You are given a transition matrix P and initial distribution vector v. Find the two-step transition matrix and the distribution vector after two steps.

P = \left[ \begin{array} { c c } 0 & 1 \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]

v = \left[ \begin{array} { l l } \frac { 1 } { 4 } & \frac { 3 } { 4 }\end{array} \right]

A)The two-step transition matrix is

\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 2 } { 3 } \\\frac { 2 } { 9 } & \frac { 7 } { 9 }\end{array} \right]

The distribution vector after two steps is

\left[ \begin{array} { l l } \frac { 1 } { 4 } & \frac { 3 } { 4 }\end{array} \right]

B) The two-step transition matrix is

\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 2 } { 9 } \\\frac { 2 } { 3 } & \frac { 7 } { 9 }\end{array} \right]

The distribution vector after two steps is

\left[ \begin{array} { l l } 0 & 1\end{array} \right]

C) The two-step transition matrix is

\left[ \begin{array} { c c } 0 & 1 \\\frac { 1 } { 9 } & \frac { 4 } { 9 }\end{array} \right]

The distribution vector after two steps is

\left[ \begin{array} { l l } \frac { 1 } { 4 } & \frac { 3 } { 4 }\end{array} \right]

D) The two-step transition matrix is

\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 2 } { 3 } \\\frac { 2 } { 9 } & \frac { 7 } { 9 }\end{array} \right]

The distribution vector after two steps is

\left[ \begin{array} { l l } 0 & 1\end{array} \right]

E) The two-step transition matrix is

\left[ \begin{array} { l l } \frac { 1 } { 3 } & \frac { 2 } { 9 } \\\frac { 2 } { 3 } & \frac { 7 } { 9 }\end{array} \right]

The distribution vector after two steps is

\left[ \begin{array} { l l } \frac { 1 } { 4 } & \frac { 3 } { 4 }\end{array} \right]

Find the Conditional Probability of the Event "The Red One 25\frac { 2 } { 5 }52​

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Find the Conditional Probability of the Event "The Red One $\frac { 2 } { 5 }$

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