= E (a(X E X ) b(Y E Y ))2 = E a2 (X E X )2 2 ab (X E X )(Y E Y ) b2 (Y E Y )2 = a2 Var X 2 ab Cov( X;Y ) b2 Var Y We have the following corollary Proposition 123 If X and Y are independent, then Var( X Y ) = Var X Var Y Proof We have Var( X Y ) = Var X Var Y 2Cov( X;Y ) = Var X Var Y Example 121 Recall that a binomial random variable is the sum of n independent
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