diff --git a/assets/image_1686901606535_0.png b/assets/image_1686901606535_0.png new file mode 100644 index 0000000..4b08084 Binary files /dev/null and b/assets/image_1686901606535_0.png differ diff --git a/pages/总复习2023t1.md b/pages/总复习2023t1.md index 32a41d0..3849805 100644 --- a/pages/总复习2023t1.md +++ b/pages/总复习2023t1.md @@ -2650,12 +2650,19 @@ ![image.png](../assets/image_1686901196592_0.png) - Property (iii) is called finite additivity. - Axiomatic Definition of Probability ![section 1.4.pdf](../assets/section_1.4_1686901294123_0.pdf) - - A collection F of subsets of Ω is a σ-algebra if - (i) Ω ∈ F ; - (ii) F ∈ F =⇒ F ∈ F ; - (iii) if Fn is a countable collection of sets, n = 1, 2, · · · such that - Fn ∈ F for all n, then - - ![image.png](../assets/image_1686901503094_0.png) + - Let P (A)(A ∈ F ) be a non-negative set function on the σ-algebra + F . P (A) is called the probability measure or probability of + event A if it satisfies the following three axioms: + Axiom 1. for every A ∈ F , P (A) ⩾ 0; + Axiom 2. P (Ω) = 1; + Axiom 3. (countable additivity) for every infinite sequence of + countable disjoint events A1 , A2 , · · · , + ![image.png](../assets/image_1686901606535_0.png){:height 185, :width 405} + The sets in σ-algebra F are called events. F is called to be the + algebra of events. ==The triple (Ω, F , P ) is a probability space + or probability triple.== + - $$P (∅) = 0.$$ + - - Properties of Probability - LATER 学积分 :LOGBOOK: