Question 1:
a) Describe about Markov process, ergodic chain and irreducible matrix?
b) which of the given matrices are stochastic?
![504_stocastic matrics.jpg](https://secure.tutorsglobe.com/CMSImages/504_stocastic%20matrics.jpg)
Question 2:
a) state and prove changing stakes result x2
b) If p = 1/3, q = 1/2, z =1, a = 1000 prove that dz = 999.
Question 3:
a) A fair coin is tossed repeatedly. If Xn denote the maximum number of numbers occurring in the first n tosses, find the transition probability matrx P of the Markov chain. Also find P2 and P (X2 = 6)
b) which of the given matrices are regular.
![639_regular matrices.jpg](https://secure.tutorsglobe.com/CMSImages/639_regular%20matrices.jpg)
Question 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.