Page 40 - Applied statistics and probability for engineers

18 Chapter 2/Probability

Call 1 2 3 4
Call duration
Time 0 5 10 15 20
Current Call 1 2 Minutes
3
Call 3 blocked
Call duration
Time 0 5 10 15 20
Voltage Minutes
FIGURE 2-3 A closer examination of the system FIGURE 2-4 Variation causes disruptions in the
identifies deviations from the model. system.

Example 2-1 Camera Flash Consider an experiment that selects a cell phone camera and records the recycle
time of a l ash (the time taken to ready the camera for another l ash). The possible values for this
time depend on the resolution of the timer and on the minimum and maximum recycle times. However, because the

time is positive it is convenient to deine the sample space as simply the positive real line
+
S = R = { x x > 0}
|
If it is known that all recycle times are between 1.5 and 5 seconds, the sample space can be
S = { | .5 < x < } 5
x
1
If the objective of the analysis is to consider only whether the recycle time is low, medium, or high, the sample space
can be taken to be the set of three outcomes
,
,
S = { low medium high}
If the objective is only to evaluate whether or not a particular camera conforms to a minimum recycle time specii ca-

tion, the sample space can be simpliied to a set of two outcomes
S = { yes no}
,
that indicates whether or not the camera conforms.
It is useful to distinguish between two types of sample spaces.

Discrete and
Continuous A sample space is discrete if it consists of a inite or countable ininite set of outcomes.

Sample Spaces

A sample space is continuous if it contains an interval (either inite or ini nite) 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
,
c
depends on the objectives of the study. As specii questions occur later in the book,
appropriate sample spaces are discussed.

Example 2-2 Camera Specifi cations Suppose that the recycle times of two cameras are recorded. The exten-
sion of the positive real line R is to take the sample space to be the positive quadrant of the plane
+
S = R × R +
If the objective of the analysis is to consider only whether or not the cameras conform to the manufacturing specii cations,
either camera may or may not conform. We abbreviate yes and no as y and n. If the ordered pair yn indicates that the i rst
camera conforms and the second does not, the sample space can be represented by the four outcomes: