Theoretical DistributionsMCQMTP May 18Question 3515 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

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 of the Poisson distribution is E(X)=m\displaystyle E(X) = m and its variance is Var(X)=m\displaystyle \text{Var}(X) = m. Thus, the mean and variance are equal. - For a Binomial distribution, the mean is np\displaystyle np and the variance is npq\displaystyle npq. Since q=1−p<1\displaystyle q = 1 - p < 1, the mean is always greater than the variance. - For a Normal distribution, the mean μ\displaystyle \mu and variance σ2\displaystyle \sigma^2 are independent parameters. Therefore, mean = variance in the Poisson distribution. 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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