Mathematics: The city of Eden completed a new light rail system to bring commuters and shoppers into the downtown area and relieve highway congestion. City planners estimate that each year, 15% of those who drive or ride in an automobile will change to the light rail system; 80% will continue to use automobiles; and the rest will no longer go to the downtown area. Of those who use light rail; 5% will go back to using an automobile, 80% will continue to use light rail, and the rest will stay out of the downtown

1.34 is the answer I think I’m not sure...

The city of Eden completed a new light rail system

ptrlvn01

28.01.2022

Step-by-step explanation:

To check which option is correct we will first make transition matrix.

Let the state 1 and state 2 represent the automobile and light rail

So, the transition is given by

$P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right]$

$P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right]$

Since P as no any entry zero so, P as not absorbing stochastic matrix

Also,

$|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0$

since |P| ≠ 0

Hence, Markov chain is a regular stochastic matrix.

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