lecture3 - LECTURE III Ou Zhao ouzhao@stat.sc.edu...

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Unformatted text preview: LECTURE III Ou Zhao ouzhao@stat.sc.edu University of South Carolina Lecture 3 p.1 Expected value The mean (or expected value) of a discrete random variable X is = 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 2 = E [( X- ) 2 ] = summationdisplay ( x- ) 2 p ( x ) , does that equal summationdisplay x 2 p ( x )- 2 ? Again, the standard deviation is defined to be 2 Can you compute 2 , or 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 one-year 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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lecture3 - LECTURE III Ou Zhao ouzhao@stat.sc.edu...

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