[HM] on dependencies of events in probability theory


Subject: [HM] on dependencies of events in probability theory
From: Vorob'ov O.Yu. (vorob@scn.ru)
Date: Wed Jun 14 2000 - 19:53:05 EDT


Dear HM list members,

please, help me to take a vote on CLASSIFICATION of dependencies of EVENTS
in probability theory.

1) If you know something about this classification, send me a message with
"Yes".

2) If you know nothing about this classification, send me a message with
"No".
(please, without fail send me a message with "No" !!!, if you know nothing).

Thanks in advance.

P.S.
I understand the classification of dependencies of EVENTS in the following
sense:
1) there are N totally independent simultaneous EVENTS;
2) there are N pairwise independent simultaneous EVENTS;
...
3) there are many other N simultaneous EVENTS with different structures of
dependencies between them.
It is a question to classify these structures of dependencies between N
simultaneous EVENTS.

Let's consider two examples of three events x,y,z.
1)
xyz Prob
000 0
100 1/4
010 1/4
001 1/4
110 0
101 0
011 0
111 1/4
These evens are pairwise independent, but P(xyz)=/=P(x)P(y)P(z).
2)
xyz Prob
000 0
100 1/6
010 1/6
001 1/6
110 0
101 1/6
011 1/6
111 1/6
These events are pairwise dependent: P(xy)=/=P(x)P(y), but
P(xyz)=P(x)P(y)P(z).

Here we have two different structures of dependnecies between three events.

Thanks once more.
Ever yours,

Prof. Dr. Oleg Yu. Vorob'ov voice: +7 3912 49-47-95
Institute of Computational Modeling
Russian Academy of Sciences FAX: +7 3912 43-27-56
Krasnoyarsk State University email: vorob@scn.ru
Akademgorodok 18-46
Krasnoyarsk, 660036, Russia



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