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PROBABILITY
Chapter 2.1
Deterministic:
dx
dt
=
bx.
Statistical:
observation = true value + error
•
error diﬀerent each time experiment
is performed.
1
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Quality control. Sample
n
,
X
= proportion defective,
p
= true de
fective rate.
X
=
p
+ error
In practice,
p
unknown,
X
observed.
What information about
p
in
X
? What
can we conclude?
2
Suppose repeat sampling experiment many
times.
Keep track
X
values.
Tab
ulate. Histogram. Frequencies show
variability = randomness in a single
X.
Would be nice if cluster about true
p
with small variability. Why?
Paddle Experiment.
3
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Lewis Fry Richardson (1881
1950) Database of 315 conﬂicts from
1820 to 1950. Poisson model (to be
discussed) ﬁt well. Suggested onset of
war is random process. (American Sci
entist JanuaryFebruary 2001).
4
Axiomatic probability: Model for de
scribing random phenomena.
Many random phenomena show regu
larity in the long run, although indi
vidual outcomes cannot be predicted.
This is what probability tries to de
scribe. In the Quality Control example,
each sample describes a possible out
come. The frequency histogram repre
sents the empirical proportion of times
each outcome occurred, or the empiri
cal probability of each outcome. Prob
ability therefore begins by considering
all possible outcomes.
5
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sample space (set of all outcomes)
A,B,C,.
..
subsets (called events)
S
A
B
C
P
(
A
) probability of A. Number reﬂect
ing our measure of how likely
A
is to
occur.
6
Objective
probability – identiﬁed with
proportion in many repetitions as in
Quality Control Example
Subjective
probability – expresses degree
of belief in outcome.
P
(
A
) = amount
willing to bet so receive 1 if
A
oc
curs, or 0 if
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This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.
 Fall '10
 drera

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