ABSTRACT
As we have seen, for a discrete random variable X with set of possible values A and probability mass function p, E(X) is defined by
∑ x∈A xp(x). For a continuous random
variable X with probability density function f , the same quantity, E(X), is defined by∫∞ −∞ xf(x) dx. Recall that for a random variable X , the expected value, E(X), might
not exist (see Examples 4.18 and 4.19 and Exercise 11, Section 6.3). In the following discussion we always assume that the expected value of a random variable exists.
