Find the mean of the following probability distribution. Round your answer to one decimal. P(x) 0.40 0.15 0.13 0.05 0.27 X 0 1 2 3 4 mean =
Find the mean of the following probability distribution. Round your answer to one decimal. P(x) 0.40 0.15 0.13 0.05 0.27 X 0 1 2 3 4 mean =
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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![### Finding the Mean of a Probability Distribution
**Problem Statement:**
Find the mean of the following probability distribution. Round your answer to one decimal.
**Data Table:**
| \( x \) | \( P(x) \) |
|:------:|:----------:|
| 0 | 0.40 |
| 1 | 0.15 |
| 2 | 0.13 |
| 3 | 0.05 |
| 4 | 0.27 |
**Formula for the Mean of a Probability Distribution:**
The mean (also called the expected value) of a probability distribution is calculated using the formula:
\[
\mu = \sum [x \cdot P(x)]
\]
**Step-by-Step Calculation:**
1. **Calculate each term \( x \cdot P(x) \):**
- For \( x = 0 \): \( 0 \cdot 0.40 = 0 \)
- For \( x = 1 \): \( 1 \cdot 0.15 = 0.15 \)
- For \( x = 2 \): \( 2 \cdot 0.13 = 0.26 \)
- For \( x = 3 \): \( 3 \cdot 0.05 = 0.15 \)
- For \( x = 4 \): \( 4 \cdot 0.27 = 1.08 \)
2. **Sum up all the terms:**
\[
0 + 0.15 + 0.26 + 0.15 + 1.08 = 1.64
\]
3. **Round the sum to one decimal place:**
\[
1.64 \approx 1.6
\]
**Conclusion:**
\[
\text{Mean} = 1.6
\]
So, the mean of the given probability distribution is 1.6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82a8ebfc-76c9-419b-9ea9-29a90be836d5%2Fd034be6d-bd08-4ff6-9648-85b6f3e35897%2F7983b8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Mean of a Probability Distribution
**Problem Statement:**
Find the mean of the following probability distribution. Round your answer to one decimal.
**Data Table:**
| \( x \) | \( P(x) \) |
|:------:|:----------:|
| 0 | 0.40 |
| 1 | 0.15 |
| 2 | 0.13 |
| 3 | 0.05 |
| 4 | 0.27 |
**Formula for the Mean of a Probability Distribution:**
The mean (also called the expected value) of a probability distribution is calculated using the formula:
\[
\mu = \sum [x \cdot P(x)]
\]
**Step-by-Step Calculation:**
1. **Calculate each term \( x \cdot P(x) \):**
- For \( x = 0 \): \( 0 \cdot 0.40 = 0 \)
- For \( x = 1 \): \( 1 \cdot 0.15 = 0.15 \)
- For \( x = 2 \): \( 2 \cdot 0.13 = 0.26 \)
- For \( x = 3 \): \( 3 \cdot 0.05 = 0.15 \)
- For \( x = 4 \): \( 4 \cdot 0.27 = 1.08 \)
2. **Sum up all the terms:**
\[
0 + 0.15 + 0.26 + 0.15 + 1.08 = 1.64
\]
3. **Round the sum to one decimal place:**
\[
1.64 \approx 1.6
\]
**Conclusion:**
\[
\text{Mean} = 1.6
\]
So, the mean of the given probability distribution is 1.6.
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