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Determine the cumulative distribution function of the

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

Solution for problem 38E Chapter 3.3

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 38E

Problem 38E

Determine the cumulative distribution function of the random variable in Exercise 3-16.

3-16.The sample space of a random experiment is {a, b, c, d,

e, f}, and each outcome is equally likely. A random variable is

defined as follows:

outcome

a

b

c

d

e

f

x

0

0

1.5

1.5

2

3

Determine the probability mass function of a. Use the probability mass function to determine the following probabilities:

Step-by-Step Solution:

Solution :

Step 1 of 1:

From the given information the sample space of a random experiment is {a, b, c, d, e, f}.

Then the table is given below.

outcome

a

b

c

d

e

f

x

0

0

1.5

1.5

2

3

Our goal is:

We need to determine the cumulative distribution function.

From the given information is the number of 0’s is 2.

Then the total number of variables is 6.

So P(x=0) is

P(x=0) =

P(x=0) = 0.333

Therefore, P(x=0) = 0.333.

The number of 1.5 is 2 and the total number of variables is 6.

P(x=1.5) =

P(x=1.5) = 0.333

Therefore, P(x=1.5) = 0.333.

The number of 2 is 1 and the total number of variables is 6.

P(x=2) =

P(x=2) = 0.167

Therefore, P(x=2) = 0.167.

The number of 3 is 1 and the total number of variables is 6.

P(x=2) =

P(x=2) = 0.167

Therefore, P(x=2) = 0.167.

From the available information, each outcome is equally likely.

Then the cumulative distribution function is

x

0

1.5

2

3

P(X) = f(x)

0.333

0.333

0.167

0.167

F(x)

0.333

(0.333+0.333)=

0.666

(0.666+0.167)=

0.833

(0.833+0.167)=1

   

 Then, F(x) is


Step 2 of 1

Chapter 3.3, Problem 38E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

Since the solution to 38E from 3.3 chapter was answered, more than 432 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. The full step-by-step solution to problem: 38E from chapter: 3.3 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. The answer to “Determine the cumulative distribution function of the random variable in Exercise 3-16.3-16.The sample space of a random experiment is {a, b, c, d,e, f}, and each outcome is equally likely. A random variable isdefined as follows:outcomeab cdefx001.51.523Determine the probability mass function of a. Use the probability mass function to determine the following probabilities:” is broken down into a number of easy to follow steps, and 53 words. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712. This full solution covers the following key subjects: function, random, determine, Probability, outcome. This expansive textbook survival guide covers 97 chapters, and 2005 solutions.

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