Stochastic Signals and Systems
Probability Theory
Virginia Tech
Fall 2008
Experiments and Outcomes
•
The basic entity treated by the theory of probability is
called a
random experiment
.
•
A random experiment is an experiment in which the
outcome
varies in an unpredictable fashion when the
experiment is repeated under the same conditions.
•
A random experiment is specified by
•
stating an experimental procedure, and
•
an identifiable outcome belonging to a fixed, known set of
possibilities.
•
Examples
•
A coin is tossed. Note if it is heads or tails.
•
Toss a coin three times and note the sequence of heads
and tails.
•
For the ABO blood typing system, each person has exactly
one of 4 blood types, A, B, O or AB. Two random people
attending a blood donor clinic have their blood type
recorded.
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Sample Space
•
When we perform a random experiment, one and only one
outcome occurs. Thus
outcomes are mutually exclusive
in
the sense that they cannot occur simultaneously.
•
The
sample space
of a random experiment is the entire
set of possible outcomes.
•
Examples
•
•
•
Sample Space
A sample space
(
S
)
can be classified according to its number
of outcomes:
•
finite
,
•
countably infinite
, or
•
Example: A block of information is transmitted repeatedly
over a noisy channel until an errorfree block arrives at the
receiver. Count the number of transmission required.
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 Fall '08
 DASILVER
 Probability, Probability theory

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