\documentclass[UTF8,a1paper,landscape]{ctexart}%UTF8，ctexart中文支持，landscape横向版面
\usepackage[svgnames]{xcolor}
\usepackage{tikz}%画图
\usetikzlibrary{arrows,shapes,positioning}
\tikzstyle arrowstyle=[scale=1]
\usepackage{geometry}%页边距设置
\geometry{top=0.5cm,bottom=0.5cm,left=0.5cm,right=0.5cm}
\usepackage{fancyhdr}%页头页尾页码设置
\pagestyle{fancy}
\begin{document}
\title{\textbf{《概率论与数理统计》学习图解}}%标题
\author{DencChaohai}%作者
\maketitle
\newpage%重新开始一页
\part{概率论}
\section{逻辑关系图解}
\begin{center}%图形居中
\begin{tikzpicture}
[level 1/.style={sibling distance=1cm},level 2/.style={sibling distance=3cm},level 3/.style={sibling distance=5cm},level 4/.style={sibling distance=7cm}]%设定树枝的长度
\tikzstyle{every node}=[scale=1]%文字缩放0.6倍
%定义 \node(编号)at(位置)[属性]{内容}
%排序，先左后右，先上后下
\node(xx)at(0,0)[draw,align=center]{现象};
\node(qdxxx)at(10,10)[draw,align=center]{确定性现象};
\node(sjxxx)at(10,-10)[draw,align=center]{随机性现象};
\node(gc)at(10+5,-10+1){观察};
\node(sy)at(20,-10)[draw,align=center]{试验}
[grow=up]
child{node{特征}
child{node{3.随机性}}
child{node{2.可观察}}
child{node{1.可重复}}
};
\node(jg)at(20+5,-10+1){（试验中可观察的特定特征的）结果};
\node(ybd)at(30,-10)[draw,align=center]{样本点\\$\omega$};
\node(dy)at(30+1,-10-5){单一};
\node(jbsj)at(30,-20)[draw,align=center]{基本事件};
\node(hs)at(32,-20-5){函数$X=X(\omega)$};
\node(sjbl)at(30,-30)[draw,align=center]{随机变量\\$X$}
[grow=left]
child{node at(-5,0){概率分布$p_i=P\{X=x_i\}$,概率密度$f(x)=F'(x)$}
child{node at(-7,0){分布函数$F(x)=P\{X\leq x\}$}}};
\node(blz)at(32,-29){变量值$x_i,x$};
\node(blz)at(38,-29){密度$p_i,f(x)$};
\node(sjxl)at(30,-40)[draw,align=center]{随机向量\\$\vec{X}=\{X_1,X_2,\dots\}$}
[grow=left]
child{node at(-5,0){联合密度$p_{ij},f(x,y)$（边缘密度$p_i^X,p_j^Y,f_X(x),f_Y(y)$）}
child{nodeat(-9,0){联合分布$F(x,y)$（边缘分布$F_X(x),F_Y(y)$）}}};
\node(qt)at(30+5,-10+1){全体};
\node(fh)at(30+5,-20+1){复合};
\node(xc)at(30+5,-30+1){相乘$x_ip_i,xf(x)$}
[grow=up]
child{node{一阶原点矩|期望$EX=\sum xp_i,\int xf(x)dx$}
child{node{二阶中心矩|方差$DX=E(X-EX)^2$}}};
\node(qh)at(35.5,-28){求和};
\node(blhs)at(36.8,-26.8){变量函数$Y=g(Y)$};
\node(ybkj)at(40,-10)[draw,align=center]{样本空间\\$\Omega$}
[grow=right]
child{node at(1,0){$\Omega=\left\lbrace \omega|P(\omega)\right\rbrace $}
child{node{样本点无限$\Omega=(a,b)$}}
child{node{样本点有限$\Omega=\{\omega_1,\omega_2,\dots,\omega_n\}$}}};
\node(zj)at(40+1,-10-5){子集}
[grow=right]
child{node at(1,0){全集（必然事件）$\Omega$}}
child{node at(2,0){子集（随机事件）$A,B,\dots $}}
child{node at(1,0){空集（不可能事件）$\emptyset$}};
\node(sj)at(40,-20)[draw,align=center]{事件\\$A,B,\dots$};
\node(cd)at(40+1,-20-5){测度}
[grow=right]
child{node at(1,0){$P(\Omega)=1$}}
child{node at(1,0){$0\leq P(A)\leq 1$}}
child{node at(1,0){可列可加}};
\node(gl)at(40,-30)[draw,align=center]{概率\\$P(A)$}
[grow=down]
child{node at(-2,-2){基本概型}
child{node{古典概型（有限等可能）}}
child{node at(2,-1){几何概型（无限等可能）}}}
child{node at(7,-2){条件概率$P(B|A)=\frac{P(AB)}{P(A)}$|乘法公式$P(AB)=P(A)P(B|A)$|独立性$P(AB)=P(A)P(B)$}
[grow=down]
child{node at(3,-3){贝叶斯$P(A_i|B)=\frac{P(A_iB)}{P(B)}=\frac{P(A_i)P(B|A_i)}{\sum P(A_j)P(B|A_j)}$}}
child{node at(4,-1){全概率$P(B)=\sum P(A_i)P(B|A_i)$}}};
\node(lj)at(45,-29){累计,离散分段阶梯，连续积分面积};
\node(dj)at(40+5,-20+1){等价};
\node(jh)at(50,-20)[draw,align=center]{集合}
[grow=right]
child{node{运算律}
child{node at(0+3,0){对偶律$\overline{A\cup B}=\overline{A}\cap \overline{B},\overline{A\cap B}=\overline{A}\cup \overline{B}$}
child{node{分配律$A\cap(B\cup C)=(A\cap B)\cup (A\cap C),A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$}
child{node{交换律$A+B=B+A$}}
child{node at(3,-5){结合律$A+(B+C)=(A+B)+C$}}
}
child{node at(3,-4){自反律$\overline{\overline{A}}=A$}}}};
\node(fbhs)at(50,-30)[draw,align=center]{分布函数\\$F(x)=P\{X\leq x\}$};
%连线 \draw[箭头](始点)--(终点)
\draw[->](xx)--(qdxxx);
\draw[->](xx)--(sjxxx);
\draw[->](sjxxx)--(sy);
\draw[->](ybd)--(jbsj);
\draw[->](sy)--(ybd);
\draw[->](ybd)--(ybkj);
\draw[->](jbsj)--(sjbl);
\draw[->](ybkj)--(sj);
\draw[->](sj)--(gl);
\draw[->](jbsj)--(sj);
\draw[->](sjbl)--(xc);
\draw[->](gl)--(xc);
\draw[->](sj)--(jh);
\draw[->](gl)--(fbhs);
\draw[->](sjbl)--(sjxl);
\draw[->](sjbl)--(gl);
\end{tikzpicture}
\end{center}
\newpage
\part{数理统计}
\section{逻辑关系图解}
\begin{center}
\begin{tikzpicture}
\node(gt)at(0,0)[fill=green,circle]{个体};
\node(zt)at(10,10)[fill=green,circle]{总体$X$};
\node(yb)at(10,-10)[fill=green,circle]{样本$(X_1,X_2,\dots)$};
\node(ztfbhs)at(20,10)[fill=green,circle]{总体分布函数$F(x)$};
\node(ybfbhs)at(20,-10)[fill=green,circle]{样本分布函数$F(x_1,x_2,\dots)$};
\node at(12,0){}
[grow=right]
child{node at(2,0){样本推断总体类型（类型由经验一般可以得出）}}
child{node at(2,0){样本推断总体参数（主要的是推断参数）}
[grow=up]
child{node at(1,2){统计量（不含总体未知参数的函数）}
child{node{方差}}
child{node{均值}}}
child{node at(8,0){枢轴量（总体类型已知，但只含一个总体未知参数的函数）}}};
\draw[->](gt)--(zt);
\draw[->](gt)--(yb);
\draw[->](yb)to node(tjtd)[right]{统计推断}(zt);
\draw[->](zt)--(ztfbhs);
\draw[->](yb)--(ybfbhs);
\end{tikzpicture}
\end{center}
\end{document}
