Commit 5526a5ff authored by Jim Hefferon's avatar Jim Hefferon

erlang edits

parent f1fde8ee
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......@@ -21047,7 +21047,7 @@ octave:5> z=[x, y];
octave:6> gplot z
\end{lstlisting}
yields this graph.
By eye we judge that if $p>0.7$ then the team is close to assurred
By eye we judge that if $p>0.7$ then the team is close to assured
of the series.
\begin{center}
\includegraphics{ws.eps}
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......@@ -28,7 +28,7 @@ after $n$ flips.
Then, for instance, we have that the probability of being in state~$s_0$
after flip~$n+1$ is
$p_{0}(n+1)=p_{0}(n)+0.5\cdot p_{1}(n)$.
This matrix equation sumarizes.
This matrix equation summarizes.
\begin{equation*}
\begin{dmat}{D{.}{.}{1}D{.}{.}{1}D{.}{.}{1}D{.}{.}{1}D{.}{.}{1}D{.}{.}{1}}
1. &.5 &0. &0. &0. &0. \\
......@@ -104,7 +104,7 @@ or \definend{stochastic matrix},\index{matrix!stochastic}%
\index{stochastic matrix}
whose entries are nonnegative reals and whose columns sum to $1$.
A characteriztic feature of
A characteristic feature of
a Markov chain model is that it is
\definend{historyless}\index{historyless}%
\index{Markov chain!historyless} in that
......@@ -146,7 +146,7 @@ a child of a middle class worker has a $0.37$~chance of being middle
class, and
a child of a lower class worker has a $0.27$ probability of
becoming middle class.
With the initial distribution of the respondents's fathers given below,
With the initial distribution of the respondent's fathers given below,
this table gives the next five generations.
\begin{center}
\begin{tabular}{c|ccccc}
......@@ -1178,7 +1178,7 @@ octave:5> gplot z
Assume that there are two states $s_T$, living in town, and $s_C$,
living elsewhere.
\begin{exparts}
\partsitem Construct the transistion matrix.
\partsitem Construct the transition matrix.
\partsitem Starting with an initial distribution $s_T=0.3$
and $s_C=0.7$, get the results for the first ten years.
\partsitem Do the same for $s_T=0.2$.
......@@ -1800,7 +1800,7 @@ octave:5> z=[x, y];
octave:6> gplot z
\end{lstlisting}
yields this graph.
By eye we judge that if $p>0.7$ then the team is close to assurred
By eye we judge that if $p>0.7$ then the team is close to assured
of the series.
\begin{center}
\includegraphics{ws.eps}
......@@ -1811,15 +1811,15 @@ octave:6> gplot z
Above we define a transition matrix to have
each entry nonnegative and each column sum to $1$.
\begin{exparts}
\item Check that the three transistion matrices shown in this Topic
\item Check that the three transition matrices shown in this Topic
meet these two conditions.
Must any transition matrix do so?
\item Observe that if $A\vec{v}_0=\vec{v}_1$ and $A\vec{v}_1=\vec{v}_2$
then $A^2$ is a transition matrix from $\vec{v}_0$ to $\vec{v}_2$.
Show that a power of a transition matrix is also a transistion matrix.
Show that a power of a transition matrix is also a transition matrix.
\item Generalize the prior item by
proving that the product of two appropriately-sized transistion matrices
is a transistion matrix.
proving that the product of two appropriately-sized transition matrices
is a transition matrix.
\end{exparts}
\begin{answer}
\begin{exparts}
......
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