Theoretical DistributionsMCQMTP Dec 2022 Series IQuestion 3535 of 230
All Questions

In _________ distribution, mean = variance.

Options

ANormal
BBinomial
CPoisson
DNone of these
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Correct Answer

✅ Option c — Poisson

All Options:

  • ANormal
  • BBinomial
  • CPoisson
  • DNone of these

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Detailed Solution & Explanation

**Distribution where Mean = Variance** Let us analyze the relationship between the mean and variance for each distribution: 1. **Normal Distribution:** - Mean = mu\displaystyle \\mu - Variance = sigma2\displaystyle \\sigma^2 - These are independent parameters and are not necessarily equal. 2. **Binomial Distribution:** - Mean = np\displaystyle np - Variance = npq=np(1−p)\displaystyle npq = np(1-p) - Since 0<q<1\displaystyle 0 < q < 1 (for a non-degenerate case), the variance npq\displaystyle npq is always strictly less than the mean np\displaystyle np. 3. **Poisson Distribution:** - The parameter m\displaystyle m represents both the mean and the variance of the distribution. - Therefore, textMean=textVariance=m\displaystyle \\text{Mean} = \\text{Variance} = m always holds. Reflecting the properties of these distributions, the Poisson distribution is the one where mean equals variance, which corresponds to Option C. Hence, **Option C** 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.

Key Concepts to Understand

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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