**1.2 Expectation Values**

An important definition which we will make use of later is the
*expectation value* of a random variable or a random variable function.
If *x* is a random variable distributed as *P(x)*, then

is the *expected* value of *x*. The integration in (5) is over all
admissible *x*. This, of course, is just the standard notion of an
average value. For a discrete variable, (5) becomes a sum

Similarly, if *f(x)* is a function of *x*, then

is the expected value of *f(x)*.

To simplify matters in the remainder of this section, we will present results assuming a continuous variable. Unless specified otherwise, the discrete case is found by replacing integrals with a summation.