Question
Download Solution PDFThe first four moments of a distribution about the origin are -1.5, 17, -30 and 108. The third moment about the mean is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Moment about orgin are given
μ’1 = -1.5
μ’2 = 17
μ’3 = -30
μ’4 = 108
Formula
Moment about mean = μ1 = μ’1 – μ’1 = 0
μ2 = μ’2 –(μ’1)2
μ3 = μ’3 – 3μ’2 × μ’1 + 2(μ’1)3
Here, μ1, μ2, μ3 are first, second, and third moment about mean
Calculation
Third moment about mean are given as
⇒ (-30) – 3 × 17 × (- 1.5) + 2 × (-1.5)3
⇒ -30 + 76.5 – 6.75
⇒ 76.5 – 36.75
∴ Third moment about mean is 39.25
The second moment about mean represent sample variance (σ2)
The first moment about mean is always zero
Moment about origin = μ’r = 1/n(∑fi(Xi – A)
Where A = 0 we get various moment about origin
Last updated on Jun 13, 2025
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