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- Experiment, Sample Space and Random Event ![section 1.2.pdf](../assets/section_1.2_1686899993390_0.pdf)
- Events as Sets
- Definition of Classical Probability, Geometric Probability and Frequency ![section 1.3.pdf](../assets/section_1.3_1686900041785_0.pdf)
collapsed:: true
- **Classical** if
- 1. E contains only different limited basic events, that is,
- 1. E contains **only different limited basic** events, that is,
$$ Ω = \{ω1 , ω2 , · · · , ωn \}. $$
We call this kind of sample space simple space, and
2. all outcomes are equally likely to occur.
- **Geometric** if
- (i) the sample space is a measurable (such as length, area,
- (i) the sample space is a **measurable** (such as length, area,
volume, etc.) region, i.e., $$0 < L(Ω) < ∞$$, and
- (ii) the probability of every event A ⊂ Ω is proportional to the
measure L(A) and has nothing to do with its position and
- (ii) the probability of every event $$A ⊂ Ω$$ is proportional to the
measure $$L(A)$$ and has nothing to do with its position and
shape.
- The **Frequency** Interpretation of Probability
- Let E be an random experiment, A be an random event.