Properties of Expectations and Variances

Abstract

It is often referred to as the first moment of Y, since it describes the location of the center of the distribution. The precise definition of the expectation of Y is that it is a weighted average of all the possible values of Y, with weights determined by the probabilities associated with each possible value. The variance of Y, often denoted by o-2 = Var(Y), is a measure of the dispersion or variability around the mean or expected value of Y. The variance is often referred to as the second central moment of Y and is defined as