Introduction to Statistics: Difference between revisions
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The simplest (albeit uninteresting) example would be an experiment with only one possible outcome, say <math>A</math>. If we remember our set theory from elementary school, we can expressed the sample space as follows: | The simplest (albeit uninteresting) example would be an experiment with only one possible outcome, say <math>A</math>. If we remember our set theory from elementary school, we can expressed the sample space as follows: | ||
<math>\Omega = \{ A \} </math> | <math>\Omega = \{ A \} </math> | ||
A more interesting example is the result of rolling a six sided dice. The sample space for this experiment is: | A more interesting example is the result of rolling a six sided dice. The sample space for this experiment is: | ||
<math>\Omega = \{ 1,2,3,4,5,6 \}</math> | <math>\Omega = \{ 1,2,3,4,5,6 \}</math> | ||
We may be interested in 'events' in an experiment. | We may be interested in 'events' in an experiment. | ||
'''Definition:''' An ''event'' is some subset of outcomes from the ''sample space'' | '''Definition:''' An ''event'' is some subset of outcomes from the ''sample space'' | ||
In the dice example, events of interest might include | In the dice example, events of interest might include | ||
- the outcome is an even number | - the outcome is an even number | ||
- the outcome is less than three | - the outcome is less than three | ||
Revision as of 15:40, 28 June 2005
Experiments, Outcomes and Events
The easiest way to think of probability is in terms of experiments and their potential outcomes. Many examples can be drawn from everyday experience: On the drive home from work, you can encounter a flat tire, or have an uneventful drive; the outcome of an election can include either a win by candidate A, B, or C, or a runoff.
Definition: The entire collection of possible outcomes from an experiment is termed the sample space, indicated as <math>\Omega</math>
The simplest (albeit uninteresting) example would be an experiment with only one possible outcome, say <math>A</math>. If we remember our set theory from elementary school, we can expressed the sample space as follows:
<math>\Omega = \{ A \} </math>
A more interesting example is the result of rolling a six sided dice. The sample space for this experiment is:
<math>\Omega = \{ 1,2,3,4,5,6 \}</math> We may be interested in 'events' in an experiment.
Definition: An event is some subset of outcomes from the sample space
In the dice example, events of interest might include
- the outcome is an even number
- the outcome is less than three