Proof of VAR(aX + b) = a2VAR(X)
Using the formula:
VAR(X) = E(X2) – [E(X)]2
= E[(aX + b)2] – [E(aX + b)]2
= E(a2X2 + 2abX +b2) – [aE(X) + b]2
= a2E(X2) + 2abE(X) + b2 − a2[E(X)]2 − 2abE(X) − b2
= a2E(X2) – a2[E(X)]2
= a2(E(X2) – [E(X)]2 )
= a2 VAR(X)
This proof should be followed, but does not need to be memorised.
Close Window