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Topic: the geometric distribution
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KINGB@WCSUB.CTSTATEU.EDU

Posts: 144
Registered: 12/6/04
the geometric distribution
Posted: Mar 14, 1997 12:21 PM
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There have been some queries here about the geometric distribution. I
leave explanation of its presence in the Acorn book to others, but
here's a little exercise that I have found provoked some interest in
one of my classes.

I was at a week-long summer workshop a few years ago, and was assigned
a room in a dormitory. The door to my room had to be opened by
simultaneously turning a key and pressing a button. For some reason,
this was not as simple as you might expect; I often had to make
multiple attempts to enter my room.

An "observation" might be regarded as a sequence of trials like FFFS,
S, FFS, FFFFFFFS, and so on. Assuming independence of trials and a
constant probability p of a success in any one trial, a collection of
such observations might be taken as a sample from a geometric
distribution.

At the end of this note is a record of n = 47 consecutive observations.
I have asked my students to decide whether this n-sample could
reasonably be modeled with a geometric distribution and, if so, to
estimate p. (I tell them that, for the theoretical distribution, mu =
1/p, and sigma^2 = (1-p)/p^2.)

At the level at which I operate, it's not all that obvious how to
decide whether this or that is a "good" model for a data set. So
students have to decide on an _approach_ to the problem, to begin with.

If you think about it, there are reasons to expect that the geometric
distribution might not be a good model. You would think, for example,
that there might be a "practice effect": I should have gotten more
skillful with practice, shouln't I? If so, then maybe the _sequence_
of observations has to be considered, also.

Anyway, see what you think...

==============================================
Bruce King
Department of Mathematics and Computer Science
Western Connecticut State University
181 White Street
Danbury, CT 06810
(kingb@wcsu.ctstateu.edu)

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