ABSTRACT
Given our discussion of random variables and their distributions in Chapter 3, we can now start to define statistics or functions that summarize the information for a particular random variable. As a starting point, Chapter 4 develops the definition of the moments of the distribution. Moment is a general term for the expected kth power of the distribution
E [ xk ]
=
xkf (x) dx. (4.1)
The first moment of a distribution (i.e., k = 1) is typically referred to as the mean of the distribution. Further, the variance of a distribution can be derived using the mean and the second moment of the distribution. As a starting point, we need to develop the concept of an expectation rigorously.
