| term | definition |
|---|---|
| Countable Additivity | The measure of the union of a countable number of nonoverlapping sets equals the sum of their measures. Allows summing of probabilities.Also called sigma-additivity (See: https://www.statlect.com/glossary/countable-additivity) |
Probability Motivation
(See links below for resources)
- Sample Space: Each experiment (n tosses of a coin, dart at a radius) has a sample space \(\Omega\).
- Probability: Measure of the likelihood of a set of outcomes (event \(E subset \Omega\))
Note
Countable Additivity is important
Countable Additivity
See link
Finite vs. Countable
Question: Toss a coint till the first tail comes up. What is the probability that the number of tosses was odd?
Take the sample space the set of all countably infinite sequences: \[ \begin{aligned} \Omega & = \{(w_1, w_2, w_3, ...): w_j \in \{H,T\}\} \\ & = \{w: N \rightarrow \{H, T\}\} \end{aligned} \]
Probability measures are countably additive