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the geometric distribution
Posted:
Mar 14, 1997 12:21 PM


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 weeklong 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 nsample 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 = (1p)/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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