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Question

Given below are moments about an arbitrary origin 5.
If μ'1 = -4, μ'2 = 22, μ'3 = -117 and μ'4 = 560, then μ3 is equal to:

This question was previously asked in
SSC CGL 2023 (Tier-II) Paper 1 Previous Year Paper (26-Oct-2023) (Shift-1)
The correct answer is

19

To convert central moments from moments about arbitrary origin, use the transformation formulas. For the third moment: μ3 = μ'3 - 3μ'1μ'2 + 2(μ'1)3
= -117 - 3(-4)(22) + 2(-4)3 = -117 + 264 - 128 = 19.

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Similar Questions

  1. The first four moments of a distribution about the value 2 are 1, 2.5, 5.5 and 16. What is the 4th moment about zero?

  2. The third order central moment of normal distribution is:

  3. If μ'r and μr, respectively, denote rth order moments about origin and mean, then:

  4. The standard deviation of a symmetrical distribution is 3. What must be the value of the fourth moment about the mean for the distribution to be mesokurtic?

  5. The first four moments of a distribution about the origin are -1.5, 17, -30 and 108. The third moment about the mean is:

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Important Questions from Central Moments

  1. The first four moments of a distribution about the value 2 are 1, 2.5, 5.5 and 16. What is the 4th moment about zero?

  2. The third order central moment of normal distribution is:

  3. If μ'r and μr, respectively, denote rth order moments about origin and mean, then:

  4. The standard deviation of a symmetrical distribution is 3. What must be the value of the fourth moment about the mean for the distribution to be mesokurtic?

  5. The first four moments of a distribution about the origin are -1.5, 17, -30 and 108. The third moment about the mean is:

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