  We also need to recall the concept of a random variable. If \(E\) is an outcome set and \(V\), some set of “values” (real numbers, pointer-readings, or what not), a \(V\)-valued random variable is simply a mapping \(f : E \rightarrow V\). The heuristic (but it need only be taken as that) is that one “measures” the random variable \(f\) by “performing” the experiment represented by \(E\) and, upon obtaining the outcome \(x \in E\), recording \(f(x)\) as the measured value. Note that if \(V\) is a set of real numbers, or, more generally, a subset of a vector space, we may define the expected value of \(f\) in a state \(\omega \in \Delta(E)\) by: