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Lecture2

Lecture2 - Lecture 2 Review of Statistics Econ 444 Winter...

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Lecture 2 : Review of Statistics Econ 444, Winter 2010 Jan 11, 2010

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Some useful properties of expected value : E ( a ) = a , where a is a constant. If a is a constant, and X is a random variable, then E ( aX ) = aE ( X ) If X and Y are random variables, then E ( X + Y ) = E ( X ) + E ( Y )
So far. .. Done Summation of a Variable denoted by the symbol . Done Done Expectation of a random variable X denoted (usually) by E ( X ) . Today we will review : 4 Variance and Correlation. 5 Population vs Sample.

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4. Variance and Correlation Variance The variance of a random variable X is denoted by Var ( X ) and is deﬁned as : Var ( X ) = E [ { X - E ( X ) } 2 ] = N X i = 1 P [ X i ] { X i - E ( X ) } 2 (1) The standard deviation denoted by S . D ( X ) is simply, S . D ( X ) = q Var ( X ) (2) Variance or squared deviation is a measure of how far the variable X is from its mean value E ( X ) . Higher the variance more volatile the variable X is on an average.
Fig 1 : Variance in Price of Coffee

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Let X i be the number resulting from a roll of a 6-sided die. Suppose we know that the probability distribution of X i is : P [ X i ] X i P [ X i ] X i X i - E ( X ) ( X i - E ( X )) 2 P [ X i ]( X i - E ( X )) 2 1/6 1 1/6 -2.5 6.25 1.04167 1/6 2 2/6 -1.5 2.25
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Lecture2 - Lecture 2 Review of Statistics Econ 444 Winter...

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