Question

I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).

Create a diagram and a transition matrix for this case.

Answer 1

Here is a diagram and transition matrix for this case:

Diagram:

+---(0.65)---> State 1 (work)

|

Start ---+

|

+---(0.35)---> State 2 (procrastinate)

|

+---(0.15)---> State 1 (work)

|

+---(0.85)---> State 2 (procrastinate)

Transition matrix:

| State 1 | State 2 |

----------+-----------+-----------+

State 1 | 1.00 | 0.00 |

----------+-----------+-----------+

State 2 | 0.15 | 0.85 |

----------+-----------+-----------+

In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.