Exam 9: Markov Chains

According to data collected during one year in a large metropolitan community, 30% of commuters used public transportation to get to work, and this rose by 4% the following year. This is modeled by the transition matrix where P represents the percentage of people that use public transportation and the percentage of people that do not. Let . Find .Round your answer to the nearest thousandths.

Given the transition matrix: Find the probability of going from state A to state D in four trials.

Identify the absorbing state(s) in the transition matrix

A new anti-gravity commuter train has been installed. It is expected that each week 90% of the riders who used the existing system will continue to do so. Of those who traveled by car, 5% will begin to use the new anti-gravity train. Use this information to write the transition matrix that describes this process.

Find a standard form for the absorbing Markov chain with the transition matrix

Find the fundamental matrix F for the absorbing Markov chain with the given matrix. Express your answer in fraction form.

10 percent of the people in one generation who have a certain physical characteristic will pass that characteristic on to the next generation. 40 percent of the people in one generation who do not have this characteristic will pass it on to the next generation.

A small town has only two dry cleaners, Fast and Speedy. Fast hopes to increase its market share by conducting an extensive advertising campaign. The initial market share for Fast was 40% and 60% for Speedy. Solve the problem: -Find the probability that a customer using Fast initially will use Fast for his third batch of clothes. Use the following transition matrix. Round your answer to the nearest hundredth.

For the transition matrix ,find the limiting matrix. Use fractional entries.

Decide whether or not the transition matrix is regular.

Decide whether or not the transition matrix is regular.

For the transition matrix P = find exactly by converting to fraction form.

A red urn contains 4 red marbles, 2 blue marbles, and 4 green marbles. A blue urn contains 2 red marbles, 2 blue marbles, and 1 green marble. A green urn contains 3 green marbles. A marble is selected from an urn, the color is noted, and the marble is returned to the urn from which it was drawn. The next marble is drawn from the urn whose color is the same as the marble just drawn. Thus, this is a Markov process with three states: draw from the red urn, draw from the blue urn, or draw from the green urn.Find the limiting matrix , if it exists, and describe the long-run behavior of this process.

Construct the transition matrix that represents the data: -If it snows today, there is a 70 percent chance of snow tomorrow; however if it does not snow today, there is a 40 percent chance that it will not snow tomorrow.

Find the limiting matrix corresponding to the transition matrix P = .Round to the nearest hundredths.

The transition matrix for a Markov process is: Find the first state matrix if the initial state is

The probability that an assembly line works correctly depends on whether the line worked correctly the last time. Find the probability that the line will work in the long run. Round your answer as appropriate.

Using a graphing utility to compute powers of ,find the smallest n such that the corresponding entries in and are, when rounded to 3 decimal places, equal.

Find the fundamental matrix F for the absorbing Markov chain with the given matrix. Express your answer in fraction form.

Find the stationary matrix for the transition matrix P = .