Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 19

If we are interested in the number of accidents that occur at a given intersection within a month, the sample space might be taken as the set consisting of all nonnegative integers. Realistically, there is a practical limit, say , of the monthly numbers of accidents at this particular intersection. Although one may think that it is simpler to take the sample space it turns out that it is often much simpler to take the infinite sample space if the “practical bound” is not very precise.

Since outcomes can be specified in various ways (as illustrated by Examples 1.1 and 1.3), it follows that the same experiment can be described in terms of different sample spaces . The choice of a sample space depends on the goal of description. Moreover, certain sample spaces for the same experiment lead to easier and simpler analysis. The choice of a “better” sample space requires some skill, which is usually gained through experience. The following two examples illustrate this point.