What is the expected value (mean) of X?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Probability Distribution and Expected Value**
Consider a random variable with the following probability distribution:
| X | P(X) |
|---|------|
| 0 | 0.25 |
| 1 | 0.5 |
| 2 | 0.25 |
**Question: What is the expected value (mean) of X?**
Choices:
- O 1.0
- O 2.0
- O 0
- O Can't be determined
To determine the expected value (mean) of a discrete random variable X, we use the following formula:
\[ E(X) = \sum [X \cdot P(X)] \]
Let's calculate:
\[ E(X) = (0 \cdot 0.25) + (1 \cdot 0.5) + (2 \cdot 0.25) \]
\[ E(X) = 0 + 0.5 + 0.5 \]
\[ E(X) = 1.0 \]
Thus, the expected value (mean) of X is 1.0. The correct answer is:
- O 1.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc42dbd0-41a9-480b-bad1-d3b723150fc3%2F02709f03-8e5d-4acc-a308-7dbe465e1a84%2Fyj2d4cj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability Distribution and Expected Value**
Consider a random variable with the following probability distribution:
| X | P(X) |
|---|------|
| 0 | 0.25 |
| 1 | 0.5 |
| 2 | 0.25 |
**Question: What is the expected value (mean) of X?**
Choices:
- O 1.0
- O 2.0
- O 0
- O Can't be determined
To determine the expected value (mean) of a discrete random variable X, we use the following formula:
\[ E(X) = \sum [X \cdot P(X)] \]
Let's calculate:
\[ E(X) = (0 \cdot 0.25) + (1 \cdot 0.5) + (2 \cdot 0.25) \]
\[ E(X) = 0 + 0.5 + 0.5 \]
\[ E(X) = 1.0 \]
Thus, the expected value (mean) of X is 1.0. The correct answer is:
- O 1.0
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