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1
ISMT
111
B
USINESS
S
TATISTICS
–
T
UTORIAL
2
created by Andrew Yam
Terminology
§
Experiment: obtaining one observation
§
Sample
Space
(
S
):
the
set
of
all
possible
outcomes
of
an
experiment
§
Simple Event: an element of the sample space
§
Event: a subset of the sample space
General Properties of Probabilities
§
If A is an event, then
( 29
1
0
≤
≤
A
P
.
§
( 29
1
=
S
P
§
If the set of simple events
E
1
, E
2
, . . ., E
r
represents the sample
space
S
for an experiment, then
( 29
1
1
1
=
∑
=
r
i
E
P
.
§
If A occurs when one of a set of k simple events
E
1
, E
2
, . . ., E
k
occurs, then
( 29
( 29 ( 29
( 29
k
E
P
E
P
E
P
A
P
+
+
+
=
...
2
1
.
Event Composition and Event Relations
§
Intersection of
A
and
B
, denoted by
AB
(also as
B
A
∩
) is the
event that both
A
and
B
occur.
§
Union of
A
or
B
, denoted by
B
A
∪
is the event that
A
or
B
or
both occur.
§
Complement of
A
, denoted by
A
(also,
c
A
or
'
A
), consists
of all the simple events in the sample space that are not in
A
.
( 29
( 29
A
P
A
P

=
1
§
Two
events
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Additional Rule of Probability
§
( 29 ( 29 ( 29 ( 29
AB
P
B
P
A
P
B
A
P

+
=
∪
§
If
A
&
B
are mutually exclusive, then
( 29 ( 29 ( 29
B
P
A
P
B
A
P
+
=
∪
.
Conditional probability
The conditional probability of
B
given that
A
has occurred is
( 29
( 29
( 29
A
P
AB
P
A
B
P
=

, for
( 29
0
A
P
.
Independent events
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 Spring '09
 AnthonyChan

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