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%TCIDATA{<META NAME="Title" CONTENT="Random Numbers">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Thu Feb 13 16:52:18 1997}
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\section{\label{Statistics, random numbers}Random Numbers}

The random-number generators in \textsl{Scientific Notebook} give you a set
of random numbers 
\index{Statistics@Statistics!random numbers@random numbers}from one of
several families of distribution functions. The choices in the dialog box
are \textsf{Beta, Binomial, Cauchy, Chi-Square, Exponential, F, Gamma,
Normal, Poisson, Student's t,} \textsf{Uniform,} and\textsf{\ Weibull}. From
the \textsf{Statistics} submenu, choose \textsf{Random Numbers}. Choose a
distribution from the dialog box, specify how many random numbers you want,
and enter appropriate parameters. Following are sample results.

\begin{quote}
$\blacktriangleright $ \textsf{Statistics + Random Numbers}
\end{quote}

\begin{quotation}
\textsf{Beta}, order 3, order 7: 
\[
.31172,\,.28533,\,7.8338\times 10^{-2},\,.14925,\,.41693 
\]
\textsf{Binomial}, number of trials 10, probability of success .5: 
\[
6,\allowbreak 2,\allowbreak 6,\allowbreak 5,\allowbreak 6 
\]
\textsf{Cauchy}, median 10, shape parameter 5: 
\[
8.8,\allowbreak 6.9,\allowbreak 7.3,\allowbreak 9.6,\allowbreak 11. 
\]
\textsf{Chi-Square}, degrees of freedom 3: 
\[
.91006,\,2.2787,\,4.4748,\,2.7026,\,1.5385 
\]
\textsf{Exponential}, mean time between arrivals 10: 
\[
16.851,\,16.865,\,8.8222,\,32.037,\,12.434 
\]
\textsf{F}, degrees of freedom 1 and 3: 
\[
1.1585\times 10^{-2},\,1.3279\times 10^{-2},\,.18187,\,1.5567,\,1.8483 
\]
\textsf{Gamma}, order 5: 
\[
6.5299,\,4.2894,\,10.473,\,6.9089,\,7.9011 
\]
\textsf{Normal}, mean 3, standard deviation 7: 
\[
5.223,\,-4.8075,\,-5.5782,\,-1.1218,\,1.357 
\]
\textsf{Poisson}, mean number of occurrences 4: 
\[
2,\,4,\,1,\,2,\,5 
\]
\textsf{Student's t}, degrees of freedom 7: 
\[
1.6568\times 10^{-2},\,.11424,\,-1.3886\times 10^{-2},\,-1.8095\times
10^{-2},\,-.14798 
\]

\textsf{Uniform}, lower end of range 0, upper end of range 20: 
\[
5.6016,\,16.744,\,10.275,\,14.057,\,10.136 
\]
\textsf{Weibull}, shape parameter 5, scale parameter 3: 
\[
3.8,\allowbreak 3.3,\allowbreak 2.7,\allowbreak 3.0,\allowbreak 3.6 
\]
\end{quotation}

\strut

\subsection{\ Related topics}

\begin{itemize}
\item  
\hyperref{Menu Items, Lists, and Matrices}{}{}{DM11-1.tex#Statistics}

\item  \hyperref{Measures of Central Tendency}{}{}{DM11-2.tex#Statistics,
mean}

\item  \hyperref{Measures of Dispersion}{}{}{DM11-3.tex#Mean deviation}

\item  \hyperref{Distributions and Densities}{}{}{DM11-4.tex#Distribution}

\item  \hyperref{Families of Continuous Distributions}{}{}{%
DM11-5.tex#Continuous distributions}

\item  \hyperref{Families of Discrete Distributions}{}{}{DM11-6.tex#Discrete
distributions}

\item  \hyperref{Curve Fitting}{}{}{DM11-8.tex#Curve fitting}

\item  \hyperref{Exercises and Solutions}{}{}{DM11-9.tex#Exercises}
\end{itemize}

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DMIndex.tex#Math Index}\quad {\small Index entries: \hyperref{Data}{}{}{%
DMIndex.tex#Data}, \hyperref{Distribution}{}{}{DMIndex.tex#Distribution}, 
\hyperref{Matrices}{}{}{DMIndex.tex#Matrices}, \hyperref{Random}{}{}{%
DMIndex.tex#Random}, \hyperref{Reshape}{}{}{DMIndex.tex#Reshape}, \hyperref{%
Statistics}{}{}{DMIndex.tex#Statistics}}

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