17.2 Expected valiirs 409 It rebums t,hc>probability that r ( t )is less than the thrediold It is clrpictcd in Fignro 17.3 for the die from Exninple 17.1 Thc rlrrivative fi’igtirc~17.3: Distribution frrrrrtion for tlie Iiurribers on a die For the die fruiri Figure 17.3, this yields a h e a r amrage pz(l) = 3.5, as in Example 17.1 Expected values can Itet dcalt with in a similar way to frtnctions, if thc eorrcspunding calculation rtxlcs ale observe& There are actually only two simple rules to remeinbcr : The expcrtcct value E(.) i s a liiicar operatotor for which the principle of sixpergosition holds IIere (I and B can also be deterministic functions of time u ( t ) and h ( t )