The Distribution of a Random Variable
When a probabilty distribution has been specified on the sample space of an experiment, we can determine a probability distribution for the possible values of each random variable X. Let A be a subset of the real line, and let Pr(X A) denote the probability that the value of X will belong to the subset A. Then Pr(X A) is eQual to the probability that the outcome s of the experiment will be such that X(s) A. In symbols,