MATLAB: An Introduction with Applications
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ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![## Uniform Continuous Distribution: Mean and Standard Deviation
In this exercise, you are required to find the mean and standard deviation for each given uniform continuous model. Please follow the instructions to round your answers appropriately.
**Instructions:**
- **Mean:** Round answers to 1 decimal place.
- **Standard Deviation:** Round answers to 4 decimal places.
**Models:**
a. \( U(2, 12) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
b. \( U(90, 250) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
c. \( U(1, 93) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
**Explanation:**
1. **Uniform Continuous Distribution:** In a uniform continuous distribution, all outcomes are equally likely within the interval \([a, b]\).
2. **Mean Formula:** The mean for a uniform continuous distribution \( U(a, b) \) is calculated as:
\[
\text{Mean} = \frac{a + b}{2}
\]
3. **Standard Deviation Formula:** The standard deviation for a uniform continuous distribution \( U(a, b) \) is calculated using the formula:
\[
\text{Standard Deviation} = \sqrt{\frac{(b - a)^2}{12}}
\]
Please input your answers accordingly in the provided table. Once completed, click on "Check my work" to validate your responses.
Note: Ensure to follow the rounding instructions precisely to match the required format.](https://content.bartleby.com/qna-images/question/cbcf5de3-296f-47d6-9d91-3d7cd8b6c4b2/de21a012-4d75-419b-8dc0-01f76726544e/evgo8rc_processed.jpeg)
Transcribed Image Text:## Uniform Continuous Distribution: Mean and Standard Deviation
In this exercise, you are required to find the mean and standard deviation for each given uniform continuous model. Please follow the instructions to round your answers appropriately.
**Instructions:**
- **Mean:** Round answers to 1 decimal place.
- **Standard Deviation:** Round answers to 4 decimal places.
**Models:**
a. \( U(2, 12) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
b. \( U(90, 250) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
c. \( U(1, 93) \)
| Mean | Standard Deviation |
|------|---------------------|
| | |
**Explanation:**
1. **Uniform Continuous Distribution:** In a uniform continuous distribution, all outcomes are equally likely within the interval \([a, b]\).
2. **Mean Formula:** The mean for a uniform continuous distribution \( U(a, b) \) is calculated as:
\[
\text{Mean} = \frac{a + b}{2}
\]
3. **Standard Deviation Formula:** The standard deviation for a uniform continuous distribution \( U(a, b) \) is calculated using the formula:
\[
\text{Standard Deviation} = \sqrt{\frac{(b - a)^2}{12}}
\]
Please input your answers accordingly in the provided table. Once completed, click on "Check my work" to validate your responses.
Note: Ensure to follow the rounding instructions precisely to match the required format.
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