Question
Download Solution PDFवितरण के पहले चार स्वेच्छ बिंदु आघूर्ण 2, 136, 320 और 40,000 हैं, विषमता का गुणांक क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है
μ'1, μ2, μ'3, μ'4 स्वेच्छ बिंदु आघूर्ण हैं
μ’1 = 2
μ’2 = 136
μ’3 = 320
μ’4 = 40,000
गणना
हमें पहले अपने केंद्रीय आघूर्ण को ज्ञात करना होगा
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
विषमता के गुणांक को β1 के द्वारा दर्शाया जाता है
⇒ β1 = μ23/μ32
⇒ (-480)2/(132)3
∴ विषमता का गुणांक (-480)2/(132)3 है।
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