Page 26 - Computational Statistics Handbook with MATLAB

12 Computational Statistics Handbook with MATLAB

2.2 Probability

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A random experiment is defined as a process or action whose outcome cannot
be predicted with certainty and would likely change when the experiment is
repeated. The variability in the outcomes might arise from many sources:
slight errors in measurements, choosing different objects for testing, etc. The
ability to model and analyze the outcomes from experiments is at the heart of
statistics. Some examples of random experiments that arise in different disci-
plines are given below.

• Engineering: Data are collected on the number of failures of piston
rings in the legs of steam-driven compressors. Engineers would be
interested in determining the probability of piston failure in each
leg and whether the failure varies among the compressors [Hand,
et al., 1994].
• Medicine: The oral glucose tolerance test is a diagnostic tool for
early diabetes mellitus. The results of the test are subject to varia-
tion because of different rates at which people absorb the glucose,
and the variation is particularly noticeable in pregnant women.
Scientists would be interested in analyzing and modeling the vari-
ation of glucose before and after pregnancy [Andrews and
Herzberg, 1985].
• Manufacturing: Manufacturers of cement are interested in the ten-
sile strength of their product. The strength depends on many fac-
tors, one of which is the length of time the cement is dried. An
experiment is conducted where different batches of cement are
tested for tensile strength after different drying times. Engineers
would like to determine the relationship between drying time and
tensile strength of the cement [Hand, et al., 1994].
• Software Engineering: Engineers measure the failure times in CPU
seconds of a command and control software system. These data
are used to obtain models to predict the reliability of the software
system [Hand, et al., 1994].

The sample space is the set of all outcomes from an experiment. It is possi-
ble sometimes to list all outcomes in the sample space. This is especially true
in the case of some discrete random variables. Examples of these sample
spaces are:

© 2002 by Chapman & Hall/CRC