Question
Download Solution PDFएक यादृच्छिक चर x के लिए, सभी क्रम के केंद्रीय क्षण (\(\mu \)i) मौजूद हैं। क्षण (\(\mu^2_2{_j}{_+}{_1}\)) के (2j + 1)वें का वर्ग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या
एक यादृच्छिक चर के लिए, सभी क्रम के केंद्रीय क्षण (μ) मौजूद हैं
क्षण (\(\mu^2_2{_j}{_+}{_1}\)) के (2j + 1)वें का वर्ग
मान लीजिये कि j = 1 है तो (2j + 1)वां क्षण निम्न रूप से दिया गया है
(μ23) = [(∑(x – x̅)3/N]2
⇒ (∑x3/N)2 ------(i)
यदि j = 1 तो μ2 = ∑x2/N
⇒ μ2j + 2 यदि j = 1 तो
⇒ μ4 = ∑x4/N
⇒ μ2 × μ2j + 2 = ∑x2/N × ∑x4/N ------(ii)
दोनों समीकरणों की तुलना करने पर
(∑x3)2/N2 = (∑x2 × ∑x4)/N2
⇒ (∑x3)2 ≤ (∑x2 × ∑x4)
∴ (μ2j + 1)2 ≤ μ2j × μ2j + 2
Last updated on Jul 16, 2025
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