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**Unformatted text preview: **This proves the formula for the mean. Now for the formula for the variance. First, recall that σ 2 p = Cov( R p , R p ) . By repeated applications of the third rule: Cov( R p , R p ) = Cov( X 1 R 1 + X 2 R 2 , X 1 R 1 + X 2 R 2 ) = Cov( X 1 R 1 , X 1 R 1 ) + Cov( X 2 R 2 , X 2 R 2 ) + 2Cov( X 1 R 1 , X 2 R 2 ) . Finally, applying the fourth rule: Cov( R p , R p ) = X 2 1 Cov( R 1 , R 1 ) + X 2 2 Cov( R 2 , R 2 ) + 2 X 1 X 2 Cov( R 1 , R 2 ) = X 2 1 σ 2 1 + X 2 2 σ 2 2 + 2 X 1 X 2 Cov( R 1 , R 2 ) . This completes the proof of the variance formula....

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