Var( ∑AiYi)

1. Apr 18, 2006

milk

Var( ∑AiYi)= ∑(Ai^2) Var(Yi)
Could you show why?
Thank you

2. Apr 19, 2006

mathman

Your equation includes an assumption that the Y's are independent random variables. In this case, you only need to show it for one variable, i.e. var(AX)=A2var(X). This then can be shown by using the definition of var in terms of first and second moments.