lecture3

# lecture3 - LECTURE III Ou Zhao [email protected]

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LECTURE III Ou Zhao [email protected] University of South Carolina Lecture 3 – p.1

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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

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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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