MathematicalStatistics.tex

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\begin{document}

\author{PSH, KSP, KMJ, PBU}
\title{수리통계학 강의록}
\subtitle{Mathematical Statistics Lecture Note\\{\normalsize 3rd DRAFT}}
\maketitle

\frontmatter%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\extrachap{$ $}

\begin{flushright}
함께했던 날들과,\\
함께할 날들을 위해.\\
2018년의 끝자락, 관악에서.
\end{flushright}

\extrachap{Acronyms}

\begin{itemize}
    \item[\texttt{\textbf{WLOG}}]{일반성을 잃지 않고(\texttt{Without Loss Of Generality})}
    \item[\texttt{\textbf{TFAE}}]{다음은 서로 동치이다.(\texttt{The Followings Are Equivalent.})}
    \item[\texttt{\textbf{ow.}}]{그렇지 않으면(\texttt{OtherWise})}
    \item[\texttt{\textbf{ae.}}]{거의 어디서나(\texttt{Almost Everywhere})}
    \item[\texttt{\textbf{LUBP}}]{\texttt{Least Upper Bound Property}}
    \item[\texttt{\textbf{GLBP}}]{\texttt{Greatest Lower Bound Property}}
    \item[\texttt{\textbf{MSP}}]{\texttt{Monotone Sequence Property}}
    \item[\texttt{\textbf{NSP}}]{\texttt{Nested Set Property}} 
    \item[\texttt{\textbf{MCT}}]{단조수렴정리(\texttt{Monotone Convergence Theorem})}
    \item[\texttt{\textbf{DCT}}]{\texttt{Lebesgue}의 지배수렴정리(\texttt{Lebesgue's Dominated Convergence Theorem})}
    \item[\texttt{\textbf{FTC}}]{미적분학의 기본정리(\texttt{Funcdamental Theorem of Calculus})}
    \item[\texttt{\textbf{MVT}}]{평균값 정리(\texttt{Mean Value Theorem})}
    \item[\texttt{\textbf{IVT}}]{중간값 정리(\texttt{Intermediate Value Theorem})}
    \item[\texttt{\textbf{INFT}}]{역함수 정리(\texttt{INverse Function Theorem})}
    \item[\texttt{\textbf{rv.}}]{확률변수(\texttt{Random Variable}) 혹은 확률벡터(\texttt{Random Vector})}
    \item[\texttt{\textbf{PDF}}]{확률밀도함수(\texttt{Probability Density Function})}
    \item[\texttt{\textbf{PMF}}]{확률질량함수(\texttt{Probability Mass Function})}
    \item[\texttt{\textbf{CDF}}]{누적분포함수(\texttt{Cumulative Distribution Function})}
    \item[\texttt{\textbf{MGF}}]{적률생성함수(\texttt{Moment Generating Function})}
    \item[\texttt{\textbf{CF}}]{특성함수(\texttt{Characteristic Function})}
    \item[\texttt{\textbf{CGF}}]{누율생성함수(\texttt{Cumulant Generating Function})}
    \item[\texttt{\textbf{PGF}}]{확률생성함수(\texttt{Probability Generating Function})}
    \item[\texttt{\textbf{iid.}}]{\texttt{Independent and Identically Distributed rv.}}
    \item[\texttt{\textbf{io.}}]{\texttt{Infinitely Often}}
    \item[\texttt{\textbf{as.}}]{거의 확실하게(\texttt{Almost Surely})}
\end{itemize}

\tableofcontents

\mainmatter%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\chapter{Preliminary}

\input{Preliminary.tex}

\part{Probability and Measure}

\chapter{Measure Theory}

\input{MeasureTheory.tex}

\chapter{Probability Theory}

\input{ProbabilityTheory.tex}

% \part{Distributions}

% \chapter{Distribution Theory}

% \input{Chapter3.tex}

\backmatter%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}