Theoretical DistributionsMCQMTP March 21Question 3511 of 230
All Questions

In Poisson distribution which of them is same.

Options

AMean and variance
BMean and SD
Cboth (a) & (b)
DNone of these
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Correct Answer

✅ Option a — Mean and variance

All Options:

  • AMean and variance
  • BMean and SD
  • Cboth (a) & (b)
  • DNone of these

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Detailed Solution & Explanation

For a Poisson distribution with parameter m\displaystyle m, the probability mass function is given by: P(X=k)=e−mmkk!P(X = k) = \frac{e^{-m} m^k}{k!} The mean and the variance of a Poisson distribution are both equal to the parameter m\displaystyle m. The standard deviation is given by m\displaystyle \sqrt{m}, which is not generally equal to the mean unless m=1\displaystyle m = 1. Therefore, the mean and the variance of a Poisson distribution are always equal, which corresponds to Option A. Note: The source key indicates Option B (Mean and SD), but this only holds true for the specific case when the parameter m=1\displaystyle m = 1. The general characteristic of any Poisson distribution is that the mean and variance are equal. Hence, **Option A** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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