A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Problem #21
![**Topic: Continuous Uniform Distribution**
Suppose \( X \) has a continuous uniform distribution over the interval \([2.2, 5.0]\).
Round your answers to 3 decimal places.
**Questions:**
(a) Determine the mean of \( X \).
```
[Input Box for Answer]
```
*[Information icon]*
(b) Determine the variance of \( X \).
```
[Input Box for Answer]
```
*[Information icon]*
(c) What is \( P(X < 4.0) \)?
```
[Input Box for Answer]
```
*[Information icon]*
**Explanation of Input Boxes:**
- Next to each question, there is a text box where you can input your answer.
- The information icons indicate that additional help or hints are available if you click on them.
**Additional Guidance:**
- For calculating the mean and the variance of a continuous uniform distribution, use the standard formulas for a uniform distribution over the interval \([a, b]\):
- Mean: \( \mu = \frac{a + b}{2} \)
- Variance: \( \sigma^2 = \frac{(b - a)^2}{12} \)
- To find the probability \( P(X < 4.0) \) for a uniform distribution, use the cumulative distribution function (CDF) formula for the uniform distribution.](https://content.bartleby.com/qna-images/question/f6a5caec-236f-4acf-a757-ef7af523a315/67dd4872-83d1-49c4-b9ba-d559b5df0e83/3ip7r8o_processed.png)
Transcribed Image Text:**Topic: Continuous Uniform Distribution**
Suppose \( X \) has a continuous uniform distribution over the interval \([2.2, 5.0]\).
Round your answers to 3 decimal places.
**Questions:**
(a) Determine the mean of \( X \).
```
[Input Box for Answer]
```
*[Information icon]*
(b) Determine the variance of \( X \).
```
[Input Box for Answer]
```
*[Information icon]*
(c) What is \( P(X < 4.0) \)?
```
[Input Box for Answer]
```
*[Information icon]*
**Explanation of Input Boxes:**
- Next to each question, there is a text box where you can input your answer.
- The information icons indicate that additional help or hints are available if you click on them.
**Additional Guidance:**
- For calculating the mean and the variance of a continuous uniform distribution, use the standard formulas for a uniform distribution over the interval \([a, b]\):
- Mean: \( \mu = \frac{a + b}{2} \)
- Variance: \( \sigma^2 = \frac{(b - a)^2}{12} \)
- To find the probability \( P(X < 4.0) \) for a uniform distribution, use the cumulative distribution function (CDF) formula for the uniform distribution.
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