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Statistics / Probability and Statistics for Engineers and the Scientists 9 / Chapter 4 / Problem 1E

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

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The current in a certain circuit as measured by an ammeter

Chapter 5, Problem 1E

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QUESTION:

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).

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QUESTION:

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).

ANSWER:

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.

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