Introduction to Sample Space and Probability - Random Signals and Processes Primer with MATLAB - page 2

We assume here that coins and dice are fair and have no memory , i.e., each
outcome is equally likely on each toss, regardless of the results of previous tosses.
It is helpful to give a geometric representation of events using a Venn diagram .
This is a diagram in which sample space is presented using a closed-plane figure
and sample points using the corresponding dots. The sample spaces ( 1.1 ) and ( 1.3 )
are shown in Fig. 1.1a , b, respectively.
The sample sets ( 1.1 ) and ( 1.3 ) are discrete and finite . The sample set can also be
discrete and infinite . If the elements of the sample set are continuous (i.e., not
countable) thus the sample set S is continuous. For example, in an experiment
which measures voltage over time T , the sample set (Fig. 1.2 ) is:

S ¼fsjV 1 < s < V 2 g: (1.4)

In most situations, we are not interested in the occurrence of specific outcomes,
but rather in certain characteristics of the outcomes. For example, in the voltage
measurement experiment we might be interested if the voltage is positive or less
than some desired value V . To handle such situations it is useful to introduce the
concept of an event.

Fig. 1.1 Sample spaces for coin tossing and die rolling. ( a ) Coin tossing. ( b ) Die rolling

S

V 1 V 2

Fig. 1.2 Example of continuous space