# Empirical Probability Function

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An Empirical Probability Function is a probability function structure that is approximated/estimated by a Probability Function Estimate/?/Probability Distribution Estimation Task based on a set of Observed Outcomes.

**Context:****range:**an Empirical Probability Value.- …

**Example(s):****Counter-Example(s):****See:**Probability Function Estimate, Trained Probability Function.

## References

### 2009

- http://www.teacherlink.org/content/math/interactive/probability/glossary/glossary.html
- Experimental Probability: Probability estimate for an outcome of an experiment based on the outcome’s experimental frequency; also called Empirical Probability.

### 1986

- (Larsen & Marx, 1986) ⇒ Richard J. Larsen, and Morris L. Marx. (1986). “An Introduction to Mathematical Statistics and Its Applications, 2nd edition." Prentice Hall
- QUOTE: Consider a sample space, [math]\displaystyle{ S }[/math], and any event, [math]\displaystyle{ A }[/math], defined on
*S*. If our experiment were performed*one*time, either [math]\displaystyle{ A }[/math] or*A*would be the outcome. If it were performed [math]\displaystyle{ n }[/math] times, the resulting set of sample outcomes would be members of [math]\displaystyle{ A }[/math] on [math]\displaystyle{ m }[/math] occasions, [math]\displaystyle{ m }[/math] being some integer between 0 and [math]\displaystyle{ n }[/math], inclusive. Hypothetically, we could continue this process an infinite number of times. As [math]\displaystyle{ n }[/math] gets large, the ratio m/n will fluctuate less and less (we will make that statement more precise a little later). The number that^{C}*m/n*convert to is called the empirical probability of [math]\displaystyle{ A }[/math] : that is, P*(*A*) = lim*_{n→∞}*(*m/n*). … the very act of repeating an experiment under identical conditions an infinite number of times is physically impossible. And left unanswered is the question of how large [math]\displaystyle{ n }[/math] must be to give a good approximation for lim*_{n→∞}*(*m/n*) …*

- QUOTE: Consider a sample space, [math]\displaystyle{ S }[/math], and any event, [math]\displaystyle{ A }[/math], defined on