MTH SC 400  Study Guide  Test 1
Coverage:
Chapter 1(1.11.5), Chapter 2(2.12.5, 2.7), Chapter 3(3.13.5)
I. DEFINITIONS:
1.
The
sample space
S: is the set of all possible outcomes of an experiment. (In theory, it
can be any set.)
2.
An
event
E: is a subset (any subset) of the sample space.
3.
Two events E and F are called mutually exclusive: if EF: = E
∩
F =
∅
. A collection
F
1
, F
2
, F
3
, ... of events are called
mutually exclusive (or pairwise disjoint)
if and only if
F
i
F
j
=
∅
,
∀
i
≠
j.
A partition of S is collection of mutually exclusive events whose union
is S; i.e., A collection of subsets of S, say {F
1
, F
2
, F
3
, ... }, is a partition of S if and only if
F
i
F
j
=
∅
,
∀
i
≠
j and S = F
1
∪
F
2
∪
F
3
∪
... =
i
=
1
F
i
.
4.
A
probability measure
on a set S: is a rule (function) P which assigns to each subset
E of S a real number P(E) so that the following conditions are satisfied:
(i) P(E)
≥
0 for all E,
(ii) P(S) = 1,
(iii) If F
1
, F
2
, F
3
, ...
is a countably infinite sequence of mutually exclusive events then
P(F
1
∪
F
2
∪
F
3
∪
...
) =
P
(
F
i
)
i
=
1
∞
∑
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 Fall '10
 BRAWLEY
 Probability, Probability theory, mutually exclusive events

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