Question

The coefficient of variation of Poisson distribution with mean 9 is:

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

Hint:

Exam Tip:
For Poisson distribution:

• Mean \(=\) Variance \(= \lambda\).
• Standard Deviation \(= \sqrt{\lambda}\).
• Coefficient of Variation \(= \frac{1}{\sqrt{\lambda}}\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The coefficient of variation (CV) is defined as: \[ \text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}} \]

Step 2: Key Formula or Approach:
For a Poisson distribution with parameter \(\lambda\) (mean):
• Mean \(= \lambda\).
• Variance \(= \lambda\).
• Standard Deviation \(= \sqrt{\lambda}\). So, \(\text{CV} = \frac{\sqrt{\lambda}}{\lambda} = \frac{1}{\sqrt{\lambda}}\).

Step 3: Detailed Explanation:
Given mean \(\lambda = 9\): \[ \text{CV} = \frac{1}{\sqrt{9}} = \frac{1}{3} \]

Step 4: Final Answer:
Therefore, option (B) is correct.