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Question

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

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

μ2 = μ2' - (μ1')2

The correct formula for converting between moments about the origin and moments about the mean is: μ2 = μ2' - (μ1')2.

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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. 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:

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

  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:

  6. μ' (r) and μ' rrepresent the factorial moment of order r about the origin and r th moment about the origin of the distribution x i|f i, i = 1, 2, … n. The value of μ' 2equals to:

  7. The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness β z?

  8. For a random variable x, the central moments ( \(\mu \)i ) of all order exist. The square of (2j + 1) th moment ( \(\mu^2_2{_j}{_+}{_1}\) ) is


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. 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:

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

  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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