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Answer: Determine the mean and variance of the random

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

Solution for problem 58E Chapter 3.4

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 58E

Determine the mean and variance of the random variable in Exercise 3-16.

Step-by-Step Solution:

Answer

Step 1 of 1

(a)

We have a sample space of a random experiment which is,

 

Each outcome is equally likely.

A random variable is defined as follows:

outcome

We are asked to find the mean and variance of the random variable.

The probability mass function (PMF) of a discrete random variable  is the function  The probability mass function is sometimes called the probability distribution.

Since we have given each outcome is equally likely.

Then the probability of each outcome  is

Let  denote the random variable.

Hence the range  can take values from the table,

We can write the probability according to the definition of probability mass function (PMF),

 

 

Hence we can form the probability mass function (PMF) table:

The mean or expected value of the discrete random variable  denote a  is

 ……….(1)

Using the PMF table, we can write the mean of a random variable,

 

Hence the mean of a random variable  is

The variance  of the discrete random variable  denote a  is

 ……….(2)

 

Hence the variance of a random variable  is


Step 2 of 1

Chapter 3.4, Problem 58E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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Answer: Determine the mean and variance of the random