Random Experiment and Sample Space
An experiment repeated under
essentially homogeneous and similar conditions results in an outcome,
which is unique or not unique but may be one of the several possible
outcomes. When the result is unique then the experiment is called a
'deterministic' experiment.
Example:
While measuring the inner radius of
an open tube, using slide callipers, we get the same result by
performing repeatedly the same experiment. Many scientific and
Engineering experiments are deterministic.
If the outcome is one of the several
possible outcomes, then such an experiment is called a "random
experiment" or 'nondeterministic' experiment.
In other words, any experiment whose
outcome cannot be predicted in advance, but is one of the set of
possible outcomes, is called a random experiment.
If we think an experiment as being
performed repeatedly, each repetition is called a trial. We observe an
outcome for each trial.
Example:
An experiment consists of 'tossing a
die and observing the number on the upper-most face'
In such cases, we talk of chance of
probability, which numerically measures the degree of chance of the
occurrence of events.
Sample Space (S)
The set of all possible outcomes of a
random experiment is called the sample space, associated with the random
experiment.
Note:
Each element of S denotes a
possible outcome. Each element of S is known as sample point.
Any trial results in an outcome and
corresponds to one and only one element of the set S.
e.g.,
1. In the experiment of tossing a
coin,
S = {H, T}
2. In the experiment of tossing two
coins simultaneously,
S = {HH, HT, TH, TT}
3. In the experiment of throwing a
pair of dice,
S = {(1,1), (1,2), (1,3), (1,4),
(1,5), (1,6), (2,1), (2,2),���. (6,1), (6,2), (6,3), (6,4), (6,5),
(6,6)}
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