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Solved: Let the random variable X have a discrete uniform

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

Solution for problem 76E Chapter 3.5

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 76E

Problem 76E

Let the random variable X have a discrete uniform distribution on the integers 0 ≤◊x ◊≤◊99. Determine the mean and variance of X.

Step-by-Step Solution:
Step 1 of 3

Solution 76E

Step1 of 3:

Let us consider a random variable X, it follows discrete Uniform distribution with

X = [0,1,2,...,99].

We need to determine the mean and variance of X.


Step2 of 3:

Suppose that a random variable X follows discrete Uniform distribution with parameters [a, b]. Then, the probability mass function of Uniform distribution is given by:

 x = 0,1,2,...,n.

We know that mean of Uniform distribution, and it is given by:

     

   

Therefore, Mean of X is 49.5.


   

Step2 of 3:

We know that Variance of Uniform distribution, and it is given by:

 

       

Therefore, Variance of X is 833.25.


Step 2 of 3

Chapter 3.5, Problem 76E is Solved
Step 3 of 3

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

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Solved: Let the random variable X have a discrete uniform