文档介绍：118 Resampling: The New Statistics
CHAPTER
Probability Theory, Part 4:
8 Estimating Probabilities from
Finite Universes
Introduction
Some Building Block Programs
Problems in Finite Universes
Summary
Introduction
The examples in Chapter 7 dealt with infinite universes, in which
the probability of a given simple event is unaffected by the
e of the previous simple event. But now we move on
to finite universes, situations in which you begin with a given
set of objects whose number is not enormous—say, a total of
two, or two hundred, or two thousand. If we liken such a situ-
ation to an urn containing balls of different colors each with a
number on it, we are interested in the probability of drawing
various sets of numbered and colored balls from the urn on
the condition that we do not replace balls after they are drawn.
In the cases addressed in this chapter, it is important to remem-
ber that the single events no longer are independent of each
other. A typical situation in which sampling without replace-
ment occurs is when items are chosen from a finite universe—
for example, when children are selected randomly from a class-
room. If the class has five boys and five girls, and if you were
to choose three girls in a row, then the chance of selecting a
fourth girl on the next choice obviously is lower than the
chance that you would pick a girl on the first selection.
The key to dealing with this type of problem is the same as
with earlier problems: You must choose a simulation proce-
dure that produces simple events having the same probabili-
ties as the simple events in the actual problem involving sam-
pling without replacement. That is, you must make sure that
your simulation does not allow duplication of events that have
already occurred. The easiest way to sample without replace-
Chapter 8—Probability Theory, Part 4: Estimating Probabilities from Finite Universes 119
ment with resampling techn