The first four moments of a distribution about the value 5 are 2, 20, 40 & 50.Fourth moment about the mean is​

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The first four moments of a distribution about the value 5 are 2, 20, 40 & 50.Fourth moment about the mean is​

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  1. Given : The first four moments of a distribution about the value 5 are 2, 20, 40 & 50. Fourth moment about the mean is ?

    Answer :

    we have given that,

    • u₁ = 2
    • u₂ = 20
    • u₃ = 40
    • u₄ = 50 .

    so,

    → Fourth moment about the mean = u₄ – 4 * u₁ * u₃ + 6 * u₂ * (u₁)² – 3 * (u₁)⁴

    putting values we get,

    → Fourth moment about the mean = 50 – 4 * 2 * 40 + 6 * 20 * (2)² – 3 * (2)⁴

    → Fourth moment about the mean = 50 – 320 + 480 – 48

    → Fourth moment about the mean = 530 – 368

    → Fourth moment about the mean = 162 (Ans.)

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