Question
Download Solution PDFदी गई प्रत्यागमन रेखाएं X + 2Y - 5 = 0, 2X + 3Y - 8 = 0 और Var(X) = 12 हैं, Var(Y) का मान है:
Answer (Detailed Solution Below)
Detailed Solution
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प्रत्यागमन रेखाएं
x + 2y - 5 = 0
2x + 3y - 8 = 0
var(x)= σx = 12
गणना
x + 2y - 5 = 0 ------(i)
माना x पर y की प्रत्यागमन रेखा y = - x/2 + 5/2 है [समीकरण 1 से]
2x + 3y - 8
x = -(3/2)y + 8/2, y पर x की प्रत्यागमन रेखा है
⇒ byx = -1/2 और bxy = -3/2
bxy = x पर y की प्रत्यागमन रेखा
byx = y पर x की प्रत्यागमन रेखा
हम जानते हैं कि y पर x की प्रत्यागमन गुणांक = r = √(byx × bxy)
⇒ r = √(-1/2 × -3/2)
∴ r = -√3/2 < 1
σx = \(\sqrt{12}\) = 2√3
हम जानते हैं कि byx = r(σy/σx)
⇒ -1/2 = -√3/2 (σy/2√3)
⇒ σy = 2
∴ var(y) = y का प्रसारण =(2)2 = 4
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