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