Empirical probability estimates an event’s likelihood from observed trials or real-world data. Calculate it as observed successes divided by total observations. section 2.1.1 section 2.5
Use empirical probability to:
- Estimate an event rate from recorded observations rather than mathematical assumptions. section 2.1.1
- Distinguish observed probability from theoretical probability and subjective probability. section 2.1.1
- Apply observed probabilities alongside counting and distribution concepts in real-world problems. section 2.4.3 section 3.2
Rainfall in Cincinnati
Suppose rainfall records cover 365 days and show rain on 75 days. The empirical probability of rain on a given day is 75 divided by 365, based on the observed frequency. section 2.1.1
Empirical probabilities can also support cumulative distributions, where successive observed or computed probabilities are added until the cumulative value reaches 1. section 2.4.3
