Applied Statistics and Probability for Engineers

2-1 SAMPLE SPACES AND EVENTS 19

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

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

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:

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

that indicate whether or not the part conforms.

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

S 5 yes, no 6

S 5 low, medium, high 6

S 5 xƒ 10 x 116

SR^5 x^0 x^06

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.

Definition

A sample space is discreteif it consists of a finite or countable infinite set of outcomes.

A sample space is continuousif it contains an interval (either finite or infinite) of

real numbers.

Definition

In Example 2-1, the choice SRis 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

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

topics.

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