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A computer disk storage device has ten concentric tracks,

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 117E 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 117E

A computer disk storage device has ten concentric tracks, numbered 1, 2, . . . , 10 from outermost to innermost, and a single access arm. Let pi = the probability that any particular request for data will take the arm to track . Assume that the tracksi(i = 1, ………,10) accessed in successive seeks are independent. Let X = the number of tracks over which the access arm passes during two successive requests (excluding the track that the arm has just left, so possible X values are x = 0, 1, …..,9). Compute the pmf of X. [Hint: P( the arm is now on track i and X = j) = P(X = j|arm now on i).p.i After the conditional probability is written in terms of p1, . . . , p10, by the law of total probability, the desired probability is obtained by summing over i.]

Step-by-Step Solution:

Answer : Step 1 : Given a computer disk storage device has ten concentric tracks, numbered 1, 2, . . . , 10 from outermost to innermost, and a single access arm. Let pi = the probability that any particular request for data will take the arm to track. We assume that the tracks i(i = 1, ………,10) accessed in successive seeks are independent. Let X = the number of tracks over which the access...

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Chapter 3, Problem 117E is Solved
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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

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A computer disk storage device has ten concentric tracks,