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Brief Notes #1
Events and Their Probability
• Definitions
Experiment: a set of conditions under which some variable is observed
Outcome of an experiment: the result of the observation (a sample point)
Sample Space, S: collection of all possible outcomes (sample points) of an experiment
Event: a collection of sample points
• Operations with events
A
c
1.
Complementation
A
c
A
2.
Intersection
A
B
A
∩
B
3.
Union
A
∪
B
B
A
• Properties of events
1. Mutual Exclusiveness  intersection of events is the null set (A
i
∩
A
j
=
∅
, for all i
≠
j)
2. Collective Exhaustiveness (C.E.)  union of events is sample space (A
1
∪
A
2
∪
...
∪
A
n
= S)
3. If the events {A
1
, A
2
, .
.. , A
n
} are both mutually exclusive and collectively exhaustive, they
form a partition of the sample space, S.
• Probability of events
• Relative frequency f
E
and limit of relative frequency F
E
of an event E
f
E
=
n
E
n
F
E
=
f
lim
E
=
lim
n
E
n
∞
→
n
∞
→
n
• Properties of relative frequency (the same is true for the limit of relative frequency
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 Fall '07
 DonHill

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