X P(x) 0 0.15 1 0.25 2 0.2 0.4 3 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places Submit Question
X P(x) 0 0.15 1 0.25 2 0.2 0.4 3 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places Submit Question
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Probability Distribution and Standard Deviation
#### Probability Distribution Table
Below is a probability distribution table that lists the values of a random variable \( x \) and their corresponding probabilities \( P(x) \):
| \( x \) | \( P(x) \) |
|---------|------------|
| 0 | 0.15 |
| 1 | 0.25 |
| 2 | 0.20 |
| 3 | 0.40 |
#### Problem Statement
Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.
#### Solution
To solve this, you need to use the formula for the standard deviation of a discrete probability distribution:
\[ \sigma = \sqrt{\sum (x_i - \mu)^2 P(x_i)} \]
1. **Calculate the mean (\( \mu \)) of the distribution**:
\[ \mu = \sum x_i P(x_i) \]
2. **Compute \( (x_i - \mu)^2 P(x_i) \) for each value of \( x \)**.
3. **Sum up these values** and take the square root.
Place your final answer in the provided input box and then click the 'Submit Question' button.
**Note:** This explanation includes how to solve the problem but does not compute the actual answer. It is structured to guide users through finding the standard deviation manually.
<button>Submit Question</button>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e5613b-1a25-4b20-8027-b25d1244d9dc%2Fe30f1a90-3d7e-47d9-aa7c-8ce819cb1952%2Fz8xxl7f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Distribution and Standard Deviation
#### Probability Distribution Table
Below is a probability distribution table that lists the values of a random variable \( x \) and their corresponding probabilities \( P(x) \):
| \( x \) | \( P(x) \) |
|---------|------------|
| 0 | 0.15 |
| 1 | 0.25 |
| 2 | 0.20 |
| 3 | 0.40 |
#### Problem Statement
Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places.
#### Solution
To solve this, you need to use the formula for the standard deviation of a discrete probability distribution:
\[ \sigma = \sqrt{\sum (x_i - \mu)^2 P(x_i)} \]
1. **Calculate the mean (\( \mu \)) of the distribution**:
\[ \mu = \sum x_i P(x_i) \]
2. **Compute \( (x_i - \mu)^2 P(x_i) \) for each value of \( x \)**.
3. **Sum up these values** and take the square root.
Place your final answer in the provided input box and then click the 'Submit Question' button.
**Note:** This explanation includes how to solve the problem but does not compute the actual answer. It is structured to guide users through finding the standard deviation manually.
<button>Submit Question</button>
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