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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### 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>
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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