Chapter 9.1, Problem 78E

(A)

To determine

To calculate: The value of $P^4$ from the given transition matrix $P$ which is given below.

$\begin{array}{l}\begin{array}{cccc}A& B& C& D\end{array}\\ P=\begin{array}{c}A\\ B\\ C\\ D\end{array}\left[\begin{array}{cccc}.5& .3& .1& .1\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ .1& .2& .3& .4\end{array}\right]\end{array}$

(B)

To determine

To calculate: The probability of going from the state $A$ to state $D$ in four trials, if the transition matrix $P$ and its powers are given in part (A).

(C)

To determine

To calculate: The probability of going from the state $C$ to state $B$ in four trials, if the transition matrix $P$ and its powers are given in part (A).

(D)

To determine

To calculate: The probability of going from the state $B$ to state $A$ in four trials, if the transition matrix $P$ and its powers are given in part (A).