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Unformatted text preview: Probability Review John Norstad email@example.com http://homepage.mac.com/j.norstad September 11, 2002 Updated: February 10, 2005 Abstract We define and review the basic notions of variance, standard deviation, covari- ance, and correlation coefficients for random variables. We give proofs of their basic properties. 1 DEFINITIONS AND SUMMARY OF THE PROPOSITIONS 1 1 Definitions and Summary of the Propositions Definition 1 E ( X ) = the expected value of a random variable X is the mean or average value of X . Definition 2 Var ( X ) = the variance of X = E ([ X- E ( X )] 2 ) . Definition 3 Stdev ( X ) = the standard deviation of X = p Var ( X ) . Definition 4 Cov ( X, Y ) = the covariance of X and Y = E ([ X- E ( X )][ Y- E ( Y )]) . Definition 5 Cor ( X, Y ) = the correlation coefficient of X and Y = Cov ( X,Y ) Stdev ( X ) Stdev ( Y ) . Proposition 1: Var( X ) = E( X 2 )- E( X ) 2 Proposition 2: Var( aX + b ) = a 2 Var( X ) Proposition 3: Stdev( aX + b ) = | a | Stdev( X ) Proposition 4: Cov( X, Y ) = E( XY )- E( X )E( Y ) Proposition 5: Cov( aX + b, cY + d ) = ac Cov( X, Y ) Proposition 6: Cov( X, X ) = Var( X ) Proposition 7: Cov( X, Y ) = Cov(...
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This note was uploaded on 10/16/2011 for the course ECONOMICS 655 taught by Professor Jeaneid during the Fall '11 term at Wilfred Laurier University .
- Fall '11