Chapter 2 Probability
2.1 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
φ
⊂
and S
⊂
S, both
φ
= { } and S are events.
•
φ
= { } is called the impossible event and has probability zero, i.e., P(
φ
) = 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.
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.,
A
B
φ
∩
=
.
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).
b)
Relative frequency approach:
P(A) is the proportion of times an event A would
occur in the long run, if the statistical experiment were repeated over and over
again,
(
29
(
)
/
lim
n
P A
f
n
→∞
=
.
c)
Axiomatic Definition:
The probability of an event A, P(A), is a number assigned
to the event A in such a way that all of the following axioms are satisfied:
i.
Let S be the sample space. Then, P(S) = 1.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Kyung
 Statistics, Probability, Probability theory, mutually exclusive events

Click to edit the document details