The mean is multiplied by a and the variance is

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Unformatted text preview: ]. (2.2) The difference X − µX is called the deviation of X (from its mean). The deviation is the error if X is predicted by µX . The mean of the deviation is E [X − µX ] = E [X ] − µX = µX − µX = 0. Sometimes Var(X ) is called the mean square deviation of X, because it is the mean of the square of the deviation. It might seem a little arbitrary that variance is defined using a power of two, rather than some other power, such as four. It does make sense to talk about the mean fourth power deviation, E [(X − µX )4 ], or the mean absolute deviation, E [|X − µX |]. However, the mean square deviation has several important mathematical properties which facilitate computation, so it is by far the most commonly used measure of how spread out a distribution is. The variance of 2 X is often denoted by σX , where σX = Var(X ) is called the standard deviation of X . If X is in 2.2. THE MEAN AND VARIANCE OF A RANDOM VARIABLE 27 some units, then σX is in the same units. For example...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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