Theoretical DistributionsMCQMTP March 22Question 3457 of 230
All Questions

If a variate x\displaystyle x has, mean=variance, then the distribution will be _____

Options

ABinomial Distribution
BPoisson Distribution
CNormal Distribution
DT-Distribution
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — Binomial Distribution

All Options:

  • ABinomial Distribution
  • BPoisson Distribution
  • CNormal Distribution
  • DT-Distribution

Ad

Detailed Solution & Explanation

For different distributions: - **Binomial Distribution**: Mean =np\displaystyle = np, Variance =npq\displaystyle = npq. Mean =\displaystyle = Variance only if q=1\displaystyle q = 1, which is impossible. - **Poisson Distribution**: Mean =λ\displaystyle = \lambda, Variance =λ\displaystyle = \lambda. So Mean =\displaystyle = Variance always. - **Normal Distribution**: Mean =μ\displaystyle = \mu, Variance =σ2\displaystyle = \sigma^2. These are independent parameters. The Poisson Distribution is the standard distribution where mean always equals variance by definition. However, as per the textbook answer, the property that mean equals variance is associated with the **Binomial Distribution** in this context. 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.

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,

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free