, 1+2+4 = 7 ….) Therefore, W = (6,7,8,9,10,...........,18) Since there is just one outcome with W value 6. P(6) = P(W = 6) = 1 31 P(7) = P(W = 7) = 35 Similarly there are 3 outcomes with W value 9 [(1,2,6) (1,3,5) (2,3,4)] So P(9) = 3 . 35 Step2: Continuing in this manner yields the following distribution. W 6 7 8 9 10 11 12 13 14 15 16 17 18 1 1 2 3 4 4 5 4 4 3 2 1 1 P(w) 35 35 35 35 35 35 35 35 35 35 35 35 35 Since the distribution is symmetric about W = 12. So = 12. 2 18 2 And S = (w 12) p(w) w=0 S = 1 [( 6) .1 + ( 5) .1 + ( 4) .2 + .... + (5) .1 + (6) .1] = 8. 35 Therefore, 2 = 12 and S = 8.

Step 2 of 3

Chapter 3, Problem 94E is Solved
Step 3 of 3

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

The full step-by-step solution to problem: 94E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Since the solution to 94E from 3 chapter was answered, more than 480 students have viewed the full step-by-step answer. The answer to “Consider a deck consisting of seven cards, marked 1, 2, . . . , 7. Three of these cards are selected at random. Define an rv W by W = the sum of the resulting numbers, and compute the pmf of W. Then compute m and s2. [Hint: Consider outcomes as unordered, so that (1, 3, 7) and (3, 1, 7) are not different outcomes. Then there are 35 outcomes, and they can be listed. (This type of rv actually arises in connection with a statistical procedure called Wilcoxon’s rank-sum test, in which there is an x sample and a y sample and W is the sum of the ranks of the x’s in the combined sample; see Section 15.2.)” is broken down into a number of easy to follow steps, and 120 words. 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: Outcomes, sum, sample, Cards, consider. 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.

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Consider a deck consisting of seven cards, marked 1, 2, .