Question
Download Solution PDFयदि x के विचरण का अंकगणित औसत और गुणांक क्रमशः 10 और 40 हैं, तो y = 10 - 2x का विचरण है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है
समान्तर माध्य = (μ) = 10
विचरण के गुणांक = CV = 40% या 0.4
सूत्र
CV = σ/μ
σ = मानक विचलन
μ = औसत
गणना
0.4 = σ/10
⇒ σ/ = मानक विचलन = 0.4 × 10 = 4
अब, विचरण = V = (मानक विचलन)2 = σ2
⇒ विचरण = 42 = 16
हम जानते हैं कि V(ax + b) = a2(V(x)
⇒ V(10 - 2x) = (-2)2 V(X)
⇒ V(10 - 2x) = 4V(x)
∴ V(10 - 2x) = 4 × 16 = 64
Important Points
मानक विचलन का प्रतीक = σ
विचरण = मानक विचलन का वर्ग = σ2
विचरण गुणांक = CV = CV = σ/μ
μ = जनसंख्या माध्य
Last updated on Jun 13, 2025
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