ch02 JWBK035-Vince February 12, 2007 6:50 Char Count= 0
CHAPTER 2 Probability Distributions
The Basics of Probability Distributions
Imagine if you will that you are at a racetrack and you want to keep a log
of the position in which the horses in a race finish. Specifically, you want
to record whether the horse in the pole position came in first, second, and
so on for each race of the day. You will record only 10 places. If the horse
came in worse than in tenth place, you will record it as a tenth-place finish.
If you do this for a number of days, you will have gathered enough data
to see thedistributionof finishing positions for a horse starting out in the
pole position. Now you take your data and plot it on a graph. The horizontal
axis represents where the horse finished, with the far left being the worst
finishing position (tenth) and the far right being a win. The vertical axis
will record how many times the pole-position horse finished in the position
noted on the horizontal axis. You would begin to see a bell-shaped curve
develop.
Under this scenario, there are 10 possible finishing positions for each
race. We say that there are 10binsin this distribution. What if, rather than
using 10 bins, we used five? The first bin would be for a first- or second-
place finish, the second bin for a third- or fourth-place finish, and so on.
What would have been the result?
Using fewer bins on the same set of data would have resulted in a prob-
ability distribution with the same profile as one determined on the same