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Var( ∑AiYi)

  1. Apr 18, 2006 #1
    Var( ∑AiYi)= ∑(Ai^2) Var(Yi)
    Could you show why?
    Thank you
  2. jcsd
  3. Apr 19, 2006 #2


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    Science Advisor

    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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