Theoretical DistributionsMCQPYQ Jan. 21Question 3547 of 230
All Questions

For a normal distribution, the value of third moment about mean is.

Options

A0
B1
C2
D3
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Correct Answer

✅ Option a — 0

All Options:

  • A0
  • B1
  • C2
  • D3

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Detailed Solution & Explanation

**Third Central Moment of a Normal Distribution** The central moments μr\displaystyle \mu_r of a distribution represent the expectation of the deviations from the mean raised to the r\displaystyle r-th power: μr=E[(X−μ)r]\mu_r = E[(X - \mu)^r] - The third central moment μ3=E[(X−μ)3]\displaystyle \mu_3 = E[(X - \mu)^3] is a measure of the asymmetry (skewness) of the distribution. - A normal distribution is perfectly symmetrical about its mean μ\displaystyle \mu. - For any symmetric probability distribution, all odd-order central moments are zero because the deviations above the mean cancel out the deviations below the mean: μ1=μ3=μ5=…=0\mu_1 = \mu_3 = \mu_5 = \ldots = 0 Therefore, for a normal distribution: μ3=0\mu_3 = 0 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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