Question
Download Solution PDFThe first four raw moments of distribution are 2, 136, 320, and 40,000, The coefficient of skewness is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
μ'1, μ2, μ'3, μ'4 are raw moments
μ’1 = 2
μ’2 = 136
μ’3 = 320
μ’4 = 40,000
Calculation
We have to find the first our central moments
μ1 = μ’1 = 2
μ2 = μ’2 – (μ’1)2
⇒ 136 – (2)2
⇒ 136 – 4
⇒ 132
μ3 = μ’3 – 3 × μ’2μ’1 + 2 × (μ’1)3
⇒ 320 – 3 × 136 × 2 + 2 × (2)3
⇒ 320 – 816 + 16
⇒ - 480
μ4 = μ’4 – 4 × μ’1 × μ’3 + 6 × μ’2 × (μ’1)2 – 3 × (μ’1)4
⇒ 40000 – 4 × 2 × 320 + 6 × 136 × 22 – 3 × 24
⇒ 40000 – 2560 + 3264 – 48
⇒ 40656
The coefficient of skewness denoted by β1
⇒ β1 = μ23/μ32
⇒ (-480)2/(132)3
∴ The coefficient of skewness is (-480)2/(132)3
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