Question

The transition matrix for a Markov process is given by $T=\begin{array}{l}\text { State } 1 \\ \text { State } 2\end{array}\left[\begin{array}{ll}\frac{1}{2} & \frac{3}{4} \\ \frac{1}{2} & \frac{1}{4}\end{array}\right]$ and the initial-state distribution vector is given by $$ X_{0}=\begin{array}{l} \text { State } 1 \\ \text { State } 2 \end{array} \quad\left[\begin{array}{l} \frac{1}{3} \\ \frac{2}{3} \end{array}\right] $$ Find $T X_{0}$ and interpret your result with the aid of a tree diagram.

          The transition matrix for a Markov process is given by
$T=\begin{array}{l}\text { State } 1 \\ \text { State } 2\end{array}\left[\begin{array}{ll}\frac{1}{2} & \frac{3}{4} \\ \frac{1}{2} & \frac{1}{4}\end{array}\right]$
and the initial-state distribution vector is given by
$$
X_{0}=\begin{array}{l}
\text { State } 1 \\
\text { State } 2
\end{array} \quad\left[\begin{array}{l}
\frac{1}{3} \\
\frac{2}{3}
\end{array}\right]
$$
Find $T X_{0}$ and interpret your result with the aid of a tree diagram.

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Added by Jose Carlos R.

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Solved by Expert Adi S

Step 1

To do this, we multiply the transition matrix $T$ by the initial-state distribution vector $X_0$: $$ TX_0 = \left[\begin{array}{ll}\frac{1}{2} & \frac{3}{4} \\ \frac{1}{2} & \frac{1}{4}\end{array}\right] \left[\begin{array}{l}\frac{1}{3} \\ Show more…

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The transition matrix for a Markov process is given by $T=\begin{array}{l}\text { State } 1 \\ \text { State } 2\end{array}\left[\begin{array}{ll}\frac{1}{2} & \frac{3}{4} \\ \frac{1}{2} & \frac{1}{4}\end{array}\right]$ and the initial-state distribution vector is given by $$ X_{0}=\begin{array}{l} \text { State } 1 \\ \text { State } 2 \end{array} \quad\left[\begin{array}{l} \frac{1}{3} \\ \frac{2}{3} \end{array}\right] $$ Find $T X_{0}$ and interpret your result with the aid of a tree diagram.

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