Determine whether the distribution is a discrete probability distribution. P(x) O 0.20 1. 0.32 0.50 0.32 4 0.20 Is the distribution a discrete probability distribution? Why? Choose the correct answer below. O A. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive. O B. No, because some of the probabilities have values greater than 1 or less than 0. O C. No, because the total probability is not equal to 1. O D. Yes, because the distribution is symmetric.
Determine whether the distribution is a discrete probability distribution. P(x) O 0.20 1. 0.32 0.50 0.32 4 0.20 Is the distribution a discrete probability distribution? Why? Choose the correct answer below. O A. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive. O B. No, because some of the probabilities have values greater than 1 or less than 0. O C. No, because the total probability is not equal to 1. O D. Yes, because the distribution is symmetric.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![**Discrete Probability Distribution Analysis**
The purpose of this exercise is to determine whether the given distribution qualifies as a discrete probability distribution. Refer to the data provided in the table and select the correct statement below regarding the nature of the distribution.
### Data Table
| x | P(x) |
|----|------|
| 0 | 0.20 |
| 1 | 0.32 |
| 2 | 0.50 |
| 3 | 0.32 |
| 4 | 0.20 |
### Question
Is the distribution a discrete probability distribution? Why? Choose the correct answer below:
- **A.** Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
- **B.** No, because some of the probabilities have values greater than 1 or less than 0.
- **C.** No, because the total probability is not equal to 1.
- **D.** Yes, because the distribution is symmetric.
### Analysis
1. **Probabilities Check:** Ensure each probability \( P(x) \) is within the range \([0, 1]\).
2. **Sum Verification:** Verify that the total sum of probabilities equals 1.
Evaluate the provided options based on these checks to determine the correct classification of the distribution.
Choose wisely!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7226e99-cda6-474c-a507-35a166b04cf3%2F30ef7ec2-077a-44f5-9517-44251f914f7d%2Fcu0flf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Discrete Probability Distribution Analysis**
The purpose of this exercise is to determine whether the given distribution qualifies as a discrete probability distribution. Refer to the data provided in the table and select the correct statement below regarding the nature of the distribution.
### Data Table
| x | P(x) |
|----|------|
| 0 | 0.20 |
| 1 | 0.32 |
| 2 | 0.50 |
| 3 | 0.32 |
| 4 | 0.20 |
### Question
Is the distribution a discrete probability distribution? Why? Choose the correct answer below:
- **A.** Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
- **B.** No, because some of the probabilities have values greater than 1 or less than 0.
- **C.** No, because the total probability is not equal to 1.
- **D.** Yes, because the distribution is symmetric.
### Analysis
1. **Probabilities Check:** Ensure each probability \( P(x) \) is within the range \([0, 1]\).
2. **Sum Verification:** Verify that the total sum of probabilities equals 1.
Evaluate the provided options based on these checks to determine the correct classification of the distribution.
Choose wisely!
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