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Let X represent the number of tires with low air pressure

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 2.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

Let X represent the number of tires with low air pressure on a randomly chosen car.

a. Which of the three functions below is a possible probability mass function of X? Explain.

 

X

 

   0

     1

            2

           3

    4

p1(x)

0.2

0.2

0.3

0.1

0.1

p2(x)

0.1

0.3

0.3

0.3

0.2

p3(x)

0.1

0.2

0.2

0.4

0.1

b. For the possible probability mass function, compute μX. and

Step-by-Step Solution:

Step 1 of 3:

Let X denote the number of tires with low air pressure on a randomly chosen car.

                                          X

0

1

2

3

4

0.2

0.2

0.3

0.1

0.1

(x)

0.1

0.3

0.3

0.3

0.2

(x)

0.1

0.2

0.2

0.4

0.1

We have to find

Which of given  three functions is a possible probability mass function of X. For the possible mass function,we have to compute E(x) and V(X).

Step 2 of 3:

The probability mass function(pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

Therefore the addition all probabilities should give a total one.

Here

                 = 0.2+ 0.2 +0. 3 +0.1+ 0.1

                               = 0.9

                = 1.2

                 = 0.1 +0.2 +0.2+ 0.4 + 0.1

                               

                                =  1

So here the third one (x) is the possible probability mass function of X since other two are not giving a total of one.

Step 3 of 3

Chapter 2.4, Problem 4E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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