Consider the probability distribution shown below. 1 2 P(x) Compute the expected value of the distribution. 0.75 0.20 0.05 Compute the standard deviation of the distribution. (Round your answer to four decimal places.)
Consider the probability distribution shown below. 1 2 P(x) Compute the expected value of the distribution. 0.75 0.20 0.05 Compute the standard deviation of the distribution. (Round your answer to four decimal places.)
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 Statistical Analysis
**Probability Distribution Table:**
The table below outlines a discrete probability distribution with outcomes \( x \) and their corresponding probabilities \( P(x) \).
| \( x \) | 0 | 1 | 2 |
|---------|-----|-----|-----|
| \( P(x) \) | 0.75 | 0.20 | 0.05 |
1. **Compute the Expected Value:**
The expected value \( E(X) \) of a probability distribution is calculated using the formula:
\[
E(X) = \sum x \cdot P(x)
\]
Fill in the blank with the calculated expected value.
2. **Compute the Standard Deviation:**
The standard deviation of a probability distribution is a measure of the dispersion of the distribution. It is calculated using the formula:
\[
\sigma = \sqrt{\sum (x - E(X))^2 \cdot P(x)}
\]
Provide the calculated standard deviation rounded to four decimal places in the blank provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42e5e83d-2fd6-4ccf-88e8-6c44a03300db%2Fb2b0999b-e7d6-4d46-a568-469076b452c9%2Fgtbsa2c_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Distribution and Statistical Analysis
**Probability Distribution Table:**
The table below outlines a discrete probability distribution with outcomes \( x \) and their corresponding probabilities \( P(x) \).
| \( x \) | 0 | 1 | 2 |
|---------|-----|-----|-----|
| \( P(x) \) | 0.75 | 0.20 | 0.05 |
1. **Compute the Expected Value:**
The expected value \( E(X) \) of a probability distribution is calculated using the formula:
\[
E(X) = \sum x \cdot P(x)
\]
Fill in the blank with the calculated expected value.
2. **Compute the Standard Deviation:**
The standard deviation of a probability distribution is a measure of the dispersion of the distribution. It is calculated using the formula:
\[
\sigma = \sqrt{\sum (x - E(X))^2 \cdot P(x)}
\]
Provide the calculated standard deviation rounded to four decimal places in the blank provided.
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