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The current in a certain circuit as measured by an ammeter

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 1E Chapter 4

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 1E

The current in a certain circuit as measured by an ammeter is a continuous random variable ?X ?with the following density function: a.? ?Graph the pdf and verify that the total area under the density curve is indeed 1. b. Calculate P(X ? 4). How does this probability compare to P(X < 4)? c.? ?Calculate P(3.5 ? X ? 4.5) and also P( 4.5 < X).

Step-by-Step Solution:

Solution : Step 1: Here the current in a certain circuit as measured by an ammeter is a continuous random variable X , with density function We have to verify that the total area under the density curve is indeed 1. And the probabilities for different intervals of X. Step 2 : a) We have to verify that the total area under the density curve is indeed 1. By using the density function we can verify this That is 5 2 5 5 0.075x + 0.2 dx = 0.075[x /2] 3 + 0.2 [x] 3 3 = 0.075*8+ 0.2*2 = 1 So it's satisfying the property of the density curve. We can a line graph of pdf by using the values X f(x) 3 0.425 4 0.5 5 0.5

Step 3 of 3

Chapter 4, Problem 1E 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

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The current in a certain circuit as measured by an ammeter

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