josia-notes/s23-probability-theory
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Josia Pietsch 2023-06-07 18:13:25 +02:00
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inputs/lecture_1.tex
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% Lecture 1 - 2023-04-04 \lecture{1}{2023-04-04}{}
First, let us recall some basic definitions: First, let us recall some basic definitions:
\begin{definition} \begin{definition}

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inputs/lecture_12.tex
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% Lecture 12 2023-05-16 \lecture{12}{2023-05-16}{}
We now want to prove \autoref{clt}. We now want to prove \autoref{clt}.
The plan is to do the following: The plan is to do the following:

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inputs/lecture_13.tex
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% Lecture 13 2023-05 \lecture{13}{2023-05}{}
%The difficult part is to show \autoref{levycontinuity}. %The difficult part is to show \autoref{levycontinuity}.
%This is the last lecture, where we will deal with independent random variables. %This is the last lecture, where we will deal with independent random variables.

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inputs/lecture_4.tex
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\lecture{4}{}{}
\todo{Lecture 4 missing} \todo{Lecture 4 missing}

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inputs/lecture_8.tex
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% Lecture 8 2023-05-02 \lecture{8}{2023-05-02}{}
\subsection{Kolmogorov's 0-1-law} \subsection{Kolmogorov's 0-1-law}
Some classes of events always have probability $0$ or $1$. Some classes of events always have probability $0$ or $1$.
One example of such a 0-1-law is the Borel-Cantelli Lemma One example of such a 0-1-law is the Borel-Cantelli Lemma

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wtheo.sty
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\DeclareSimpleMathOperator{Exp} \DeclareSimpleMathOperator{Exp}
\newcommand*\dif{\mathop{}\!\mathrm{d}} \newcommand*\dif{\mathop{}\!\mathrm{d}}
\newcommand\lecture[3]{{\color{gray}\hfill Lecture #1 (#2)}} \newcommand\lecture[3]{\hrule{\color{darkgray}\hfill{\tiny[Lecture #1, #2]}}}