Suppose there are 3 red balls and 3 white balls evenly distributed in two boxes. At each step, each marble is taken from the boxes and then exchanged. Let represent the state of the system after n steps. Define the following questions:

a. What is Markov chain? Explain.

b. Determine the transition matrix P.

c. Determine the probability limit equation.

d. Determine the stationary probability vector & its meaning.