TABLE OF CONTENTS A great appreciation for probability theory comes from observing the outcome of a real experiment. These experiments are called random experiments. Common characteristics of a random experiment include:
The outcome of the experiment cannot be predicted with certainty.
Under unchanged conditions, the experiment could be repeated with the outcomes appearing in a haphazard manner. As the experiment-repeating process increases, a certain pattern in the frequency of outcome emerges.
To illustrate random experiments with an associated sample space, consider the following example:
Toss a pair of dice and observe the "up" faces. The total sample space is shown in Table 3.14. Suppose a random variable X is defined as the sum of the "up" faces as events in X that are defined as R X. Then R X = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) and the probabilities are (1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36), respectively. Assuming the dice are true and are equally likely, there will be 36 outcomes as listed above. The same output is presented in the equivalent events in Table 3.15.
| (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) |
