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# Let X denote the voltage at the output of a microphone, ISBN: 9780321629111 32

## Solution for problem 18E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 18E

Let ?X ?denote the voltage at the output of a microphone, and suppose that ?X ?has a uniform distribution on the interval from to –1. The voltage is processed by a “hard limiter” with cutoff values and – .5, so the limiter output is a random variableY? ?related to ?X ?by Y = X if |X| ? .5 Y = .5 if X> .5, andY = – .5 if X

Step-by-Step Solution:

Answer : Step 1 : Given, Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from to –1. The voltage is processed by a “hard limiter” with cutoff values and – .5, From the given information X is uniform distribution on interval -1 to +1. a). Now we have to find P( Y =0.5) P(Y=0.5) = f (x) dx X 0.5 P(Y=0.5) = 1 dx 2 0.5 P(Y=0.5) =1 4 P(Y=0.5) = 0.25

Step 2 of 2

##### ISBN: 9780321629111

Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The answer to “Let ?X ?denote the voltage at the output of a microphone, and suppose that ?X ?has a uniform distribution on the interval from to –1. The voltage is processed by a “hard limiter” with cutoff values and – .5, so the limiter output is a random variableY? ?related to ?X ?by Y = X if |X| ? .5 Y = .5 if X> .5, andY = – .5 if X<– .5 . a. What is P( Y = .5)? b. Obtain the cumulative distribution function ofY? ?and graph it.” is broken down into a number of easy to follow steps, and 89 words. Since the solution to 18E from 4 chapter was answered, more than 522 students have viewed the full step-by-step answer. This full solution covers the following key subjects: voltage, output, limiter, distribution, microphone. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The full step-by-step solution to problem: 18E from chapter: 4 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9.

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Let X denote the voltage at the output of a microphone,

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