Introduction to Sample Space and Probability - Random Signals and Processes Primer with MATLAB - page 3

Any subset of the sample space S is called an event and denoted with capital
letters ( A , B , etc.). Thus, the event for the voltage measurement can be A ¼ { v > 0}.

In the die rolling experiment the event can be, for example, the occurrence of even
number of dots,

A ¼f 2 ; 4 ; 6 g: (1.5)

Note that an outcome can also be an event. For example, in the sample space
( 1.1 ), the event is either H, or T (i.e., A ¼ {H} is the event that “heads” occurred).
Similarly, B ¼ {T} is the event that “tails” occurred in the experiment.
An event that has no sample points is called a null event .
Figure 1.3 illustrates a Venn diagram representation of a sample space S , with
the element s i and events A 1 , A 2 , and A 3 .
Example 1.1.1 A coin is tossed until either “heads” or “tails” appears twice in
succession. Find the sample space S and its subset which corresponds to the event
A ¼ {“No more than three tosses are necessary”}.

Solution The sample space is formed by the outcomes of two “heads” denoted by
H, or two “tails,” denoted by T, independent of the number of tosses.
Two tosses:

s 1 ¼f H ; H g;

s 2 ¼f T ; T g; (1.6)

Three tosses:

s 3 ¼f T ; H ; H g;

s 4 ¼f H ; T ; T g; (1.7)

Four tosses:

s 5 ¼f H ; T ; H ; H g;

s 6 ¼f T ; ; ;

T g;

H T (1.8)

etc.

Fig. 1.3 Venn diagram illustration of sample space S , element s i and events A 1 , A 2 , and A 3