On Any Particular Day an Individual Can Take One of Two

question 34

Essay

On any particular day an individual can take one of two routes to work. Route A has a 25% chance of being congested, whereas route B has a 40% chance of being congested.
The probability of the individual taking a particular route depends on his previous day's experience. If one day he takes route A and it is not congested, he will take route A again the next day with probability .8. If it is congested, he will take route B the next day with probability .7.
On the other hand, if on a day he takes route B and it is not congested, he will take route B again the next day with probability .9. Similarly if route B is congested, he will take route A the next day with probability .6.
a.Construct the transition matrix for this problem. (HINT: There are 4 states corresponding to the route taken and the congestion. The transition probabilities are products of the independent probabilities of congestion and next day choice.)
b.What is the long-run proportion of time that route A is taken?

---

Definitions:

Palpated

The act of examining or exploring by touch, especially used in a medical context to detect characteristics or abnormalities of an organ.

Superficial

Located near the surface of the body or an organ.

Pulse Pressure

The difference between systolic and diastolic blood pressure readings, reflecting the force that the heart generates each time it contracts.

Arterial Pressure

The pressure of the blood within the arteries, typically reflecting the force exerted by the heart when pumping blood through the arterial system.