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Identifying Probability Distributions In Exercises 9 and 10, determine whether the table represents a probability distribution. If it is a probability distribution, sketch its graph. If it is not a probability distribution, state any properties that are not satisfied. x 0 1 2 3 4 5 P ( x ) 1 25 3 25 5 25 7 25 8 25 1 25

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 10RE
Textbook Problem
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Identifying Probability Distributions In Exercises 9 and 10, determine whether the table represents a probability distribution. If it is a probability distribution, sketch its graph. If it is not a probability distribution, state any properties that are not satisfied.

x 0 1 2 3 4 5
P(x) 1 25 3 25 5 25 7 25 8 25 1 25

To determine

Whether the table of values represents a probability distribution. If it is a probability distribution, graph the distribution and if it is not a probability distribution, state the properties not satisfied to be a probability distribution.

x

0

1

2

3

4

5

P(x)

125

325

525

725

825

125

Explanation of Solution

Given Information:

The table of values and probabilities:

x

0

1

2

3

4

5

P(x)

125

325

525

725

825

125

Consider the provided table.

x

0

1

2

3

4

5

P(x)

125

325

525

725

825

125

The two properties that must be satisfied for a distribution to be a probability distribution are:

1. All the probabilities must be a number between 2. 3.0 and 14. 5.

0P(x)1

6. Sum of all probabilities must be equal to 7. 18. 9.

In the provided table of values, all the probabilities lies between 0 and 1. So, the first property is satisfied.

To check whether the second property is satisfied, sum up all the probabilities and it must be equal to 1.

Sum of all probabilities=125+325+525+725+825+125=1+3+5+7+8+125=2525=1

As the sum of all probabilities is equal to 1, the second property is also satisfied

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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