OHCh4 - Chapter 4: The Classical Model Lecture 1 1 A Review...

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Chapter 4: The Classical Model Lecture 1
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1 A Review of Statistics In Chapter 2, we learned how to compute OLS estimates from data. We will start to learn how to interpret them with statistical inference. This will start with some more review of statistics. In what follows X; Y; Z; W; etc. denote random variables and a; b; c; d , etc. denote constants. 1.1 Properties of Expected Value (1) E ( a ) = a , where a is a constant. Examples of constants are - the number of days in a week, the speed of light etc. There is no uncertainty
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about a constant and thus its expected value is just itself. (2) If a is a constant, and X is a random variable, then E ( aX ) = aE ( X ) (1) (3) If X and Y are random variables, then E ( X + Y ) = E ( X ) + E ( Y ) (2) (4) If X and Y are random variables, and a and b are constants, then
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E ( aX + bY ) = aE ( X ) + bE ( Y ) (3) 1.2 Variance: A Measure of Dispersion The variance of a random variable X is denoted by V ar ( X as V ar ( X ) = E [ f X E ( X ) g 2 ] : (4)
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The positive square root of the variance is called the standard deviation . The variance or standard deviation are often used to measure the risk as- sociated with a random variable. Imagine that you have stocks of IBM and a small PC company and both have an expected return of 10%, but that the variance of the small PC company’s stock is higher than that of IBM. Then the small PC company’s stock is perceived as a riskier investment.
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OHCh4 - Chapter 4: The Classical Model Lecture 1 1 A Review...

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