Theoretical DistributionsMCQPYQ Nov. 20Question 3545 of 230
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If we change the parameter(s) of a distribution the shape of probability curve does not change.

Options

ANormal
BBinomial
CPoisson
DNon-Gaussian
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Correct Answer

✅ Option a — Normal

All Options:

  • ANormal
  • BBinomial
  • CPoisson
  • DNon-Gaussian

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Detailed Solution & Explanation

**Effect of Parameter Changes on Probability Curves** Let us analyze how changing parameters affects the shape of different probability curves: - **Binomial Distribution**: The shape of the curve is determined by its parameters n\displaystyle n and p\displaystyle p. If p=0.5\displaystyle p = 0.5, it is symmetric. If p≠0.5\displaystyle p \neq 0.5, it is skewed. Thus, changing p\displaystyle p directly alters the shape of the probability curve. - **Poisson Distribution**: The shape is determined by the parameter m\displaystyle m. The skewness is given by 1/m\displaystyle 1/\sqrt{m}, meaning the curve becomes more symmetrical as m\displaystyle m increases. Changing m\displaystyle m alters the shape of the curve. - **Normal Distribution**: The normal distribution is defined by two parameters: mean μ\displaystyle \mu and standard deviation σ\displaystyle \sigma. 1. Changing μ\displaystyle \mu shifts the curve left or right along the horizontal axis, but has no effect on its shape. 2. Changing σ\displaystyle \sigma changes the spread (flatness or peakedness), but the curve always remains a symmetric, bell-shaped curve. In statistical theory, the fundamental bell-shaped, symmetric nature of the normal probability curve is considered invariant under parameter changes. 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

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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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