From 366fefd38a556dcf2b1a3e518419cd9bc25cba24 Mon Sep 17 00:00:00 2001 From: Youwen Wu Date: Thu, 9 Jan 2025 00:49:33 -0800 Subject: [PATCH] auto-update(nvim): 2025-01-09 00:49:32 --- .../by-course/pstat-120a/course-notes/main.typ | 14 ++++++++++++-- 1 file changed, 12 insertions(+), 2 deletions(-) diff --git a/documents/by-course/pstat-120a/course-notes/main.typ b/documents/by-course/pstat-120a/course-notes/main.typ index efcd39c..ca78488 100644 --- a/documents/by-course/pstat-120a/course-notes/main.typ +++ b/documents/by-course/pstat-120a/course-notes/main.typ @@ -10,7 +10,7 @@ #outline() -= Lecture 1 += Lecture #datetime(day: 6, month: 1, year: 2025).display() == Preliminaries @@ -349,8 +349,18 @@ This is mostly a formal manipulation to derive the obviously true proposition fr This is a stronger result of axiom 3, which generalizes for all sets $A$ and $B$ regardless of whether they're disjoint. ] +#remark[ + These are mostly intuitively true statements (think about the probabilistic + concepts represented by the sets) in classical probability that we derive + rigorously from our axiomatic probability function $P$. +] + #example[ + Now let us consider some trivial concepts in classical probability written in + the parlance of combinatorial probability. + Select one card from a deck of 52 cards. + Then the following is true: $ Omega = {1,2,...,52} \ @@ -374,7 +384,7 @@ This is mostly a formal manipulation to derive the obviously true proposition fr == Countable sample spaces #definition[ - A sample space $Omega$ is said to be *countable* if its finite or countably infinite. + A sample space $Omega$ is said to be *countable* if it's finite or countably infinite. ] In such a case, one can list the elements of $Omega$.