M.Sc. (OR SQC) DEGREE EXAMINATION, APRIL/MAY 2018.
Second Semester
STOCHASTIC PROCESSES
2 21223-A
Time 3 Hours Max. Marks 70
SECTION — A
Answer any FIVE questions. 6 30 Marks)
1. Explain stochastic process with suitable examples.
2. What is countable State Markov Chain?
3. Explain Random walk in two dimension.
4. Write the procedure of GAMBLE's Ruin problem.
5. Explain Poisson process.
6. What is discrete state continuous time Markov chain?
7. 'Wiener process as a limit of Random comment.
8. Write the process of renewal process.
SECTION — B
Answer ALL questions. 10 40 Marks)
9. Prove that, for a countable-state Markov chain, either all states in a class are
transient or all are recurrent.
Or
10. State the Markov property and use it to prove the Chapman-Kolmogorov equations
for a process with a discrete state space.

11. Write the applications of Gamble's Ruin problem. Also explain about Random walk
hitting probability.
Or
12. In genetics, one method for identifying dominated traits is to pair a specimen with
a known hybrid their offspring is once again paired with a known hybrid and so on.
In this way, the probability of a particular offspring being purely dominent, purely
recessive, or hybrid for the trait is given in the following table.
States Child dominant Child hybrid Child recessive
Parent dominant 0.5 0.5 0
Parent hybrid 0.25 0.5 0.25
Parent recessive 0 0.5 0.5
What is a stationary distribution for this Markov Chain?
13. Explain birth and death process of a discrete state space Markov chain.
Or
14. Write the properties of Poisson process. Also prove any four properties of Poisson
process.
15. What is stationary process? Derive mean and covariance of stationary process.
Or
16. Explain elementary properties of Weiner process.
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