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Markov process and irreducible matrix

**Question 1**:

a) Describe about Markov process, ergodic chain and irreducible matrix?

b) which of the given matrices are stochastic?

**Question 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.

**Question 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.

**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.

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## Q : Finding median if there are odd number of values in the set

If there are an odd number of data values in the set, the median would be the value which appears the greatest number of times, value which appears in the centre, average of the two end values, average of all of the values divided by number of values