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In: Statistics and Probability

A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the...

A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the way to work each day. Over a period of time, the following pattern has emerged:

- Each day the first light is green

- If a light is green, then the next one is always red

- If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4.

- If he encounters two red lights in a row, then the next will be green with probability p and red with probability 1-p.

Formulate a Markov Chain model for this situation (Identify states and find the transition matrix).

Expert Solution

Since each transition is dependent on last two traffic lights, we can model the Markov chain with 4 states.

GR - 1st light is Green and 2nd light is Red

RG - 1st light is Red and 2nd light is Green

GG - 1st light is Green and 2nd light is Green

RR - 1st light is Red and 2nd light is Red

Each day the first light is green. If a light is green, then the next one is always red.

So, Initial state is GR

If he encounters a green light and then a red one, then the next will be green with probability 0.6 and red with probability .4.

Thus, the transition probability from state GR to state RG is 0.6 and transition probability from state GR to state RR is 0.4

If he encounters two red lights in a row, then the next will be green with probability p and red with probability 1-p.

Thus, the transition probability from state RR to state RG is p and transition probability from state RR to state RR is 1-p

If a light is green, then the next one is always red

Thus, the transition probability from state RG to state RR is 1 and transition probability from state GG to state GR is 1

The transition matrix is,

orchestra answered 1 year ago

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A Bloomington resident commutes to work in Indiannapolis, and he encounters several traffic lights on the...

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