Notes - Probability MT22, Axioms of probability space
Flashcards
Can you state the three axioms related to $\mathcal F$ in a probability space $(\Omega, \mathcal F, \mathbb P)$?
- $\Omega \in \mathcal F$,
- If $A \in \mathcal F$, then $A^C \in \mathcal F$,
- If $\{A _ i : i \in I\}$ is a finite or countably infinite collection of members of $\mathcal F$, then $\cup _ {i \in I} A _ i \in \mathcal F$.
Can you state the three axioms related to $\mathbb P$ in a probability space $(\Omega, \mathcal F, \mathbb P)$?
- $\mathbb P(A) \ge 0$ for all $A \in \mathcal F$.
- $\mathbb P (\Omega) = 1$
- If $\{A _ i : i \in I\}$ is a finite or countably infinite collection of members of $\mathcal F$, and they are pairwise disjoint, then $\cup _ {i \in I} A _ i = \sum _ {i \in I} \mathbb P (A _ i)$.