From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Fri, 23 Aug 2019 01:55:14 +0000 (+1000)
Subject: [spec] normal distribution graph
X-Git-Tag: yr12~58
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/774f1e17c8ce4d519877f744d951c2cf112df951?ds=inline

[spec] normal distribution graph
---

diff --git a/spec/statistics.pdf b/spec/statistics.pdf
index 357175e..56f9c83 100644
Binary files a/spec/statistics.pdf and b/spec/statistics.pdf differ
diff --git a/spec/statistics.tex b/spec/statistics.tex
index 7c89068..0b6f4ce 100644
--- a/spec/statistics.tex
+++ b/spec/statistics.tex
@@ -45,7 +45,7 @@
   \begin{align*}
     \Pr(Y \le y) &= \Pr(aX+b \le y) \\
     &= \Pr\left(X \le \dfrac{y-b}{a}\right) \\
-    &= \int^{\dfrac{y-b}{a}}_{-\infty} f(x) \> dx
+    &= \int^{\frac{y-b}{a}}_{-\infty} f(x) \> dx
   \end{align*}
 
   \begin{align*}
@@ -68,7 +68,7 @@
 
   where \(n\) is the size of the sample (number of sample points) and \(x\) is the value of a sample point
 
-  \subsubsection*{\colorbox{cas}{On CAS:}}
+  \begin{tcolorbox}[colframe=cas!75!black, title=On CAS]
 
   \begin{enumerate}
     \item Spreadsheet
@@ -77,6 +77,7 @@
     \item Input range as A1:An where \(n\) is the number of samples
     \item Graph \(\rightarrow\) Histogram
   \end{enumerate}
+  \end{tcolorbox}
 
   \subsubsection*{Sample size of \(n\)}
 
@@ -84,8 +85,13 @@
 
   Sample mean is distributed with mean \(\mu\) and sd \(\frac{\sigma}{\sqrt{n}}\) (approaches these values for increasing sample size \(n\)).
 
-  \colorbox{cas}{On CAS:} Spreadsheet \(\rightarrow\) Catalog \(\rightarrow\) \verb;randNorm(sd, mean, n); where \verb;n; is the number of samples. Show histogram with Histogram key in top left \\
-  To calculate parameters of a dataset: Calc \(\rightarrow\) One-variable
+  \begin{tcolorbox}[colframe=cas!75!black, title=On CAS]
+  
+    \begin{itemize}
+      \item Spreadsheet \(\rightarrow\) Catalog \(\rightarrow\) \verb;randNorm(sd, mean, n); where \verb;n; is the number of samples. Show histogram with Histogram key in top left
+      \item To calculate parameters of a dataset: Calc \(\rightarrow\) One-variable
+    \end{itemize}
+  \end{tcolorbox}
   
   \section{Normal distributions}
 
@@ -93,27 +99,44 @@
 
   \[ Z = \frac{X - \mu}{\sigma} \]
 
-  Normal distributions must have are (total prob.) of 1 \(\implies \int^\infty_{-\infty} f(x) \> dx = 1\)
+  Normal distributions must have area (total prob.) of 1 \(\implies \int^\infty_{-\infty} f(x) \> dx = 1\)
 \pgfmathdeclarefunction{gauss}{2}{%
   \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
 }
 
-\begin{tikzpicture}
+{\begin{center} \begin{tikzpicture}
+  \pgfplotsset{set layers}
 \begin{axis}[every axis plot post/.append style={
-  mark=none,domain=-3:3,samples=50,smooth}, % All plots: from -2:2, 50 samples, smooth, no marks
-  axis x line*=bottom, % no box around the plot, only x and y axis
-  axis y line*=left, % the * suppresses the arrow tips
+  mark=none,domain=-3:3,samples=50,smooth}, 
+  axis x line=bottom, 
+  axis y line=left,
   enlargelimits=upper,
-  ytick={0.5},
+  x=\textwidth/10,
+  ytick={0.55},
   yticklabels={\(\frac{1}{\sigma \sqrt{2\pi}}\)}, 
   xtick={-2,-1,0,1,2},
-  xticklabels={\(\mu-2\sigma\), \(\mu-\sigma\), \(\mu\), \(\mu+\sigma\), \(\mu+2\sigma\)},
+  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)};
 \end{axis}
-\end{tikzpicture}
+\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}}
 
   \section{Central limit theorem}