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\mode<presentation>

\title{Using R as a Calculator (on the final exam)\footnote{ This slide show is an open-source document. See last slide for copyright information.}}
\subtitle{STA 260 Spring 2020}
\date{} % To suppress date

\begin{document}

\begin{frame}
  \titlepage
\end{frame}

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\begin{frame}
\frametitle{R is a wonderful calculator} 
%\framesubtitle{} 
\begin{itemize}
    \item You are going to have access to a computer during the final exam anyway.
    \item Even a cell phone will do.
    \item You may already have it and know how to use it. \pause
    \item Free download at 
\href{https://www.r-project.org} {\small\texttt{https://www.r-project.org}}
    \item Run free online at
\href{https://rdrr.io/snippets} {\small\texttt{https://rdrr.io/snippets}}
\end{itemize}
\end{frame}

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\begin{frame}[fragile]
\frametitle{R is a Basic Calculator}
\framesubtitle{} \pause
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> 1+1
\end{verbatim}
} % End color
\begin{verbatim}
[1] 2
\end{verbatim} \pause

{\color{blue}
\begin{verbatim}

> 1:40
\end{verbatim}
} % End color
\begin{verbatim}
 [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
[21] 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
\end{verbatim} 
} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{R is an advanced calculator}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> n = 50; xbar = 1.56
> Gsq = 2*n*(xbar*log(xbar) - (1+xbar)*(log(1+xbar)-log(2))); Gsq
\end{verbatim}
} % End color
\begin{verbatim}
[1] 6.174808
\end{verbatim} 
} % End size
\end{frame}

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\begin{frame}
\frametitle{No More Tables} 
%\framesubtitle{} 
We will use R for CDFs and quantiles of all the familiar distributions. \pause
        \begin{itemize}
            \item Critical values.
            \item $p$-values.
            \item Posterior probabilities.
        \end{itemize} 
\end{frame}

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\begin{frame}[fragile]
\frametitle{Normal Distribution}
\framesubtitle{Faster than the table} \pause
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> pnorm(0) # CDF of standard normal
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.5
\end{verbatim}  \pause
} % End size

You can specify $\mu$ and $\sigma$ (not $\sigma^2$). \pause \vspace{2mm}

IQ tests are designed to have $\mu=100$ and $\sigma=15$. What's $P(IQ>160)$? \pause

{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
1 - pnorm(160,mean=100,sd=15) # Or just pnorm(160,100,15)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 3.167124e-05
\end{verbatim}  \pause
{\color{blue}
\begin{verbatim}
> options(scipen=999) # Supress scientific notation
> 1 - pnorm(160,mean=100,sd=15)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.00003167124
\end{verbatim} 
} % End size

\end{frame}

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\begin{frame}[fragile]
\frametitle{Quantiles}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> qnorm(0.975)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 1.959964
\end{verbatim} \pause

{\color{blue}
\begin{verbatim}
> # An IQ of ___ is higher than 90% of the population,
> qnorm(0.90,100,15) # q for quantile
\end{verbatim} 
} % End color
\begin{verbatim}
[1] 119.2233
\end{verbatim} 

} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{$\chi^2$ Distribution}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> n = 50; xbar = 1.56
> Gsq = 2*n*(xbar*log(xbar) - (1+xbar)*(log(1+xbar)-log(2))); Gsq
\end{verbatim}
} % End color
\begin{verbatim}
[1] 6.174808
\end{verbatim}  \pause

{\color{blue}
\begin{verbatim}
> 1-pchisq(Gsq,df=1) # p-value
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.0129582
\end{verbatim}  \pause

{\color{blue}
\begin{verbatim}
> qchisq(0.95,1) # Critical value at alpha = 0.05
\end{verbatim}
} % End color
\begin{verbatim}
[1] 3.841459
\end{verbatim} 

} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{$t$ distribution}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> 2*(1 - pt(2.14,df=10) ) # Two-tailed p-value
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.05803497
\end{verbatim}  \pause

{\color{blue}
\begin{verbatim}
> qt(0.975,df=10) # Critical value
\end{verbatim}
} % End color
\begin{verbatim}
[1] 2.228139
\end{verbatim} 

} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{$F$ Distribution}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> 1 - pf(3.17,6,114) 
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.006504761
\end{verbatim} \pause

{\color{blue}
\begin{verbatim}
> qf(0.95,6,114) # Not in the table
\end{verbatim}
} % End color
\begin{verbatim}
[1] 2.1791
\end{verbatim} 

} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{Gamma with $\alpha=$shape, $\lambda=$rate} \pause
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> pgamma(1,shape=21,rate=23.35) # P(Lambda < 1 |x)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.7146466
\end{verbatim} 
} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{Beta Distribution}
%\framesubtitle{} 
For the coffee taste test, 60/100 consumers chose the new blend of coffee beans, yielding $\alpha^\prime = \alpha + \sum_{i=1}^nx_i = 61$ and $\beta^\prime = \beta + n-\sum_{i=1}^nx_i = 41$. \pause \vspace{5mm}
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> pbeta(1/2,61,41)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.02302203
\end{verbatim}  
} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{Binomial Distribution}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> # 20-question abcd multiple choice, probability of passing
> 1 - pbinom(9,20,0.25)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.01386442
\end{verbatim}  \pause

{\color{blue}
\begin{verbatim}
> # Probability of exactly 50 heads in 100 tosses of a fair coin
> dbinom(50,100,0.5)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.07958924
\end{verbatim} 

} % End size
\end{frame}

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\begin{frame}[fragile]
\frametitle{Poisson Distribution}
%\framesubtitle{} 
If there are really only a population mean of 8 rat hairs in a peanut butter jar, what is the probability of obtaining a sample mean of 9.2 (or more) from a random sample of 30 jars? \pause Distribution of $S = \sum_{i=1}^nX_i$ is Poisson$(30*8)$. \pause
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
> 9.2*30
\end{verbatim}
} % End color
\begin{verbatim}
[1] 276
\end{verbatim}  \pause

{\color{blue}
\begin{verbatim}
> 1 - ppois(275,240) # P(S geq 276)
\end{verbatim}
} % End color
\begin{verbatim}
[1] 0.01226396
\end{verbatim} 
} % End size
\end{frame}

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\begin{frame}
\frametitle{Copyright Information}

This slide show was prepared by  \href{http://www.utstat.toronto.edu/~brunner}{Jerry Brunner},
Department of Mathematical and Computational Sciences, University of Toronto Mississauga. It is licensed under a 
\href{http://creativecommons.org/licenses/by-sa/3.0/deed.en_US}
     {Creative Commons Attribution - ShareAlike 3.0 Unported License}. Use any part of it as you like and share the result freely. The \LaTeX~source code is available from the course website:

\vspace{5mm}
\href{http://www.utstat.toronto.edu/~brunner/oldclass/260s20} {\small\texttt{http://www.utstat.toronto.edu/$^\sim$brunner/oldclass/260s20}}

\end{frame}


\end{document}

\begin{frame}[fragile]
\frametitle{Title here}
%\framesubtitle{} 
{\footnotesize % or scriptsize
{\color{blue}
\begin{verbatim}
R input in blue
\end{verbatim}
} % End color
\begin{verbatim}
R output in black
\end{verbatim} 
} % End size
\end{frame}