Probability with R, 2nd Edition

15Introduction to Continuous Distributions

So far, the random variables that we have considered have been discrete. They resulted from situations where we counted, for example, the number of errors in a program, the number of defectives in a batch, or the number of job arrivals in a day. In many practical situations, our experiment will consist of measuring rather than counting, and the results will be continuous rather than discrete.

Consider, for example, the experiment of submitting a program and measuring the time, , that it takes to be executed. Clearly, is a time interval. We may know from past experience that the response time will never be greater that five seconds, so it would be natural to take the sample space to be the interval from 0 to 5, that is

In this case, although is a “finite interval,” the number of actual points in is infinite and not even countably infinite. This ...