Subject: [HM] on dependencies of events in probability theory
From: Vorob'ov O.Yu. (vorob@scn.ru)
Date: Fri Jun 16 2000 - 21:55:17 EDT
Dear HM list members,
the current result of voting is 19 "NO" and 1 "YES".
I would like to continue and ask all HM listmembers once more.
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.
R e m a r k.
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,
Oleg Yu. Vorob'ov
Institute of Computational Modeling
Russian Academy of Sciences
Krasnoyarsk State University
Akademgorodok 18-46
Krasnoyarsk, 660036, Russia
voice: +7 3912 49-47-95
FAX: +7 3912 43-27-56
mailto: vorob@scn.ru
This archive was generated by hypermail 2b28 : Fri Jun 16 2000 - 21:05:01 EDT