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2-1 SAMPLE SPACES AND EVENTS 19

concepts of sets and operations on sets. It is assumed that the reader is familiar with these
topics.

Definition
The set of all possible outcomes of a random experiment is called the sample space
of the experiment. The sample space is denoted as S.

A sample space is often defined based on the objectives of the analysis.

EXAMPLE 2-1 Consider an experiment in which you select a molded plastic part, such as a connector, and
measure its thickness. The possible values for thickness depend on the resolution of the meas-
uring instrument, and they also depend on upper and lower bounds for thickness. However, it
might be convenient to define the sample space as simply the positive real line

S R 5x 0 x 06

because a negative value for thickness cannot occur.
If it is known that all connectors will be between 10 and 11 millimeters thick, the sample
space could be

S 5x ƒ 10 x 116

If the objective of the analysis is to consider only whether a particular part is low, medium,
or high for thickness, the sample space might be taken to be the set of three outcomes:

S 5low, medium, high6

If the objective of the analysis is to consider only whether or not a particular part con-
forms to the manufacturing specifications, the sample space might be simplified to the set of
two outcomes

S 5yes, no6

that indicate whether or not the part conforms.

It is useful to distinguish between two types of sample spaces.

Definition
A sample space is discrete if it consists of a finite or countable infinite set of outcomes.
A sample space is continuous if it contains an interval (either finite or infinite) of
real numbers.

In Example 2-1, the choice S R is an example of a continuous sample space, whereas
S {yes, no} is a discrete sample space. As mentioned, the best choice of a sample space