Question

The coefficient of variation of Poisson distribution with mean 9 is

• A. $100 \times 3$
• B. $100 \times 9$
• C. $100 \times (1/3)$
• D. $100 \times (1/9)$

Hint:

For any Poisson distribution, the coefficient of variation is simplified as $\text{CV} = \frac{\sqrt{\lambda}}{\lambda} \times 100 = \frac{100}{\sqrt{\lambda}}$. With $\lambda = 9$, $\text{CV} = \frac{100}{3}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Coefficient of Variation (CV) is a relative measure of dispersion, expressed as a percentage of the mean.
Key Formula or Approach:
The formula for the Coefficient of Variation is: \[ \text{CV} = \frac{\sigma}{\mu} \times 100 \] where $\sigma$ is the standard deviation and $\mu$ is the mean.

Step 2: Detailed Explanation:
For a Poisson distribution with parameter $\lambda$: \[ \text{Mean} (\mu) = \lambda \] \[ \text{Variance} (\sigma^2) = \lambda \implies \text{Standard Deviation} (\sigma) = \sqrt{\lambda} \]
Given that the mean of the Poisson distribution is $\lambda = 9$: \[ \mu = 9 \] \[ \sigma = \sqrt{9} = 3 \]
Substitute these values into the CV formula: \[ \text{CV} = \frac{3}{9} \times 100 = \frac{1}{3} \times 100 = 100 \times \left(\frac{1}{3}\right) \]
This calculation yields a coefficient of variation equal to $33.33%$.

Step 3: Final Answer:
The coefficient of variation is $100 \times (1/3)$.