problem 1:
a) Describe about Markov process, ergodic chain and irreducible matrix?
b) which of the given matrices are stochastic?
problem 2:
a) state and prove changing stakes result x_{2}
b) If p = 1/3, q = 1/2, z =1, a = 1000 prove that d_{z} = 999.
problem 3:
a) A fair coin is tossed repeatedly. If X_{n} denote the maximum number of numbers occurring in the first n tosses, find the transition probability matrx P of the Markov chain. Also find P^{2} and P (X_{2} = 6)
b) which of the given matrices are regular.
problem 4: Three boys A, B and C are throwing a ball to each other. A always throws the ball to B and B always throws to C; but C is just as likely to throw the ball to B as to A. Show that the process is Markovian. Find out the transition matrix and categorize the states.