\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
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\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{quantumrustler}
\pdfinfo{
  /Title (r.pdf)
  /Creator (Cheatography)
  /Author (quantumrustler)
  /Subject (R Cheat Sheet)
}

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% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
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% Font and Colours
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\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{R Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{quantumrustler} via \textcolor{DarkBackground}{\uline{cheatography.com/212850/cs/46340/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}quantumrustler \\
  \uline{cheatography.com/quantumrustler} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 14th May, 2025.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{4.4 cm} x{3.6 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{R Environment}}  \tn
% Row 0
\SetRowColor{LightBackground}
`Ctrl + L` (Windows) & Clear command window \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
`ls()` & List objects in environment \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
`rm(obj)` & Remove object \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
`print('text')`\{\{nl\}\}`print(obj)` & Displays text or object \tn 
% Row Count 7 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4.08 cm} x{3.92 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Operations and Special Characters}}  \tn
% Row 0
\SetRowColor{LightBackground}
`+, -, *, /, \textasciicircum{}` & Arithmetic operations \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
`\%*\%` & Matrix multiplication \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
`'` & Transpose \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
`==, !=, \textless{}, \textgreater{}, \textless{}=, \textgreater{}=` & Relational operators \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`\#` & Comment \tn 
% Row Count 8 (+ 1)
% Row 5
\SetRowColor{white}
`\textless{}-` or `=` & Assignment \tn 
% Row Count 9 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.04 cm} x{4.96 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Elementary Math Functions}}  \tn
% Row 0
\SetRowColor{LightBackground}
`sqrt(x)` & Square root \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
`exp(x=3)` & Exponential of x \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
`abs(x=-1)` & Absolute value of x \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
`log(x=exp(1), b=exp(1))` & Logarithm with base b. If b is not specified, e is assumed by default \tn 
% Row Count 6 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vectors, Matrices, Arrays, Lists, Data Frames}}  \tn
% Row 0
\SetRowColor{LightBackground}
`c(1,2,3)` & Combine values into vector \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
`m:n` & Sequence from m to n (can't do spacing) \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
`seq(from=1,to=10,by=2)` & Sequence with step. For decreasing step, by must be -ve \tn 
% Row Count 8 (+ 3)
% Row 3
\SetRowColor{white}
`seq(from=3,to=27,length.out=40)` & Sequence with as many numbers specified \tn 
% Row Count 10 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`rep(x=c(3,62,8.3),times=3,each=2)` & Repeat values. The value for times provides the number of times to repeat x, and each provides the number of times to repeat each element of x. \tn 
% Row Count 18 (+ 8)
% Row 5
\SetRowColor{white}
`sort(x=c(2.5,-1,-10,3.44),decreasing=FALSE)` & Sort a vector in increasing or decreasing order \tn 
% Row Count 21 (+ 3)
% Row 6
\SetRowColor{LightBackground}
`length(x=c(3,2,8,1))` & Determines how many entries exist in a vector given as the argument x \tn 
% Row Count 25 (+ 4)
% Row 7
\SetRowColor{white}
`myvec{[}1{]}\{\{nl\}\}myvec{[}c(1,3,5){]}` & Retrieve specific elements from a vector \tn 
% Row Count 27 (+ 2)
% Row 8
\SetRowColor{LightBackground}
`myvec{[}-1{]}\{\{nl\}\}myvec{[}-c(1,3,5){]}` & Delete elements by using negative versions of the indexes \tn 
% Row Count 30 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vectors, Matrices, Arrays, Lists, Data Frames (cont)}}  \tn
% Row 9
\SetRowColor{LightBackground}
`myvec{[}m:n{]}` & Retrieve elements from a vector with a sequence of indices from m to n \tn 
% Row Count 4 (+ 4)
% Row 10
\SetRowColor{white}
`prod(myvec)` & Multiply all elements in a vector \tn 
% Row Count 6 (+ 2)
% Row 11
\SetRowColor{LightBackground}
`matrix(data=c(-3,2,893,0.17),nrow=2,ncol=2,byrow=FALSE)` & Create a matrix filled in a column-by-column fashion \tn 
% Row Count 9 (+ 3)
% Row 12
\SetRowColor{white}
`rbind(1:3,4:6)` & Bind together vectors as rows of a matrix \tn 
% Row Count 12 (+ 3)
% Row 13
\SetRowColor{LightBackground}
`cbind(c(1,4),c(2,5),c(3,6))` & Bind together vectors as columns of a matrix \tn 
% Row Count 15 (+ 3)
% Row 14
\SetRowColor{white}
`dim(mymat)`\{\{nl\}\}`nrow(mymat)`\{\{nl\}\}`ncol(mymat)` & Provides the dimensions of a matrix \tn 
% Row Count 18 (+ 3)
% Row 15
\SetRowColor{LightBackground}
`A{[},n{]}` & Refers to the elements in all the rows of column n of the matrix A \tn 
% Row Count 22 (+ 4)
% Row 16
\SetRowColor{white}
`A{[}n,{]}` & Refers to the elements in all the columns of row n of the matrix A \tn 
% Row Count 26 (+ 4)
% Row 17
\SetRowColor{LightBackground}
`A{[},m:n{]}` & Refers to the elements in all the rows between columns m and n of the matrix A \tn 
% Row Count 30 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vectors, Matrices, Arrays, Lists, Data Frames (cont)}}  \tn
% Row 18
\SetRowColor{LightBackground}
`A(m:n,)` & Refers to the elements in all the columns between rows m and n of the matrix A \tn 
% Row Count 4 (+ 4)
% Row 19
\SetRowColor{white}
`A{[}m:n,p:q{]}` & Refers to the elements in rows m through n and columns p through q of the matrix A. \tn 
% Row Count 9 (+ 5)
% Row 20
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{Indexing can be done using individual indices in vectors.\{\{nl\}\}To delete or omit elements from a matrix, use negative indexes.} \tn 
% Row Count 12 (+ 3)
% Row 21
\SetRowColor{white}
`diag(x=3)` & Create an identity matrix of size 3 x 3 \tn 
% Row Count 14 (+ 2)
% Row 22
\SetRowColor{LightBackground}
`diag(x=A)` & Identify the values along the diagonal of a square matrix \tn 
% Row Count 17 (+ 3)
% Row 23
\SetRowColor{white}
`t(A)` & Find the transpose of a matrix \tn 
% Row Count 19 (+ 2)
% Row 24
\SetRowColor{LightBackground}
`solve(A)` & Find the inverse of a matrix \tn 
% Row Count 21 (+ 2)
% Row 25
\SetRowColor{white}
\seqsplit{`list(matrix(data=1:4},nrow=2,ncol=2),c(T,F,T,T),"hello")` & Create a list containing mixed object types. To name the components of a list as it's being created, assign a label to each component in the list command \tn 
% Row Count 29 (+ 8)
% Row 26
\SetRowColor{LightBackground}
`lst{[}{[}i{]}{]}` & Access the ith element of a list \tn 
% Row Count 31 (+ 2)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Vectors, Matrices, Arrays, Lists, Data Frames (cont)}}  \tn
% Row 27
\SetRowColor{LightBackground}
`lst{[}1:2{]}` & Returns a sublist of selected elements \tn 
% Row Count 2 (+ 2)
% Row 28
\SetRowColor{white}
`names(lst)` & Name list components to make the elements more recognizable and easier to work with \tn 
% Row Count 7 (+ 5)
% Row 29
\SetRowColor{LightBackground}
`lst\$name`\{\{nl\}\}`x{[}{[}'name'{]}{]}` & Access element by name (or create new column) \tn 
% Row Count 10 (+ 3)
% Row 30
\SetRowColor{white}
`x\$nested \textless{}- list(a=1:3)` & Add a nested list to an existing list \tn 
% Row Count 12 (+ 2)
% Row 31
\SetRowColor{LightBackground}
\seqsplit{`data.frame(person=c("Peter"},"Lois","Meg","Chris","Stewie"),\{\{nl\}\}age=c(42,40,17,14,1),\{\{nl\}\}gender=factor(c("M","F","F","M","M")),\{\{nl\}\}stringsAsFactors=TRUE)` & Create a data frame. stringsAsFactors is used to control automatic conversion of character strings to factors \tn 
% Row Count 20 (+ 8)
% Row 32
\SetRowColor{white}
`df{[}df\$gender == 'M', {]}` & Logical Subset\{\{nl\}\}Subset rows where gender is M \tn 
% Row Count 23 (+ 3)
% Row 33
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{Data frames are treated like matrices,\{\{nl\}\}so you can also use functions like nrow(df).} \tn 
% Row Count 25 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Non-numeric Values}}  \tn
% Row 0
\SetRowColor{LightBackground}
`TRUE` (or `T`)\{\{nl\}\}`FALSE` (or `F`) & Logical values \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
`any(mat)` & Returns TRUE if any of the logicals in the vector are TRUE and returns FALSE otherwise \tn 
% Row Count 7 (+ 5)
% Row 2
\SetRowColor{LightBackground}
`all(mat)` & Returns a TRUE only if all of the logicals are TRUE, and returns FALSE otherwise \tn 
% Row Count 11 (+ 4)
% Row 3
\SetRowColor{white}
`"This is a character string"` & Character strings \tn 
% Row Count 13 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`nchar(x=str)` & Returns the number of characters in a string.\{\{nl\}\}length(x=str) != nchar(x=str) \tn 
% Row Count 17 (+ 4)
% Row 5
\SetRowColor{white}
`cat("Hello",\{\{nl\}\}"worldd\textbackslash{}b",\{\{nl\}\}".\textbackslash{}n",\{\{nl\}\}sep=" ")` & Sends output directly to the console screen and doesn't formally return anything \tn 
% Row Count 22 (+ 5)
% Row 6
\SetRowColor{LightBackground}
`paste("Hello",\{\{nl\}\}"world",\{\{nl\}\}".",\{\{nl\}\}sep=" ")` & Concatenates and then returns the final character string as a usable R object \tn 
% Row Count 26 (+ 4)
% Row 7
\SetRowColor{white}
`substr(x=str,\{\{nl\}\}start=21,\{\{nl\}\}stop=27)` & Extracts a substring from x, starting at start and ending at stop \tn 
% Row Count 30 (+ 4)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Non-numeric Values (cont)}}  \tn
% Row 8
\SetRowColor{LightBackground}
\seqsplit{`sub(pattern="chuck"},\{\{nl\}\}replacement="hurl",\{\{nl\}\}x=str)` & Replaces the first match of pattern in x with replacement \tn 
% Row Count 3 (+ 3)
% Row 9
\SetRowColor{white}
\seqsplit{`gsub(pattern="chuck"},\{\{nl\}\}replacement="hurl",\{\{nl\}\}x=bar)` & Replaces all matches of pattern in x with replacement \tn 
% Row Count 6 (+ 3)
% Row 10
\SetRowColor{LightBackground}
`factor(x=c("low",\{\{nl\}\}"medium",\{\{nl\}\}"high",\{\{nl\}\}"medium"))` & Converts a vector x into a categorical variable with labeled levels (similar to enums from other languages) \tn 
% Row Count 12 (+ 6)
% Row 11
\SetRowColor{white}
`levels(x=myvec)` & Lists the categories (levels) in the factor x \tn 
% Row Count 15 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Multidimensional Arrays}}  \tn
% Row 0
\SetRowColor{LightBackground}
`array(data=1:24, dim=c(3, 4, 2))` & Creates a 3D array with 3 rows, 4 columns, and 2 layers \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\seqsplit{`array(data=rep(1:24},times=3),dim=c(3,4,2,3))` & Creates a 4D array with dimensions 3×4×2×3 \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
`A{[} , , n{]}` & All rows and columns in the n-th matrix (3rd dim) of A \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
`A{[} , m, n{]}` & All rows in column m of the n-th matrix \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`A{[}i, , {]}` & All columns and layers of row i \tn 
% Row Count 13 (+ 2)
% Row 5
\SetRowColor{white}
`A{[} , , , p{]}` & All rows, columns, and matrices in the p-th 4th dimension slice \tn 
% Row Count 17 (+ 4)
% Row 6
\SetRowColor{LightBackground}
`A{[}m:n, , , {]}` & All columns and dimensions for rows m through n \tn 
% Row Count 20 (+ 3)
% Row 7
\SetRowColor{white}
`A{[} , , m:n{]}` & All rows and columns for matrices m through n \tn 
% Row Count 23 (+ 3)
% Row 8
\SetRowColor{LightBackground}
`A{[}1:2, 2:3, 1, 1{]}` & A specific 2×2 submatrix from layer 1, 4th-dim slice 1 \tn 
% Row Count 26 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Statistics}}  \tn
% Row 0
\SetRowColor{LightBackground}
`sum(xdata)` & Sum all elements in a vector \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
`mean(xdata, na.rm=FALSE)` & Calculates the arithmetic mean \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
`median(xdata)` & Finds the median of a data \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
`table(xdata)` & Returns the frequencies \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
`xtab{[}xtab==max(xtab){]}` & Returns the mode,\{\{nl\}\}where xtab is a table of xdata \tn 
% Row Count 11 (+ 3)
% Row 5
\SetRowColor{white}
`min(xdata)` & Returns the smallest value \tn 
% Row Count 13 (+ 2)
% Row 6
\SetRowColor{LightBackground}
`max(xdata)` & Returns the largest value \tn 
% Row Count 15 (+ 2)
% Row 7
\SetRowColor{white}
`range(xdata)` & Returns the smallest and largest values \tn 
% Row Count 17 (+ 2)
% Row 8
\SetRowColor{LightBackground}
`round(x, n)` & Round to the specified number of decimal places (n) \tn 
% Row Count 20 (+ 3)
% Row 9
\SetRowColor{white}
\seqsplit{`tapply(chickwts\$weight},\{\{nl\}\}INDEX=chickwts\$feed,\{\{nl\}\}FUN=mean)` & Applies mean to the numerical data for each grouping variable \tn 
% Row Count 24 (+ 4)
% Row 10
\SetRowColor{LightBackground}
`quantile(x=xdata, prob=0.8`)\{\{nl\}\}`quantile(x=xdata, prob=c(0.25,0.5,0.75)`) & Returns the quantile(s) of interest \tn 
% Row Count 28 (+ 4)
% Row 11
\SetRowColor{white}
`summary(xdata)` & Provides statistics automatically \tn 
% Row Count 30 (+ 2)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Statistics (cont)}}  \tn
% Row 12
\SetRowColor{LightBackground}
`var(xdata)`\{\{nl\}\}`sd(xdata)`\{\{nl\}\}`IQR(xdata)` & Direct R commands for computing measures of spread (variance, standard deviation, interquartile range) \tn 
% Row Count 6 (+ 6)
% Row 13
\SetRowColor{white}
`cov(xdata,ydata)`\{\{nl\}\}`cor(xdata,ydata)` & Computes the covariance between two numeric vectors\{\{nl\}\}Computes the correlation coefficient between two numeric vectors \tn 
% Row Count 13 (+ 7)
% Row 14
\SetRowColor{LightBackground}
`plot(x, y, line="l", xlab="x-axis",ylab="y-axis")` & Creates a scatter plot of y versus x \tn 
% Row Count 16 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Probability}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{{\bf{Basic Probability Formulas}}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{Pr(A ∪ B) = Pr(A) + Pr(B) - Pr(A ∩ B)} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Pr(A ∩ B) = 0 & If A and B are disjoint/mutually exclusive (cannot happen at the same time) \tn 
% Row Count 6 (+ 4)
% Row 3
\SetRowColor{white}
Pr(A ∩ B) = Pr(A) × Pr(B) & If A and B are independent (not related) \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{Pr(A\textasciicircum{}C\textasciicircum{}) = 1 - Pr(A)} \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{Pr(A | B) = Pr(A ∩ B) / Pr(B)} \tn 
% Row Count 10 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{P(X \textgreater{} x) = 1 - P(X \textless{}= x)} \tn 
% Row Count 11 (+ 1)
% Row 7
\SetRowColor{white}
cumsum(X.prob) & Calculates CDF of discrete RV \tn 
% Row Count 13 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\seqsplit{sum(X.prob*X.outcomes)} & Calculates E{[}X{]} (X is discrete RV) \tn 
% Row Count 15 (+ 2)
% Row 9
\SetRowColor{white}
sum((X.outcomes{\emph{X.mean)\textasciicircum{}2 }}X.prob)) & Calculates Var(X) (X is discrete RV)\{\{nl\}\}Alternative: E{[}X\textasciicircum{}2\textasciicircum{}{]} - (E{[}X{]})\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 19 (+ 4)
% Row 10
\SetRowColor{LightBackground}
F(x) = ∫\textasciicircum{}x\textasciicircum{} f(u) du & CDF (continuous) \tn 
% Row Count 21 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{{\bf{Plot Probabilities vs. Realizations}}} \tn 
% Row Count 22 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\seqsplit{`barplot(height=X.prob},\{\{nl\}\}ylim=c(0,0.5),\{\{nl\}\}names.arg=X.outcomes,\{\{nl\}\}space=0,\{\{nl\}\}xlab="x",\{\{nl\}\}ylab="Pr(X = x)")` & PMF \tn 
% Row Count 29 (+ 7)
% Row 13
\SetRowColor{white}
`barplot(X.cumul,\{\{nl\}\}names.arg=X.outcomes,\{\{nl\}\}space=0,\{\{nl\}\}xlab="x",\{\{nl\}\}ylab="Pr(X \textless{}= x)")` & CDF (discrete) \tn 
% Row Count 34 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Probability (cont)}}  \tn
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{{\bf{Common Probability Distributions}}} \tn 
% Row Count 1 (+ 1)
% Row 15
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{{\emph{X\textasciitilde{}Binomial(size, prob)}} (X is discrete RV)} \tn 
% Row Count 2 (+ 1)
% Row 16
\SetRowColor{LightBackground}
dbinom(x=5,size=8,prob=1/6) & Calculates P(X = x) where x is no. of trials \tn 
% Row Count 5 (+ 3)
% Row 17
\SetRowColor{white}
sum(dbinom(x=0:5,size=8,prob=1/6))\{\{nl\}\}pbinom(q=5,size=8,prob=1/6) & Calculates P(X \textless{}= q) where x is no. of trials \tn 
% Row Count 9 (+ 4)
% Row 18
\SetRowColor{LightBackground}
qbinom(p=0.95,size=8,prob=1/6) & Finds smallest x given P(X \textless{}= x) = p (inverse of CDF) \tn 
% Row Count 12 (+ 3)
% Row 19
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{{\emph{X\textasciitilde{}Pois(λ)}} (X is discrete RV)} \tn 
% Row Count 13 (+ 1)
% Row 20
\SetRowColor{LightBackground}
dpois(x=3,lambda=3.22) & Calculates P(X = x) where x is no. of events observed \tn 
% Row Count 16 (+ 3)
% Row 21
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{{\emph{Tip:}} P(X = 5) is meaningless so\{\{nl\}\}P(X \textless{} 5) = P(X \textless{}= 5)} \tn 
% Row Count 18 (+ 2)
% Row 22
\SetRowColor{LightBackground}
ppois(q=3,lambda=3.22) & Calculates P(X \textless{}= q) where q is no. of events \tn 
% Row Count 21 (+ 3)
% Row 23
\SetRowColor{white}
qpois(p=0.95,lambda=3.22) & Finds smallest x given P(X \textless{}= x) = p (inverse of CDF) \tn 
% Row Count 24 (+ 3)
% Row 24
\SetRowColor{LightBackground}
rpois(n=15,lambda=3.22) & Generates n random numbers from a Poisson distribution given lambda \tn 
% Row Count 28 (+ 4)
% Row 25
\SetRowColor{white}
\mymulticolumn{2}{x{8.4cm}}{{\emph{X\textasciitilde{}Normal(μ, σ)}} (X is continuous RV)} \tn 
% Row Count 29 (+ 1)
% Row 26
\SetRowColor{LightBackground}
dnorm(x, mean, sd) & Returns the height of the normal distribution curve at x \tn 
% Row Count 32 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Probability (cont)}}  \tn
% Row 27
\SetRowColor{LightBackground}
pnorm(q, mean, sd)\{\{nl\}\}Default: μ = 0, σ = 1 & Calculates P(X \textless{}= q) given μ and σ\{\{nl\}\}or P(Z \textless{}= z) if defaults are used \tn 
% Row Count 4 (+ 4)
% Row 28
\SetRowColor{white}
qnorm(p, mean, sd) & Finds smallest x given P(X \textless{}= x) = p (inverse of CDF) \tn 
% Row Count 7 (+ 3)
% Row 29
\SetRowColor{LightBackground}
qnorm(p, lower.tail=FALSE) & Finds smallest z given P(Z \textgreater{} z) = p\{\{nl\}\}Equal to P(Z \textless{}= z) = 1 - p \tn 
% Row Count 11 (+ 4)
% Row 30
\SetRowColor{white}
rnorm(n, mean, sd) & Generates n random numbers from a Normal distribution given μ and σ \tn 
% Row Count 15 (+ 4)
% Row 31
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{8.4cm}}{{\bf{QQ Plots and Histograms}}} \tn 
% Row Count 16 (+ 1)
% Row 32
\SetRowColor{white}
\seqsplit{hist(chickwts\$weight}, main="", xlab="weight", xlim=c(xi,xf)) & Draws a histogram of the given data \tn 
% Row Count 19 (+ 3)
% Row 33
\SetRowColor{LightBackground}
\seqsplit{qqnorm(chickwts\$weight}, main="Normal QQ plot of weights") & Creates a QQ plot \tn 
% Row Count 22 (+ 3)
% Row 34
\SetRowColor{white}
\seqsplit{qqline(chickwts\$weight}, col="gray") & Adds a reference line to the QQ plot \tn 
% Row Count 24 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}