Lecture 9

# Lecture 9 - Diversification r 0 Random variable ~ a number...

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 9, Spring 2010, page 1 Diversification 0. Random variable ( r ~ ): a number whose realization is not yet known 0.1 Expected value: probability weighted average of all possible outcomes E( r ~ ) = Pr 1 r 1 + Pr 2 r 2 + Pr 3 r 3 + … + Pr n r n = n s s s r 1 Pr 0.2 Variance : a measure of the spread of the probability distribution σ 2 ( r ~ ) = n s s s r E r 1 2 )) ~ ( ( Pr for a small sample : σ 2 (r) = 1 )) ( ( 1 2 n r E r n s s 0.3 Standard Deviation : also a measure of the spread σ( r ~ ) = ) ~ ( 2 r = n s s s r E r 1 2 )) ~ ( ( Pr for a small sample : σ(r) = ) ( 2 r = 1 )) ( ( 1 2 n r E r n s s 0.4 Covariance: measure of the relationship between two random variables Cov( r ~ 1 , r ~ 2 ) = Pr 1 [r 1 (1) – E( r ~ 1 )][r 2 (1) – E( r ~ 2 )] + … + Pr n [r 1 (n) – E( r ~ 1 )][r 2 (n) – E( r ~ 2 )]

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 9, Spring 2010, page 2 = n s s r E s r r E s r 1 2 2 1 1 )] ~ ( ) ( )][ ~ ( ) ( [ Pr small sample: Cov(r 1 , r
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## This note was uploaded on 07/21/2010 for the course ECON 1710 taught by Professor Qiu during the Spring '10 term at Brown.

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Lecture 9 - Diversification r 0 Random variable ~ a number...

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