Use the Given Transition Matrix P and the Given Initial $P = \left[ \begin{array} { c c } 0.9 & 0.1 \\0 & 1\end{array} \right]$

question 114

Multiple Choice

Use the given transition matrix P and the given initial distribution vector v to obtain the two-step transition matrix and the distribution vector after two steps. $P = \left[ \begin{array} { c c } 0.9 & 0.1 \\0 & 1\end{array} \right]$ , $v = \left[ \begin{array} { l l } 0.9 & 0.1\end{array} \right]$

• A)The two-step transition matrix is \(\left[ \begin{array} { c c }
• 0.81 & 0.19 \\
• 0 & 1
• \end{array} \right]\) The distribution vector is \(\left[ \begin{array} { l l }
• 1 & 0
• \end{array} \right]\)
• B) The two-step transition matrix is \(\left[ \begin{array} { c c }
• 0 & 1 \\
• 0.81 & 0.19
• \end{array} \right]\)
• The distribution vector is \(\left[ \begin{array} { l l }
• 0 & 1
• \end{array} \right]\)
• C) The two-step transition matrix is \(\left[ \begin{array} { c c }
• 0.81 & 0.01 \\
• 0 & 1
• \end{array} \right]\)
• The distribution vector is \(\left[ \begin{array} { l l }
• 0.729 & 0.271
• \end{array} \right]\)
• D) The two-step transition matrix is \(\left[ \begin{array} { c c }
• 0.81 & 0.19 \\
• 0 & 1
• \end{array} \right]\)
• The distribution vector is \(\left[ \begin{array} { l l }
• 0.81 & 0
• \end{array} \right]\)
• E) The two-step transition matrix is \(\left[ \begin{array} { c c }
• 0.81 & 0.19 \\
• 0 & 1
• \end{array} \right]\)
• The distribution vector is \(\left[ \begin{array} { l l }
• 0.729 & 0.271
• \end{array} \right]\)

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Definitions:

Arousal

A physiological and psychological state of being awake, alert, and engaged, often characterized by increased heart rate and sensory alertness.

Emotional Reactions

Manifestations of feelings that occur in response to stimuli, emphasizing the variability and complexity of human emotions.

Unrelated Event

An occurrence that has no connection or relevance to the current context or situation being considered or discussed.

Excitation Transfer Theory

A theory suggesting that arousal from one event can transfer to a subsequent event, amplifying the emotional response to the second event.