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Unformatted text preview: LECTURE III Ou Zhao [email protected] University of South Carolina Lecture 3 – p.1 Expected value • The mean (or expected value) of a discrete random variable X is μ = E [ X ] = ∑ xp ( x ) . As you can see, the mean comes out of a summation, so it may not be a possible value for X at all; but it certainly tells roughly where X would very much like to take values. • Example: Consider the mass function shown below: x 1 2 4 10 p(x) .2 .4 .2 .2 what is the mean? Lecture 3 – p.2 • The variance of a random variable X is σ 2 = E [( X μ ) 2 ] = summationdisplay ( x μ ) 2 p ( x ) , does that equal summationdisplay x 2 p ( x ) μ 2 ? Again, the standard deviation is defined to be √ σ 2 • Can you compute σ 2 , or σ for the previous example? Lecture 3 – p.3 Exercise about the mean • Suppose you work for an insurance company and you sell a $ 10,000 oneyear term insurance policy at an annual premium of $ 290. This premium is targeted on those customers (with certain age, sex, health, etc), for whom...
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This note was uploaded on 06/06/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.
 Spring '10
 Zhao

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