TABLE OF CONTENTS We are usually interested in a summary of outcomes rather than in the details of individual outcomes. If a baseball team plays 162 games in a season, we may prefer to know the total number of games they won rather than a complete listing of which games were won or lost. In this section we generalize and extend some previous results. We begin with two definitions.
Definition: A random variable associates a numerical value with each outcome of an experiment.
Definition: The values that a random variable assumes together with the corresponding probabilities is called the distribution of the random variable.
Example 4.1. The new commissioner of baseball wants to shorten the World Series so he decides that the first team to win two games will win the series. Suppose the series is between the Braves and the Red Sox, and the Braves are twice as likely to win each game as the Red Sox.
Let B = Braves win a game and R = Red Sox win a game.
A sample space for this example would be
where the first letter refers to the first game, second letter to second game, etc.
Since the Braves are twice as likely to win a game as the Red Sox, 
, and 
. Note that S is not an equally probable sample space.
Let X = number of games in the series. Then X is...
