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Unformatted text preview: 109 = 0.2089 (0.5075)(0.5364) That is, there is a positive correlation between the number of lines in a newspaper ad and the volume of inquiries about the apartment rental. 34 Chapter 5 Useful Results for the Variance of a Linear Combination of Random Variables For two random variables X and Y a result is: Var(X + Y ) = Var(X ) + Var(Y ) + 2 Cov(X , Y ) This result can be shown: Var(X + Y ) = E[{ X + Y − E(X + Y )} 2 ] = E[{(X − E(X )) + (Y − E(Y ))} 2 ] = E[(X − E(X ))2 + (Y − E(Y ))2 + 2 (X − E(X ))(Y − E(Y ))] = E[(X − E(X ))2 ] + E[(Y − E(Y ))2 ] + 2 E[(X − E(X ))(Y − E(Y ))] = Var(X ) + Var(Y ) + 2 Cov(X , Y ) Another result is: Var(X − Y ) = Var(X ) + Var(Y ) − 2 Cov(X , Y ) When X and Y are independent then the covariance is zero and: Var(X + Y ) = Var(X − Y ) = Var(X ) + Var(Y ) For constant fixed numbers a and b, a general rule is: 35 Var (aX + bY ) = a 2 Var ( X ) + b2 Var (Y ) + 2 a b Cov( X , Y ) Chapter 5 Example: Portfolio Analysis, Example 5.18 page 177. The job of a financial advisor may be to recommend a mix of stocks or a portfolio for investment purposes. Consider the random variables: X 1 price of one share of stock for company A X 2 price of one share of stock for compa...
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This note was uploaded on 02/06/2014 for the course ECON ECON 325 taught by Professor Whistler during the Spring '10 term at UBC.

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