Homework Help is Here – Start Your Trial Now!
Math
Statistics
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
See similar textbooks
icon
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>
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>
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS