Question

The coefficient of variation of Poisson distribution with mean 36 is

• A. \(\frac{1}{6} \times 100\)
• B. \(6 \times 100\)
• C. \(4 \times 100\)
• D. \(2 \times 100\)

Hint:

For Poisson distribution, \(CV = \frac{1}{\sqrt{\lambda}} \times 100\).
This is useful for comparing variability across different Poisson distributions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For a Poisson distribution, the mean and variance are equal to \(\lambda\).
The coefficient of variation is \(\frac{\sigma}{\mu} \times 100\).

Step 2: Key Formula or Approach:
For Poisson, \(\mu = \lambda\), \(\sigma = \sqrt{\lambda}\).
\[ CV = \frac{\sqrt{\lambda}}{\lambda} \times 100 = \frac{1}{\sqrt{\lambda}} \times 100. \]

Step 3: Detailed Explanation:
Given \(\lambda = 36\).
Then \(\sqrt{\lambda} = 6\).
So \(CV = \frac{1}{6} \times 100\).
This is option (A).
The coefficient of variation for Poisson decreases as the mean increases.
For large \(\lambda\), the distribution becomes more symmetric.