Probability theory and Mathematical statistics illustration

\documentclass[utf8,a1paper,landscape]{ctexart}%utf8,ctexart Chinese support, Landscape landscape layout \usepackage[svgnames]{xcolor}\usepackage{tikz}%Drawing \usetikzlibrary{arrows,shapes,positioning}\tikzstyle Arrowstyle=[scale=1]\usepackage{geometry}%Margin settings \geometry{top=0.5cm,bottom=0.5cm,left=0.5cm,right=0. 5CM}\USEPACKAGE{FANCYHDR}%page Footer page set \pagestyle{fancy}\begin{document} \title{\textbf{learning plot of probability and Mathematical Statistics}}%title \author{dencchaohai}%author \maketitle \newpage%restart a page \part{probability theory} \section{logical relationship plot} \begin{center}%graphics Centered \begin{tikzpicture} [ level1/.style={sibling Distance=1cm},level2/.style={sibling Distance=3cm},level3/.style={sibling Distance=5cm},level4/.style={sibling distance=7cm}]%set the length of the Tree \tikzstyle{every node}=[scale=1]%text zoom 0.6 times times%define \node (number) at (position) [Property]{content}%sort, first left and right, first up and down \node (XX) at (0,0) [draw,align=Center]                {phenomenon}; \node (qdxxx) at (Ten,Ten) [draw,align=Center]        {Deterministic phenomenon}; \node (sjxxx) at (Ten,-Ten) [draw,align=Center]        {Random phenomenon}; \node (GC) at (Ten+5,-Ten+1) {observe}; \node (SY) at ( -,-Ten) [draw,align=Center]                Test [Grow=Up ] child{node{feature} child{node{3. Randomness}} child{node{2. can be observed}} child{node{1. Repeatable}}        }; \node (JG) at ( -+5,-Ten+1{The result of a particular characteristic observable in the experiment}; \node (YBD) at ( -,-Ten) [draw,align=Center]        {Sample Point \\$\omega$}; \node (DY) at ( -+1,-Ten-5) {single}; \node (JBSJ) at ( -,- -) [draw,align=Center]        {Basic event}; \node (HS) at ( +,- --5) {function $x=X (\omega) $}; \node (SJBL) at ( -,- -) [draw,align=Center]        {random variable \ \ $X $} [Grow=Left ] Child{node at (-5,0) {probability distribution $p_i=p\{x=x_i\}$, probability density $f (X) =f'(x) $}Child{node at (-7,0) {distribution function $f (x) =P\{x\leq x\}$}}; \node (BLZ) at ( +,- in) {variable value $x_i,x$}; \node (BLZ) at ( -,- in) {density $p_i,f (x) $}; \node (SJXL) at ( -,- +) [draw,align=center]{random vector \\$\vec{x}=\{x_1,x_2,\dots\}$} [Grow=Left ] Child{node at (-5,0) {Joint density $p_{ij},f (x, y) $ (Edge density $p_i^x,p_j^y,f_x (X), F_y (Y) $)} child{nodeat (-9,0{Federated Distribution $f (x, y) $ (Edge distribution $f_x (×), F_y (y) $)}}}; \node (QT) at ( -+5,-Ten+1) {all}; \node (FH) at ( -+5,- -+1) {composite}; \node (XC) at ( -+5,- -+1) {multiply $x_ip_i,xf (x) $} [Grow=Up ] child{node{First Order original point moment| expect $ex=\sum xp_i,\intXF (x) dx$} child{node{second-order center moment| Variance $dx=e (X-EX) ^2$}}}; \node (QH) at (35.5,- -) {sum}; \node (BLHS) at (36.8,-26.8) {variable function $y=g (Y) $}; \node (YBKJ) at ( +,-Ten) [draw,align=Center]            {Sample Space \\$\omega$} [Grow=Right ] Child{node at (1,0) {$\omega=\left\lbrace \omega|P (\omega) \right\rbrace $} child{node{Sample Point Infinity $\omega=(A, b) $}} child{node{Sample points Limited $\omega=\{\omega_1,\omega_2,\dots,\omega_n\}$}}}; \node (ZJ) at ( ++1,-Ten-5) {subset} [grow=Right ] Child{node at (1,0) {Complete (inevitable event) $\omega$}} Child{node at (2,0{subset (random event) $A, B,\dots $}} Child{node at (1,0{Empty set (Impossible event) $\emptyset$}}; \node (SJ) at ( +,- -) [draw,align=Center]        {event \ \ $A, b,\dots$}; \node (CD) at ( ++1,- --5) {measure} [Grow=Right ] Child{node at (1,0) {$P (\omega) =1$}} Child{node at (1,0){$0\leq P (A) \leq1$}} Child{node at (1,0) {can be added}}; \node (GL) at ( +,- -) [draw,align=Center]        {probability \ $P (A) $} [Grow=Down ] Child{node at (-2,-2{Basic Approximate} child{node{Classical Overview (limited, etc.)}} Child{node at (2,-1{geometric approximate (infinite) }}} Child{node at (7,-2) {conditional probability $p (b| A) =\frac{p (AB)}{p (a)}$| multiplication formula $p (AB) =p (a) P (b| A) $| Independence $p (AB) =p (A) p (B) $} [Grow=Down ] Child{node at (3,-3) {Bayesian $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) {full probability $p (B) =\sum P (a_i) p (b|a_i) $}}; \node (LJ) at ( $,- in) {cumulative, discrete segment ladder, continuous integral area}; \node (DJ) at ( ++5,- -+1) {equivalent}; \node (JH) at ( -,- -) [draw,align=Center]        Collection [Grow=Right ] child{node{operation Law} Child{node at (0+3,0) {Dual law $\overline{a\cup b}=\overline{a}\cap \overline{b},\overline{a\cap b}=\overline{a}\cup \overline{b}$} child{node{Distribution Law $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{Exchange Law $ A+b=b+a$}} Child{node at (3,-5) {Binding Law $a+ (b+c) = (a+b) +C $}} } Child{node at (3,-4) {reflexive Law $\overline{\overline{a}}=a$}}}; \node (FBHS) at ( -,- -) [draw,align=center]{distribution function \ \ $F (x) =P\{x\leq x\}$}; % Connection \draw[Arrows] (starting point)--(end) \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{Mathematical Statistics} \section{logical relationship plot} \begin{center} \BEGIN{TIKZP Icture} \node (GT) at (0,0) [fill=Green,circle]        {individual}; \node (ZT) at (Ten,Ten) [fill=Green,circle]        {Total $x$}; \node (YB) at (Ten,-Ten) [fill=Green,circle]        {Sample $ (x_1,x_2,\dots) $}; \node (ZTFBHS) at ( -,Ten) [fill=Green,circle]        {Total distribution function $f (x) $}; \node (YBFBHS) at ( -,-Ten) [fill=Green,circle]        {Sample distribution function $f (x_1,x_2,\dots) $}; \node at ( A,0) {} [Grow=Right ] Child{node at (2,0{The sample infers the overall type (which the type is generally derived from experience)}} Child{node at (2,0{The sample infers the overall parameters (mainly inferred parameters)} [Grow=Up ] Child{node at (1,2{Statistics (functions without overall unknown parameters)} child{node{Variance}} child{node{mean}}} Child{node at (8,0{The pivot volume (a function with a known overall type but with only one overall unknown parameter)}}}; \draw[->] (GT)--(ZT); \draw[->] (GT)--(YB); \draw[-] (YB) to Node (TJTD) [right]{Statistical Inference} (ZT); \draw[->] (ZT)--(ZTFBHS); \draw[->] (YB)--(YBFBHS); \end{tikzpicture} \end{center}\end{document}

Probability theory and Mathematical statistics illustration