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2.1 Sample Spaces, Outcomes, and Events

Let us now be more precise about our terminology and define some additional terms that lead to the concept of a pdf. Consistent with standard textbooks (e.g., [Hamming] or [DeGroot]), we will refer to the physical or mathematical process as an experiment, and this experiment has a number (possibly infinite) of outcomes, to which we will assign probabilities. The sample space S of the experiment is the collection of all possible outcomes s. Thus if the experiment is carried out, its outcome is assured to be in the sample space S. We will also describe one realization of the experiment as a trial, and by definition a trial will have an outcome s in the sample space S. The experiment may result in the occurrence of a specific event . An event may be viewed as a consequence of the outcome (or outcomes) of the experiment. Let us now illustrate these concepts with a simple example.