Numerical-Valued Random Phenomena

In the foregoing we have considered mainly random phenomena whose sample description spaces were finite. We next consider random phenomena for which this is not necessarily the case. The simplest example of a random phenomenon whose sample description space is not necessarily finite is one which is numerical valued. The height of waves on a windswept sea, the number of alpha particles emitted from a radioactive source, the number of telephone calls arriving at a switchboard, the velocity of a particle in Brownian motion, the scores of students on an examination, the collar sizes of men, the dress sizes of women, and so on, constitute examples of numerical-valued random phenomena. In this chapter we discuss the notions and techniques used to treat numerical-valued random phenomena.