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A system consists of five identical components connectedin

Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore ISBN: 9781305251809 122

Solution for problem 69 Chapter 4.4

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Probability and Statistics for Engineering and the Sciences | 9th Edition | ISBN: 9781305251809 | Authors: Jay L. Devore

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 69

A system consists of five identical components connectedin series as shown: As soon as one component fails, the entire system willfail. Suppose each component has a lifetime that is exponentiallydistributed with l 5 .01 and that componentsfail independently of one another. Define events Ai 5{ith component lasts at least t hours}, i 5 1,, 5, sothat the Ais are independent events. Let X 5 the time atwhich the system failsthat is, the shortest (minimum)lifetime among the five components.a. The event {X $ t} is equivalent to what event involvingA1,, A5?b. Using the independence of the Ai9s, computeP(X $ t). Then obtain F(t) 5 P(X # t) and the pdf ofX. What type of distribution does X have?c. Suppose there are n components, each having exponentiallifetime with parameter l. What type of distributiondoes X have?

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1.1Statistics EX: (look at notebook) Noise (the spread of the dots): normal or expected variability Signal: fertilizer 1.2Types of Evidence I. Types of Evidence a. Anecdotal: something that sparks a study of investigation. A single instinct that can lead. i. EX: (A plane trip) A mom stops the...

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Textbook: Probability and Statistics for Engineering and the Sciences
Edition: 9
Author: Jay L. Devore
ISBN: 9781305251809

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A system consists of five identical components connectedin