7-1 Section 7: Mathematical Expectation Recall the following definition for the expected value of a discrete random variable. Note that we have now replaced the notation ? ?P X x? with the p.m.f. ? ?f x . Also recall that the expected value is an average; it is not necessarily the most likely possible value of the random variable. Remark: If X can take on an infinite number of different values, then the sum above is an infinite series. In this case, it is possible that the sum will fail to converge, in which case we say that the expected value of X does not exist. In fact, it is necessary to require that the series is absolutely convergent; that is we must require that ? ? x x f x? ? ?? .