DEFINITIONS
Chapter 1 defines a probability model. It begins with a physical model of an experiment. An experiment consists of a procedure and observations. The set of all possible observations, S , is the sample space of the experiment. S is the beginning of the mathematical probability model. In addition to S, the mathematical model includes a rule for assigning numbers between 0 and 1 to subsets A of S. Thus for every , the model gives us a probability P[A], where .
In this chapter and for most of the remainder of the couse, we will examine probability models in which a number is assigned to each outcome in the sample space. When we observe one of these numbers, we refer to the observation as a random variable. In our notation,the name of a random variable is always a capital letter, for example, X . The set of possible values of X is the range of X. Since we often consider more than one random variable at a time, we denote the range a random variable by the letter S with a subscript which is the name of the random variable. Thus is the range of random variable X and is the range of random variable Y and so forth. We use to denote the range of X since the set of all possible values of X is analogous to S, the set of all possible outcomes of an experiment.
A probability model always begins with an experiment. Each random variable is related directly to this experiment. There are three types of relationships.
