Calculate the standard deviation o of X for the probability distribution. (Round your answer to two decimal places.) X 0 1 2 3 P(X = x) 0.1 0.3 0.4 0.2 6 = Read It Watch It Need Help?
Calculate the standard deviation o of X for the probability distribution. (Round your answer to two decimal places.) X 0 1 2 3 P(X = x) 0.1 0.3 0.4 0.2 6 = Read It Watch It Need Help?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Calculate the standard deviation ? of X for the probability distribution. (Round your answer to two decimal places.)
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
|
P(X = x)
|
0.1 | 0.3 | 0.4 | 0.2 |
? =
![**Title: Calculating the Standard Deviation for a Probability Distribution**
**Problem Statement:**
Calculate the standard deviation, σ, of X for the probability distribution. (Round your answer to two decimal places.)
**Probability Distribution Table:**
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 \\
\hline
P(X = x) & 0.1 & 0.3 & 0.4 & 0.2 \\
\hline
\end{array}
\]
**Calculation:**
The standard deviation formula for a probability distribution is:
\[ \sigma = \sqrt{\sum (x_i - \mu)^2 P(x_i)} \]
Where \( \mu \) is the mean of the distribution, given by:
\[ \mu = \sum x_i P(x_i) \]
**Steps:**
1. Calculate the mean \( \mu \).
2. Compute the variance \( \sigma^2 \).
3. Take the square root of the variance to get the standard deviation \( \sigma \).
**Help Resources:**
For further assistance, use the following resources:
- [Read It](#)
- [Watch It](#)
[Note: The actual links need to be provided for "Read It" and "Watch It"]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62f7585f-4634-4199-81a6-58188b278fc8%2Fd24a9325-4260-473e-824f-5006bf3ac2ac%2F91p0z8o_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Standard Deviation for a Probability Distribution**
**Problem Statement:**
Calculate the standard deviation, σ, of X for the probability distribution. (Round your answer to two decimal places.)
**Probability Distribution Table:**
\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 \\
\hline
P(X = x) & 0.1 & 0.3 & 0.4 & 0.2 \\
\hline
\end{array}
\]
**Calculation:**
The standard deviation formula for a probability distribution is:
\[ \sigma = \sqrt{\sum (x_i - \mu)^2 P(x_i)} \]
Where \( \mu \) is the mean of the distribution, given by:
\[ \mu = \sum x_i P(x_i) \]
**Steps:**
1. Calculate the mean \( \mu \).
2. Compute the variance \( \sigma^2 \).
3. Take the square root of the variance to get the standard deviation \( \sigma \).
**Help Resources:**
For further assistance, use the following resources:
- [Read It](#)
- [Watch It](#)
[Note: The actual links need to be provided for "Read It" and "Watch It"]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
