Exam 9: Markov Chains

The probability that an assembly line operation works correctly depends on whether it worked correctly the last time it was used. There is a 0.91 chance that the line will work correctly if it worked correctly the time before and a 0.68 chance that it will work correctly if it did not work correctly the time before. After setting up a transition matrix with this information, find the long-run probability that the line will work correctly.

The transition matrix for a Markov process is: Find .

Suppose that for a certain absorbing Markov chain the fundamental matrix is found to be What is the expected number of times a person will have $3, given that he started with $2?

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

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

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

Decide whether or not the transition matrix is regular.

Find the stationary matrix for the transition matrix P = .

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

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

Laurinburg is experiencing a population movement out of the city to the suburbs. Currently 85% of the total population live in the city with the remaining 15% living in the suburbs. It has been shown that each year 7% of the city residents move to the suburbs, while only 1% of the suburb population move back to the city. Assuming population remains constant for both, what percent of the total will remain in the city after 5 years. Express your answer rounded to hundredths of a percent.

Find all absorbing states for the transition matrix, and indicate whether or not the matrix is that of an absorbing Markov chain.

Decide whether or not the transition matrix is regular.

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

From statistics gathered over many seasons, it was determined that the probability a basketball player will make a basket after having made a basket on his previous attempt is .55, while the probability he will make a basket if he missed on his previous attempt is .48. In a current game a player has made 45% of his attempted shots. If the player shoots many more times in the game, what would be the overall percentage of baskets that he makes in this game?

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

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

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.Write the transition matrix P.

Suppose that for a certain absorbing Markov chain the fundamental matrix is found to be What is the expected number of times a person will have $3, given that she started with $1?

Decide whether or not the transition matrix is regular.