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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

A Red Urn Contains 4 Red Marbles, 2 Blue Marbles