Theoretical DistributionsMTP June 2023 Series IIQuestion 3977 of 230
All Questions

The mean and variance are equal for which of the following:

Options

APoisson Distribution
BNormal Distribution
CGaussian Distribution
DNone of these
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Correct Answer

✅ Option a — Poisson Distribution

All Options:

  • APoisson Distribution
  • BNormal Distribution
  • CGaussian Distribution
  • DNone of these

Detailed Solution & Explanation

**Distribution with Equal Mean and Variance** Let us examine the properties of the listed probability distributions: **1. Poisson Distribution:** For a Poisson distribution with parameter m\displaystyle m, the probability mass function is: P(X=x)=frace−mmxx!P(X = x) = \\frac{e^{-m} m^x}{x!} - Mean (E(X)\displaystyle E(X)) = m\displaystyle m - Variance (textVar(X)\displaystyle \\text{Var}(X)) = m\displaystyle m Since both the mean and the variance are equal to m\displaystyle m, the relation textMean=textVariance\displaystyle \\text{Mean} = \\text{Variance} always holds. **2. Normal (Gaussian) Distribution:** For a Normal distribution N(mu,sigma2)\displaystyle N(\\mu, \\sigma^2): - Mean = mu\displaystyle \\mu - Variance = sigma2\displaystyle \\sigma^2 Here, mu\displaystyle \\mu and sigma2\displaystyle \\sigma^2 are independent parameters, so they are not necessarily equal. **Conclusion:** The mean and variance are equal for the **Poisson Distribution**, which corresponds to Option A. 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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For a Poisson distribution,

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