Probability Scores 0.16 0 0.08 3 0.24 11 0.17 13 0.35 14 Find the expected value of the above random variable.
Probability Scores 0.16 0 0.08 3 0.24 11 0.17 13 0.35 14 Find the expected value of the above random variable.
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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![### Understanding Expected Value in Probability
In this section, we will learn how to calculate the expected value of a random variable using a given probability distribution.
#### Example:
We are given a table that lists different scores and their corresponding probabilities.
| Probability | Scores |
|-------------|--------|
| 0.16 | 0 |
| 0.08 | 3 |
| 0.24 | 11 |
| 0.17 | 13 |
| 0.35 | 14 |
**Task**: Find the expected value of the above random variable.
The expected value \(E(X)\) of a discrete random variable \(X\) is calculated as follows:
\[ E(X) = \sum [P(x_i) \cdot x_i] \]
Where:
- \( P(x_i) \) is the probability of each outcome
- \( x_i \) is the value of each outcome
**Steps to Calculate**:
1. **Multiply each score by its corresponding probability**.
2. **Sum up all these products**.
**Calculation**:
\[
\begin{align*}
E(X) &= (0.16 \times 0) + (0.08 \times 3) + (0.24 \times 11) + (0.17 \times 13) + (0.35 \times 14) \\
&= 0 + 0.24 + 2.64 + 2.21 + 4.9 \\
&= 9.99
\end{align*}
\]
Therefore, the expected value of the given random variable is **9.99**.
#### Next Step:
Click the "Next Question" button to proceed with further exercises.
By understanding and applying this method, you can determine the expected value for various probability distributions!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9d300d-1c07-4ae7-bdcf-7bcca0d57eba%2F331af12e-52c5-4e6b-9d0a-63fa86d13062%2Fzzro6jj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Expected Value in Probability
In this section, we will learn how to calculate the expected value of a random variable using a given probability distribution.
#### Example:
We are given a table that lists different scores and their corresponding probabilities.
| Probability | Scores |
|-------------|--------|
| 0.16 | 0 |
| 0.08 | 3 |
| 0.24 | 11 |
| 0.17 | 13 |
| 0.35 | 14 |
**Task**: Find the expected value of the above random variable.
The expected value \(E(X)\) of a discrete random variable \(X\) is calculated as follows:
\[ E(X) = \sum [P(x_i) \cdot x_i] \]
Where:
- \( P(x_i) \) is the probability of each outcome
- \( x_i \) is the value of each outcome
**Steps to Calculate**:
1. **Multiply each score by its corresponding probability**.
2. **Sum up all these products**.
**Calculation**:
\[
\begin{align*}
E(X) &= (0.16 \times 0) + (0.08 \times 3) + (0.24 \times 11) + (0.17 \times 13) + (0.35 \times 14) \\
&= 0 + 0.24 + 2.64 + 2.21 + 4.9 \\
&= 9.99
\end{align*}
\]
Therefore, the expected value of the given random variable is **9.99**.
#### Next Step:
Click the "Next Question" button to proceed with further exercises.
By understanding and applying this method, you can determine the expected value for various probability distributions!
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