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### 2.1.5 Mean, Variance and Standard deviation

Two important characteristics of random variables are their mean average'' and standard deviation spread'' or scale''

Definition 8   If is a discrete r.v. with distribution function then the mean of is:

and the variance of is:

The standard deviation of is:

Similarly for a continuous r.v. we have:

Definition 9   If is a continuous r.v. with density function then the mean of is:

and the variance of is:

The standard deviation of is:

Remarks

1. is a weighted average
2. is the (weighted) average squared distance from

Eran Borenstein
2007-05-04