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\author{Teschl Gerald}
\title{Quiz 9}
\date{11 Sep. 1995}

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\hfill {\bf Name}: $\ul{\hspace*{5cm}}$\\[2mm]
\hspace*{2mm}\hfill {\bf ID \#}: $\ul{\hspace*{5cm}}$\\[5mm]

{\Huge Quiz 9}\\[5mm]

\noindent 1a) A city is serviced by three major airports, $A1$, $A2$, and $A3$.
Customer daily car rental habits are described as follows: 12\% of the cars rented
at $A1$ are returned at $A2$ and 20\% at $A3$. 22\% of the cars rented
at $A2$ are returned at $A3$ and 17\% at $A1$. 33\% of the cars rented
at $A3$ are returned at $A1$ and 17\% at $A2$. Exhibit the transition
matrix.~\hfill(2pts)\\[3cm]

\noindent 1b) If all airports have the same number of cars on Monday morning, what
percentage of cars will be at $A2$ on Wednesday morning?~\hfill(2pts)\\[3cm]

\noindent 2) Given the transition matrix
$$
T= \left[\ba{cc} 0.6 & 0. 4 \\ 0.3 & 0.7 \ea\right],
$$
find the steady state matrix.~\hfill(3pts)\\[3cm]

\noindent 3) In a shooting test a soldier fires 10 shots at a target. To pass the
test at least  8 shots must hit. If the soldier has a 90\% chance of hitting on each
shot, what is the probability that the soldier passes the test?~\hfill(3pts)
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