Question
Download Solution PDFमान लीजिए X और Y के बीच सहसंबंध गुणांक 0.6 है। यादृच्छिक चर Z और W इस प्रकार परिभाषित हैं कि Z = X + 5 और
Answer (Detailed Solution Below)
Detailed Solution
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माना कि Z = aX + bY
Z की प्रत्याशा = E(Z) = aE(X) + bE(Y)
Z का प्रसरण = Var(Z) = a2Var(X) + b2Var(Y) + 2abρXYσXσY
ρXY = X और Y का सहसंबंध गुणांक
X और Y का सहप्रसरण = Cov(X, Y) = E(XY) - E(X)E(Y)
यदि Z = X + a जहां a कुछ स्थिरांक है तो Var(Z) = Var(X)
X और Y का सहप्रसरण = Cov(X, Y) = E(XY) - E(X)E(Y)
गणना
Z = X + 5
⇒ Var(Z) = Var(X)
⇒ σZ = σX
Cov(Z, W)
= E(ZW) – E(Z)E(W)
Z और W का सहसंबंध गुणांक है
= ρXY
So ρZW = ρXY = 0.6
सही विकल्प (4) है।
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