Problem 1

A patient has a medical condition which requires medication based upon day-to-day pain levels. Either the patient will take a full dose, a partial dose, or no dose at all. The following Markov chain describes his probability of taking a particular size dose the next day after taking his current dose.

Some of the problems require extensive matrix calculations. Please use Matlab for computing the product of transition matrices.

a)Construct and label the transition matrix that corresponds to this drawing. Label it A. (Assign the rows of the matrix in the order : F,P, and N)

b)If the patient takes a full dose today, what is the probability that he will take a full dose again tomorrow?

c)If the patient took no medication today, what is the probability that he will take no medication again tomorrow?

d)Today is Wednesday and the patient took a full dose. What is the probability that he will take no medication on Friday?

e)Matrix A is the transition matrix for one day. Find the transition matrix for two days (for example, if today is Monday, what are the chances of taking each kind of dose on Wednesday?).

f)If the patient takes no medication this Friday, what is the probability that he will take no medication next Friday? Give your answer accurate to two decimal places.

g)Find, to two decimal places, the matrix to which matrix A would appear to cover many days.

h)Explain the meaning of your solution to problem g.