Var(∑AiYi): Calculating & Explaining the Formula

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