STA3032, Chapter 4, Page 1 of 4
Chapter 4 Probability
4.1 Definitions of Some Basic Terms
Definition
: A Statistical Experiment
is an experiment that has
Two or more outcomes
and
Uncertainty
as to which outcome will be observed.
Definition:
Probability is the study of uncertainty in a statistical experiment.
Definition:
S = Sample space
is the set of all possible outcomes of a statistical
experiment.
Definition:
An event
is any subset of the sample space.
Notes:
Since
S
and S
S, both
= { } and S are events.
= { } is called the impossible event and has probability zero, i.e., P(
) = 0.
S is called the definite event and has probability of 1, i.e., P(S) = 1.
Probability of any other event, say A, is between zero and one, i.e., 0 ≤ P(A) ≤
1 for any event A.
Set notation and set algebra, such as
,,
, and complement (
'
c
A
A
A
) are used in
defining some events. Venn diagrams will be helpful to understand some of the concepts
and solve some of the problems. (See pages 154 – 159)
Definition:
Mutually exclusive events:
Two events A and B are said to be mutually
exclusive (or disjoint) if
they cannot occur at the same time,
i.e.,
AB
.
4.2 Definitions of probability:
a)
Equally likely approach:
If an experiment has n(S) equally likely outcomes and
an event A has n(A) elements in it then P(A) = n(A) / N(S).
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 Summer '08
 Kyung
 Statistics, Probability, Probability theory

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