The following is a Poisson probability distribution with P(x) 0 0.9020 1 0.0835 2 0.0115 3 0.0030 The variance of the distribution is XO
The following is a Poisson probability distribution with P(x) 0 0.9020 1 0.0835 2 0.0115 3 0.0030 The variance of the distribution is XO
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
11. Multiple Choice
-
0.3800
-
0.8990
-
3.0000
-
1.0000
![### Poisson Probability Distribution Example
The following is a Poisson probability distribution with a mean (\(\mu\)) of 0.4.
#### Probability Distribution Table:
| x | \(P(x)\) |
|---|----------|
| 0 | 0.9020 |
| 1 | 0.0835 |
| 2 | 0.0115 |
| 3 | 0.0030 |
The variance of the distribution is ______.
In this table, \(x\) represents the number of occurrences, and \(P(x)\) represents the probability of \(x\) occurrences happening.
- When \(x = 0\), the probability \(P(x)\) is 0.9020.
- When \(x = 1\), the probability \(P(x)\) is 0.0835.
- When \(x = 2\), the probability \(P(x)\) is 0.0115.
- When \(x = 3\), the probability \(P(x)\) is 0.0030.
### Important Concept: Variance in Poisson Distribution
For a Poisson distribution, the mean (\(\mu\)) and variance (\(\sigma^2\)) are equal. Therefore, for this distribution:
\[ \mu = 0.4 \]
\[ \text{Variance} (\sigma^2) = 0.4 \]
Understanding this property of Poisson distribution simplifies many calculations related to the distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55f0052a-9d0d-41a8-9339-203ce40e3605%2F50e94b8c-0f2e-4261-9cd3-fa333ec207af%2Fw7y1haq_processed.png&w=3840&q=75)
Transcribed Image Text:### Poisson Probability Distribution Example
The following is a Poisson probability distribution with a mean (\(\mu\)) of 0.4.
#### Probability Distribution Table:
| x | \(P(x)\) |
|---|----------|
| 0 | 0.9020 |
| 1 | 0.0835 |
| 2 | 0.0115 |
| 3 | 0.0030 |
The variance of the distribution is ______.
In this table, \(x\) represents the number of occurrences, and \(P(x)\) represents the probability of \(x\) occurrences happening.
- When \(x = 0\), the probability \(P(x)\) is 0.9020.
- When \(x = 1\), the probability \(P(x)\) is 0.0835.
- When \(x = 2\), the probability \(P(x)\) is 0.0115.
- When \(x = 3\), the probability \(P(x)\) is 0.0030.
### Important Concept: Variance in Poisson Distribution
For a Poisson distribution, the mean (\(\mu\)) and variance (\(\sigma^2\)) are equal. Therefore, for this distribution:
\[ \mu = 0.4 \]
\[ \text{Variance} (\sigma^2) = 0.4 \]
Understanding this property of Poisson distribution simplifies many calculations related to the distribution.
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