MOTM

> 
> While taking some probability, statistics and stochastic processes courses 
> about ten years ago, these confusions came up a lot due to term "chaos" 
> suddenly bursting out inappropriately from several media. To clear up this 
> confusion, the instructor explained the difference something like this: the 
> definition of random events, such as the toss of a fair coin (probability of 
> either event = 0.5) supposes that there is no information about the initial 
> conditions nor prior trials which will in anyway help to determine the 
> outcome of the succeeding trials.
This description really applies to independent events (which
you basically mentioned) (especially the classic coin toss experiment).
There are many situations (e.g., Markov processes, Bayesian) where the
outcomes are conditional on prior outcomes, typically in a sequence of
trials, so then one considers conditional probabilities.  The latter are
still random events, only not independent events.


 The term "chaos" refers to a particular 
> type of nonlinear partial differential equation (possibly recursive?) where 
> the input directly effects the output, but in a nonlinear way (I'm treading 
> deep water here).
I'm probably treading water with you, as my area in statistics is
ecological sampling, but there is active statistical research into chaos,
especially with certain areas of stochastic processes.  I suspect that
conditional aspects of event outcomes is integral in this research.

Jeff

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Jeffrey S. Pontius
Associate Professor
Department of Statistics   =^..^=
Kansas State University
Manhattan KS 66506-0802
pontius@...
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