Chapter 1
Modeling a Probabilisti c
Experiment
1.1. Elementar y Experiment s
We wil l star t b y presentin g th e mathematica l mode l tha t describe s
a probabilisti c experimen t havin g a finite numbe r d o f possibl e out -
comes. Eac h outcom e i s represente d b y a variabl e UJ %, and th e sample
space i s th e se t Q := {UJ 1 ,UJ2,... ,uu d} o f al l possibl e outcomes . T o
each outcom e uJ 1 w e associat e a probability pi. Eac h probabilit y p
%
i s
a nonnegativ e rea l numbe r an d ^2
i=1
Pi = 1.
It i s importan t t o not e tha t w e assum e tha t th e probabilit y o f
each outcom e i s give n a priori . Th e wor k consistin g o f determinin g
these probabilitie s fro m observation s belong s t o th e stud y o f statis -
tics, a branc h o f mathematic s tha t i s relate d t o bu t distinc t fro m
probability theory . Th e stud y o f statistic s use s tool s an d result s tha t
are presente d i n thi s book , bu t w e wil l no t dea l wit h statistic s directly .
Let u s retur n t o ou r mode l i n orde r t o introduc e som e vocabulary .
A subse t o f O i s calle d a n event an d th e probability o f a n even t i s th e
sum o f th e probabilitie s o f th e outcome s belongin g t o tha t event . I n
symbols, i f A C Q i s a n event , the n it s probabilit y P(A) i s define d b y
P(A) := J2
Pi-
UJX£A
3
http://dx.doi.org/10.1090/stml/028/02
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