From 0db1737da7b6ed320e3937708af5275aedc56291 Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 9 Sep 2019 21:59:08 +1000 Subject: [PATCH 1/1] [spec] clean up --- spec/normal-dist-graph.tex | 81 ++++++++++++++++++++++++++++ spec/spec-collated.pdf | Bin 450195 -> 453748 bytes spec/spec-collated.tex | 107 ++++++++++++++++++++----------------- spec/statistics.pdf | Bin 249150 -> 249144 bytes spec/statistics.tex | 87 ++---------------------------- 5 files changed, 142 insertions(+), 133 deletions(-) create mode 100644 spec/normal-dist-graph.tex diff --git a/spec/normal-dist-graph.tex b/spec/normal-dist-graph.tex new file mode 100644 index 0000000..b0b558a --- /dev/null +++ b/spec/normal-dist-graph.tex @@ -0,0 +1,81 @@ +\pgfmathdeclarefunction{gauss}{2}{% + \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}% +} + +\pgfkeys{/pgf/decoration/.cd, + distance/.initial=10pt +} + +\pgfdeclaredecoration{add dim}{final}{ + \state{final}{% + \pgfmathsetmacro{\dist}{5pt*\pgfkeysvalueof{/pgf/decoration/distance}/abs(\pgfkeysvalueof{/pgf/decoration/distance})} + \pgfpathmoveto{\pgfpoint{0pt}{0pt}} + \pgfpathlineto{\pgfpoint{0pt}{2*\dist}} + \pgfpathmoveto{\pgfpoint{\pgfdecoratedpathlength}{0pt}} + \pgfpathlineto{\pgfpoint{(\pgfdecoratedpathlength}{2*\dist}} + \pgfsetarrowsstart{latex} + \pgfsetarrowsend{latex} + \pgfpathmoveto{\pgfpoint{0pt}{\dist}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedpathlength}{\dist}} + \pgfusepath{stroke} + \pgfpathmoveto{\pgfpoint{0pt}{0pt}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedpathlength}{0pt}} +}} + +\tikzset{dim/.style args={#1,#2}{decoration={add dim,distance=#2}, + decorate, + postaction={decorate,decoration={text along path, + raise=#2, + text align={align=center}, + text={#1}}}} +} + +\begin{tikzpicture} + \begin{axis}[every axis plot post/.style={ + mark=none,domain=-3:3,samples=50,smooth}, + axis x line=bottom, + axis y line=left, + enlargelimits=upper, + x=\textwidth/10, + ytick={0.55}, + yticklabels={\(\frac{1}{\sigma \sqrt{2\pi}}\)}, + xtick={-2,-1,0,1,2}, + x tick label style = {font=\footnotesize}, + xticklabels={\((\mu-2\sigma)\), \((\mu-\sigma)\), \(\mu\), \((\mu+\sigma)\), \((\mu+2\sigma)\)}, + xlabel={\(x\)}, + every axis x label/.style={at={(current axis.right of origin)},anchor=north west}, + every axis y label/.style={at={(axis description cs:-0.02,0.2)}, anchor=south west, rotate=90}, + ylabel={\(\Pr(X=x)\)}] + \addplot {gauss(0,0.75)}; + \fill[red!30] (-3,0) -- plot[id=f3,domain=-3:3,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-((x)^2)/(2*0.75^2))} -- (3,0) -- cycle; + \fill[darkgray!30] (3,0) -- plot[id=f3,domain=-3:3,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (3,0) -- cycle; + \fill[lightgray!30] (-2,0) -- plot[id=f3,domain=-2:2,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (2,0) -- cycle; + \fill[white!30] (-1,0) -- plot[id=f3,domain=-1:1,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (1,0) -- cycle; + \begin{scope}[<->] + \draw (-1,0.35) -- (1,0.35) node [midway, fill=white] {68.3\%}; + \draw (-2,0.25) -- (2,0.25) node [midway, fill=white] {95.5\%}; + \draw (-3,0.15) -- (3,0.15) node [midway, fill=white] {99.7\%}; + \end{scope} + \begin{scope}[-, dashed, gray] + \draw (-1,0) -- (-1, 0.35); + \draw (1,0) -- (1, 0.35); + \draw (-2,0) -- (-2, 0.25); + \draw (2,0) -- (2, 0.25); + \draw (-3,0) -- (-3, 0.15); + \draw (3,0) -- (3, 0.15); + \end{scope} + \end{axis} + \begin{axis}[every axis plot post/.append style={ + mark=none,domain=-3:3,samples=50,smooth}, + axis x line=bottom, + enlargelimits=upper, + x=\textwidth/10, + xtick={-2,-1,0,1,2}, + axis x line shift=30pt, + hide y axis, + x tick label style = {font=\footnotesize}, + xlabel={\(Z\)}, + every axis x label/.style={at={(axis description cs:1,-0.25)},anchor=south west}] + \addplot {gauss(0,0.75)}; + \end{axis} +\end{tikzpicture} diff --git a/spec/spec-collated.pdf 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-\usepackage[a4paper,margin=2cm]{geometry} -\usepackage{multicol} -\usepackage{dblfloatfix} -\usepackage{multirow} +\usepackage[dvipsnames, table]{xcolor} \usepackage{amsmath} \usepackage{amssymb} -\usepackage{harpoon} -\usepackage{tabularx} -\usepackage{makecell} -\usepackage{enumitem} -\usepackage[obeyspaces]{url} -\usepackage[dvipsnames, table]{xcolor} \usepackage{blindtext} +\usepackage{dblfloatfix} +\usepackage{enumitem} +\usepackage{fancyhdr} +\usepackage[a4paper,margin=2cm]{geometry} \usepackage{graphicx} -\usepackage{wrapfig} +\usepackage{harpoon} +\usepackage{import} +\usepackage{keystroke} +\usepackage{listings} +\usepackage{makecell} +\usepackage{mathtools} +\usepackage{mathtools} +\usepackage{multicol} +\usepackage{multirow} +\usepackage{pgfplots} +\usepackage{pst-plot} +\usepackage{subfiles} +\usepackage{tabularx} +\usepackage{tcolorbox} +\usepackage{tikz-3dplot} \usepackage{tikz} \usepackage{tkz-fct} -\usepackage{tikz-3dplot} -\usepackage{pgfplots} -\usetikzlibrary{arrows, - decorations, - decorations.markings, - decorations.text, - decorations.pathreplacing, - scopes +\usepackage[obeyspaces]{url} +\usepackage{wrapfig} + + +\usetikzlibrary{% + angles, + arrows, + arrows.meta, + calc, + datavisualization.formats.functions, + decorations, + decorations.markings, + decorations.text, + decorations.pathreplacing, + decorations.text, + scopes } -\usetikzlibrary{datavisualization.formats.functions} -\usetikzlibrary{decorations.markings} -\usepgflibrary{arrows.meta} -\usetikzlibrary{decorations.markings} + +\newcommand{\midarrow}{\tikz \draw[-triangle 90] (0,0) -- +(.1,0);} + \usepgflibrary{arrows.meta} -\usepackage{pst-plot} +\pgfplotsset{compat=1.16} +\pgfplotsset{every axis/.append style={ + axis x line=middle, % put the x axis in the middle + axis y line=middle, % put the y axis in the middle + axis line style={->}, % arrows on the axis + xlabel={$x$}, % default put x on x-axis + ylabel={$y$}, % default put y on y-axis +}} + \psset{dimen=monkey,fillstyle=solid,opacity=.5} \def\object{% \psframe[linestyle=none,fillcolor=blue](-2,-1)(2,1) @@ -40,49 +64,32 @@ \uput[-90]{*0}(0,-2){$\vec{w}$}} } -\usetikzlibrary{calc} -\usetikzlibrary{angles} -\usetikzlibrary{datavisualization.formats.functions} -\usetikzlibrary{decorations.markings} -\usepgflibrary{arrows.meta} -\usepackage{fancyhdr} \pagestyle{fancy} \fancyhead[LO,LE]{Year 12 Specialist} \fancyhead[CO,CE]{Andrew Lorimer} -\usepackage{mathtools} -\usepackage{xcolor} % used only to show the phantomed stuff + \renewcommand\hphantom[1]{{\color[gray]{.6}#1}} % comment out! -\setlength\fboxsep{0pt} \setlength\fboxrule{.2pt} % for the \fboxes \newcommand*\leftlap[3][\,]{#1\hphantom{#2}\mathllap{#3}} \newcommand*\rightlap[2]{\mathrlap{#2}\hphantom{#1}} +\linespread{1.5} +\setlength{\parindent}{0pt} +\setlength\fboxsep{0pt} \setlength\fboxrule{.2pt} % for the \fboxes + \newcolumntype{L}[1]{>{\hsize=#1\hsize\raggedright\arraybackslash}X}% \newcolumntype{R}[1]{>{\hsize=#1\hsize\raggedleft\arraybackslash}X}% + \definecolor{cas}{HTML}{e6f0fe} \definecolor{important}{HTML}{fc9871} \definecolor{dark-gray}{gray}{0.2} -\linespread{1.5} -\newcommand{\midarrow}{\tikz \draw[-triangle 90] (0,0) -- +(.1,0);} + \newcommand{\tg}{\mathop{\mathrm{tg}}} \newcommand{\cotg}{\mathop{\mathrm{cotg}}} \newcommand{\arctg}{\mathop{\mathrm{arctg}}} \newcommand{\arccotg}{\mathop{\mathrm{arccotg}}} -\pgfplotsset{every axis/.append style={ - axis x line=middle, % put the x axis in the middle - axis y line=middle, % put the y axis in the middle - axis line style={->}, % arrows on the axis - xlabel={$x$}, % default put x on x-axis - ylabel={$y$}, % default put y on y-axis -}} -\usepackage{tcolorbox} + \newtcolorbox{warning}{colback=white!90!black, leftrule=3mm, colframe=important, coltext=important, fontupper=\sffamily\bfseries} \newtcolorbox{cas}{colframe=cas!75!black, title=On CAS, left*=3mm} -\usepackage{keystroke} -\usepackage{listings} -\usepackage{mathtools} -\pgfplotsset{compat=1.16} -\usepackage{subfiles} -\usepackage{import} -\setlength{\parindent}{0pt} + \begin{document} \begin{multicols}{2} diff --git a/spec/statistics.pdf b/spec/statistics.pdf index 5ee10734e799982484a0982968768e6497d8b606..5408f9ead6b38066451bad55ab97ad94bf715d32 100644 GIT binary patch delta 11322 zcmaiaRZN}@&?QpbrMSDh%UcS?-QC^&#d&adcbDRn;#S<<-QArch5y^^?!{j1#Uyhk zGnwREOmZ@(I}5Ef3$0!j1B#D7eOC#J4!G1?k0X+F@jKRBhz=mB?nrqahk|87!X)oy zOOu5%(4FhQkW(cxWid;}ZhCtJ(KfJTE-ng-q5dNaKs#`=lr%S&kjUY~NKLJLYf{~u zr~Ulc8(rQmXL;t&nCbFdeVGZj>nLIV0JE}m>p57^7E zU9i+n)zxiv3$EK>1#kMg`m}BP(NTOlxBO{ey`1*DbEL5O?%BpQqQ)S}{#ZW{E~UU)MhL2~9fz^y;dK9c?cQ zaSBQobaUHl;<}=Y3mx$ksvND``8l2M^T0!nbyL$uK7Vfi5bJIn`Th}P{qwK7)7#_O z;o|)9WpZ=8H)gu|`?)oW%_Bjb_p#;T?i__0Yv8qhoc>wrt@u@4aKhl; zp%qrCk;ar!cNY@4(M`%2*z;@twSHv4$Xi!rz!@>4n=G*I^FWovipG6rJi6$)Jkk4v zK*K%q-n}F~;$S}IPFko*AIp)>n2XM}bDZqwC@;64Qp4`V!Wf+=3Ej4uyNy%v{qIp6 zz?D}_#>cEDBhEDy&DtVLFR!+?IOH{$u0{HdM~sP+X_Y#kS{rEc*f 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z2=?X4JyBU<7(bHRcHy8==nluYhWRr5$MA+dAw-NYy)x+V5*kkTWwHm8IivLH?k+6p z8U`eub!EG2h1UAI>>VfJ)yb>6cS3rH9H$t@5n#8wbwc)2`jd}MOp^O2D-SEzPw}5(oMMuk5^Q|j!lZ)#=ZGOZi-LutmAf@52L~JJ z{|8%%rg%68RWXP6?zio}wG0>>QMIOBLjSrN@GTIevh72bFToe9Wt5h%gEq=F@R4$r z0kfG6on<~pJjXe0+7j&ZQiJ*OcQV~kf9Jn>CEO9nQEy@G;u(`w*~QYvcy+1F%<~jd zWRpqN&BJ4Rg+XV28-wWog}Lr6lH5@-=Ayt(RYS%kX!f7WGSvTtk>EnQG})9ff60;( znJs0J$087E+>gkh2j$^q(dekDNT%x diff --git a/spec/statistics.tex b/spec/statistics.tex index d7e7723..323ec2a 100644 --- a/spec/statistics.tex +++ b/spec/statistics.tex @@ -105,89 +105,10 @@ Always express \(z\) as +ve. Express confidence \textit{interval} as ordered pair. \end{warning} -\pgfmathdeclarefunction{gauss}{2}{% - \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}% -} - \pgfplotsset{every axis/.append style={ - axis x line=middle, % put the x axis in the middle - axis y line=middle, % put the y axis in the middle - }} \pgfkeys{/pgf/decoration/.cd, - distance/.initial=10pt -} \pgfdeclaredecoration{add dim}{final}{ -\state{final}{% -\pgfmathsetmacro{\dist}{5pt*\pgfkeysvalueof{/pgf/decoration/distance}/abs(\pgfkeysvalueof{/pgf/decoration/distance})} - \pgfpathmoveto{\pgfpoint{0pt}{0pt}} - \pgfpathlineto{\pgfpoint{0pt}{2*\dist}} - \pgfpathmoveto{\pgfpoint{\pgfdecoratedpathlength}{0pt}} - \pgfpathlineto{\pgfpoint{(\pgfdecoratedpathlength}{2*\dist}} - \pgfsetarrowsstart{latex} - \pgfsetarrowsend{latex} - \pgfpathmoveto{\pgfpoint{0pt}{\dist}} - \pgfpathlineto{\pgfpoint{\pgfdecoratedpathlength}{\dist}} - \pgfusepath{stroke} - \pgfpathmoveto{\pgfpoint{0pt}{0pt}} - \pgfpathlineto{\pgfpoint{\pgfdecoratedpathlength}{0pt}} -}} -\tikzset{dim/.style args={#1,#2}{decoration={add dim,distance=#2}, - decorate, - postaction={decorate,decoration={text along path, - raise=#2, - text align={align=center}, - text={#1}}}}} - \begin{figure*}[hb] - \centering - {\begin{center} \begin{tikzpicture} - \pgfplotsset{set layers, axis x line=middle, axis y line=middle} -\begin{axis}[every axis plot post/.append style={ - mark=none,domain=-3:3,samples=50,smooth}, - axis x line=bottom, - axis y line=left, - enlargelimits=upper, - x=\textwidth/10, - ytick={0.55}, - yticklabels={\(\frac{1}{\sigma \sqrt{2\pi}}\)}, - xtick={-2,-1,0,1,2}, - x tick label style = {font=\footnotesize}, - xticklabels={\((\mu-2\sigma)\), \((\mu-\sigma)\), \(\mu\), \((\mu+\sigma)\), \((\mu+2\sigma)\)}, - xlabel={\(x\)}, - every axis x label/.style={at={(current axis.right of origin)},anchor=north west}, - every axis y label/.style={at={(axis description cs:-0.02,0.2)}, anchor=south west, rotate=90}, - ylabel={\(\Pr(X=x)\)}] - \addplot {gauss(0,0.75)}; -\fill[red!30] (-3,0) -- plot[id=f3,domain=-3:3,samples=50] - function {1/(0.75*sqrt(2*pi))*exp(-((x)^2)/(2*0.75^2))} -- (3,0) -- cycle; - \fill[darkgray!30] (3,0) -- plot[id=f3,domain=-3:3,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (3,0) -- cycle; - \fill[lightgray!30] (-2,0) -- plot[id=f3,domain=-2:2,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (2,0) -- cycle; - \fill[white!30] (-1,0) -- plot[id=f3,domain=-1:1,samples=50] function {1/(0.75*sqrt(2*pi))*exp(-x*x*0.5/(0.75*0.75))} -- (1,0) -- cycle; - \begin{scope}[<->] - \draw (-1,0.35) -- (1,0.35) node [midway, fill=white] {68.3\%}; - \draw (-2,0.25) -- (2,0.25) node [midway, fill=white] {95.5\%}; - \draw (-3,0.15) -- (3,0.15) node [midway, fill=white] {99.7\%}; - \end{scope} - \begin{scope}[-, dashed, gray] - \draw (-1,0) -- (-1, 0.35); - \draw (1,0) -- (1, 0.35); - \draw (-2,0) -- (-2, 0.25); - \draw (2,0) -- (2, 0.25); - \draw (-3,0) -- (-3, 0.15); - \draw (3,0) -- (3, 0.15); - \end{scope} -\end{axis} -\begin{axis}[every axis plot post/.append style={ - mark=none,domain=-3:3,samples=50,smooth}, - axis x line=bottom, - enlargelimits=upper, - x=\textwidth/10, - xtick={-2,-1,0,1,2}, - axis x line shift=30pt, - hide y axis, - x tick label style = {font=\footnotesize}, - xlabel={\(Z\)}, - every axis x label/.style={at={(axis description cs:1,-0.25)},anchor=south west}] - \addplot {gauss(0,0.75)}; -\end{axis} -\end{tikzpicture}\end{center}} - \end{figure*} + \begin{figure*}[hb] + \centering + \include{normal-dist-graph} + \end{figure*} \subsection*{Central limit theorem} -- 2.47.1