Write Down the Transition Matrix Associated with the Given State $$A = B = C = \frac { 1 } { 3 }$$

question 185

Multiple Choice

Write down the transition matrix associated with the given state transition diagram. $$A = B = C = \frac { 1 } { 3 }$$ , $$D = E = H = \frac { 2 } { 3 }$$

• A) \(P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\ \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 & 0 \\ 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 \\ 0 & 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } \\ 0 & 0 & 0 & 0 & 1 \end{array} \right]\)
• B) \(P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\ \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 & 0 \\ 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } & 0 \\ 0 & 0 & \frac { 2 } { 3 } & 0 & \frac { 1 } { 3 } \\ 0 & 0 & 0 & 1 & 0 \end{array} \right]\)
• C) \(P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\ \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\ 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\ 0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\ 0 & 0 & 0 & 1 & 0 \end{array} \right]\)
• D) \(P = \left[ \begin{array} { c c c c c } 0 & 1 & 0 & 0 & 0 \\ \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\ 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\ 0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\ 0 & 0 & 0 & 1 & 0 \end{array} \right]\)
• E) \(P = \left[ \begin{array} { c c c c c } 1 & 0 & 0 & 0 & 0 \\ \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 & 0 \\ 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } & 0 \\ 0 & 0 & \frac { 1 } { 3 } & 0 & \frac { 2 } { 3 } \\ 0 & 0 & 0 & 0 & 1 \end{array} \right]\)

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A numerical or mathematical way to express a part of a whole or a fraction of something in terms of 100.

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The primary factor or condition that dominates in bringing about an effect, such as a disease or social issue.

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