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Question
Prove that V(X + b) = V(X)
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Solution
L.H.S = V(x + b)
= E(x + b)2 – [E(x + b)]2
= E(x2 + 2bx + b2) – [E(x) + b]2
= E(x2) + 2bE(x) + b2 – [E(x)]2 + b2 + 2bE(x)]
= E(x2) + 2bE(x) + b2 – [E(x)]2 + b2 – 2bE(x)]
= E(x2) – [E(x)]2
= V(x)
= R.H.S
L.H.S = R.H.S
Hence proved.
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