x P(x) 0 0.25 1 0.3 2 0.05 3 0.4 Find the mean of this probability distribution. Round your answer to one decimal place.
x P(x) 0 0.25 1 0.3 2 0.05 3 0.4 Find the mean of this probability distribution. Round your answer to one decimal place.
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 Problem
**Table of Probability Distribution:**
| \( x \) | \( P(x) \) |
|--------|------------|
| 0 | 0.25 |
| 1 | 0.3 |
| 2 | 0.05 |
| 3 | 0.4 |
**Question:**
Find the mean of this probability distribution. Round your answer to one decimal place.
**Solution:**
To find the mean \( \mu \) of a probability distribution, you use the formula:
\[
\mu = \sum (x \cdot P(x))
\]
Using the values in the table:
1. For \( x = 0 \), \( x \cdot P(x) = 0 \cdot 0.25 = 0 \)
2. For \( x = 1 \), \( x \cdot P(x) = 1 \cdot 0.3 = 0.3 \)
3. For \( x = 2 \), \( x \cdot P(x) = 2 \cdot 0.05 = 0.1 \)
4. For \( x = 3 \), \( x \cdot P(x) = 3 \cdot 0.4 = 1.2 \)
Now, sum these values:
\[
\mu = 0 + 0.3 + 0.1 + 1.2 = 1.6
\]
So, the mean of the probability distribution is **1.6**.
**Answer:** 1.6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82a8ebfc-76c9-419b-9ea9-29a90be836d5%2F62c0cbbb-22cf-4f14-88cd-e41d5506f9f4%2Ftabi3fg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Distribution Problem
**Table of Probability Distribution:**
| \( x \) | \( P(x) \) |
|--------|------------|
| 0 | 0.25 |
| 1 | 0.3 |
| 2 | 0.05 |
| 3 | 0.4 |
**Question:**
Find the mean of this probability distribution. Round your answer to one decimal place.
**Solution:**
To find the mean \( \mu \) of a probability distribution, you use the formula:
\[
\mu = \sum (x \cdot P(x))
\]
Using the values in the table:
1. For \( x = 0 \), \( x \cdot P(x) = 0 \cdot 0.25 = 0 \)
2. For \( x = 1 \), \( x \cdot P(x) = 1 \cdot 0.3 = 0.3 \)
3. For \( x = 2 \), \( x \cdot P(x) = 2 \cdot 0.05 = 0.1 \)
4. For \( x = 3 \), \( x \cdot P(x) = 3 \cdot 0.4 = 1.2 \)
Now, sum these values:
\[
\mu = 0 + 0.3 + 0.1 + 1.2 = 1.6
\]
So, the mean of the probability distribution is **1.6**.
**Answer:** 1.6
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