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documents/by-course/pstat-120a/course-notes/main.typ
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@ -10,7 +10,7 @@
#outline() #outline()
= Lecture 1 = Lecture #datetime(day: 6, month: 1, year: 2025).display()
== Preliminaries == 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. 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[ #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. Select one card from a deck of 52 cards.
Then the following is true:
$ $
Omega = {1,2,...,52} \ Omega = {1,2,...,52} \
@ -374,7 +384,7 @@ This is mostly a formal manipulation to derive the obviously true proposition fr
== Countable sample spaces == Countable sample spaces
#definition[ #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 $Omega$. In such a case, one can list the elements of $Omega$.