Hi, can someone help me prove this theorem:
If X has the variance σ^2 then var(aX+b)=[a^2]*[σ^2]
And I'm sure there's a proof somewhere on MHF. The Search toll might uncover it (as well as other interesting things).
What attempt have you made on the proof?
This is what I've worked on
Var(aX +b) = E[(aX +b)^2] − (E[aX +b])^2
= E[a^2X^2+2abX +b^2] − (aE[X] + b)^2
= a^2E[X2] + 2abE[X] + b^2
−(a^2(E[X])2+2abE[X] + b^2)
= a^2(E[X^2] − (E[X])^2)
I'm not the best with proofs so I'd like to see whether its the same as someone else's