mirror of
https://github.com/janishutz/eth-summaries.git
synced 2026-04-28 10:09:23 +02:00
95 lines
3.4 KiB
TeX
95 lines
3.4 KiB
TeX
\documentclass{article}
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\PassOptionsToPackage{skip=0pt}{parskip}
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\input{~/projects/latex/janishutz-helpers.tex}
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\usepackage{bm}
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\usepackage{lmodern}
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\setFontType{sans}
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\setupCheatSheet{Wahrscheinlichkeit und Statistik}
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\loadGerman
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\setnumberingpreset{off}
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\renewcommand{\definitionShortNamingDE}{Def}
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\renewcommand{\propositionShortNamingDE}{Prop}
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\renewcommand{\remarkShortNamingDE}{Bem}
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\setsubsectionnumbering{section}
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\renewcommand{\examplenumbering}{off}
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\newcommand{\cov}{\text{cov}}
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\renewcommand{\vec}[1]{\bm{#1}}
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\begin{document}
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\startDocument
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\noverticalspacing
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% TODO: Short combinatorics summary
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% TODO: Most important sequences transforms
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% TODO: Logarithms (maybe including table), trick with -\ln(...) using \ln(1) - \ln(...)
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% TODO: Basic analysis stuff (some common integrals, fundamental theorem)
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\section{Basics}
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\input{parts/00_basics/00_probability-space.tex}
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\input{parts/00_basics/01_examples-probability-spaces.tex}
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\input{parts/00_basics/02_properties-of-events.tex}
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\input{parts/00_basics/03_properties-of-measures.tex}
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\input{parts/00_basics/04_conditional-probability.tex}
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\input{parts/00_basics/05_independence.tex}
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\newsection
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\section{Zufallsvar., Verteilungsfunktionen}
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\input{parts/01_random-variables/00_definition.tex}
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\input{parts/01_random-variables/01_distribution-function.tex}
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\input{parts/01_random-variables/02_independence.tex}
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\input{parts/01_random-variables/03_transformations.tex}
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\input{parts/01_random-variables/04_construction.tex}
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\newsectionNoPB
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\section{Diskrete und stetige ZV}
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\input{parts/02_discrete-continuous-rv/00_continuity-of-pdf.tex}
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\input{parts/02_discrete-continuous-rv/01_almost-certain-events.tex}
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\input{parts/02_discrete-continuous-rv/02_discrete-rv.tex}
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\input{parts/02_discrete-continuous-rv/03_distributions/00_bin.tex}
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\input{parts/02_discrete-continuous-rv/03_distributions/01_geom.tex}
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\input{parts/02_discrete-continuous-rv/03_distributions/02_negbin.tex}
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\input{parts/02_discrete-continuous-rv/03_distributions/03_hyp-geom.tex}
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\input{parts/02_discrete-continuous-rv/03_distributions/04_poisson.tex}
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\input{parts/02_discrete-continuous-rv/04_cont-dist.tex}
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\input{parts/02_discrete-continuous-rv/05_cont-distributions/00_eq.tex}
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\input{parts/02_discrete-continuous-rv/05_cont-distributions/01_exp.tex}
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\input{parts/02_discrete-continuous-rv/05_cont-distributions/02_cauchy.tex}
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\input{parts/02_discrete-continuous-rv/05_cont-distributions/03_normal.tex}
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% \input{parts/02_discrete-continuous-rv/}
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\newsectionNoPB
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\section{Erwartungswert}
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\input{parts/03_expected-value/00_intro.tex}
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\input{parts/03_expected-value/01_disc.tex}
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\input{parts/03_expected-value/02_cont.tex}
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\input{parts/03_expected-value/03_properties.tex}
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\input{parts/03_expected-value/04_inequalities.tex}
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\input{parts/03_expected-value/05_variance.tex}
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\input{parts/03_expected-value/06_covariance.tex}
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% \input{parts/03_expected-value/}
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\newsection
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\section{Gemeinsame Verteilungen}
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\input{parts/04_joint-distribution/00_discrete.tex}
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\input{parts/04_joint-distribution/01_continuous.tex}
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% \input{parts/04_joint-distribution/}
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\newsection
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\section{Das Gesetz der grossen Zahlen}
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\input{parts/05_limit-theorems/00_intro.tex}
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\input{parts/05_limit-theorems/01_weak-law-of-large-numbers.tex}
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\input{parts/05_limit-theorems/02_strong-law-of-large-numbers.tex}
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\input{parts/05_limit-theorems/03_central-limit-theorem.tex}
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\input{parts/05_limit-theorems/04_chernoff-bounds.tex}
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% \input{parts/05_limit-theorems/}
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\end{document}
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