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In the transmission of digital information, the

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 12E Chapter 5.1

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 12E

Problem 12E

In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion of the three transmitted, respectively. Determine the following:

Step-by-Step Solution:

Answer

Step 1 of 4

(a)

Let  denote the number of bits with high and moderate distortion of three transmitted, respectively.

We are asked to find the probability that two bits have high distortion and one has moderate distortion.

We have given

A number of possible combinations in which two bits have the high distortions can be selected is  from the three bits.

Hence we can write,

 

Where

Hence the probability that two bits have high distortion and one have moderate distortion is


Step 2 of 4

Chapter 5.1, Problem 12E is Solved
Step 3 of 4

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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In the transmission of digital information, the