Determine whether the distribution represents a probability distribution. X 3 7 10 13 P(X) 0.1 0.3 0.8 -0.7
Determine whether the distribution represents a probability distribution. X 3 7 10 13 P(X) 0.1 0.3 0.8 -0.7
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Unit 3 Test: Probability Distribution Analysis
#### Question 1 of 21 (1 Point) - Attempt 1 of 1
**Objective:** Determine whether the given distribution represents a probability distribution.
#### Task
Examine the following table of values for \(X\) and \(P(X)\):
| \(X\) | 3 | 7 | 10 | 13 |
|---------|------|------|------|------|
| \(P(X)\)| 0.1 | 0.3 | -0.7 | 0.8 |
#### Instructions
- Determine if the distribution provided represents a valid probability distribution.
- If applicable, explain why the distribution is valid or invalid according to the properties of a probability distribution.
#### Properties of a Probability Distribution:
1. Each probability \(P(X)\) must be between 0 and 1, inclusive.
2. The sum of all probabilities \(P(X)\) must equal 1.
#### Steps to Complete the Task:
1. Examine each \(P(X)\) value.
- Verify that all probabilities are within the range [0, 1].
2. Add up all \(P(X)\) values.
- Confirm if the sum equals 1.
#### Example Analysis:
Given values:
- \(P(3) = 0.1\)
- \(P(7) = 0.3\)
- \(P(10) = -0.7\)
- \(P(13) = 0.8\)
Step 1: Check individual probabilities:
- \(0.1\) is between 0 and 1.
- \(0.3\) is between 0 and 1.
- \(-0.7\) is not between 0 and 1 (invalid).
- \(0.8\) is between 0 and 1.
Step 2: Sum of the probabilities:
\(0.1 + 0.3 + (-0.7) + 0.8 = 0.5\) (does not equal 1).
#### Final Step
- Use the dropdown menu to select whether this distribution:
The distribution \( \text{(Choose one)} \) a probability distribution.
**Part 1 of 2** - Indicates there are two parts to completing this evaluation.
This analysis ultimately aids in understanding whether the provided data adheres to the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2b55b8f-b578-48f1-bdd3-ee0ba2cc179e%2F474f2c8c-91a8-486a-833d-0da7f1ffed21%2Fk3esby_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Unit 3 Test: Probability Distribution Analysis
#### Question 1 of 21 (1 Point) - Attempt 1 of 1
**Objective:** Determine whether the given distribution represents a probability distribution.
#### Task
Examine the following table of values for \(X\) and \(P(X)\):
| \(X\) | 3 | 7 | 10 | 13 |
|---------|------|------|------|------|
| \(P(X)\)| 0.1 | 0.3 | -0.7 | 0.8 |
#### Instructions
- Determine if the distribution provided represents a valid probability distribution.
- If applicable, explain why the distribution is valid or invalid according to the properties of a probability distribution.
#### Properties of a Probability Distribution:
1. Each probability \(P(X)\) must be between 0 and 1, inclusive.
2. The sum of all probabilities \(P(X)\) must equal 1.
#### Steps to Complete the Task:
1. Examine each \(P(X)\) value.
- Verify that all probabilities are within the range [0, 1].
2. Add up all \(P(X)\) values.
- Confirm if the sum equals 1.
#### Example Analysis:
Given values:
- \(P(3) = 0.1\)
- \(P(7) = 0.3\)
- \(P(10) = -0.7\)
- \(P(13) = 0.8\)
Step 1: Check individual probabilities:
- \(0.1\) is between 0 and 1.
- \(0.3\) is between 0 and 1.
- \(-0.7\) is not between 0 and 1 (invalid).
- \(0.8\) is between 0 and 1.
Step 2: Sum of the probabilities:
\(0.1 + 0.3 + (-0.7) + 0.8 = 0.5\) (does not equal 1).
#### Final Step
- Use the dropdown menu to select whether this distribution:
The distribution \( \text{(Choose one)} \) a probability distribution.
**Part 1 of 2** - Indicates there are two parts to completing this evaluation.
This analysis ultimately aids in understanding whether the provided data adheres to the
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