Why does Var(∑AiYi) = ∑(Ai²)Var(Yi)?

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

Discussion

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.
 

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