Description

UTTAR PRADESH RAJARSHI TANDON OPEN UNIVERSITY (UPRTOU)

Course Code: PGSTAT-203/MASTAT-203
Course Title: Stochastic Process
Maximum Marks : 30

Section- A
Long Answer Questions
Note: Attempt any three questions. Each question should be answered in 800 to 1000 Words.
1. For a two state Markov chain, under suitable assumptions, derive the expression for the probability that the process occupies state 1 at time n given that the initial probability vector is (PO P1).
2. State and prove the Chapman Kolmogorov equation for a Markov Chain. Giving some counter example, show that the equations are satisfied by non-Markovian processes also.
3. Stating the underlying assumptions, give the derivation of a Poisson process.
4. Describe the state space and and there one step and two step marunon probability matness for the homogenous markov chain {xn}

Section – B
Short Answer Questions
Note: Answer any four questions. Answer should be given in 200 to 300 Words.
1. Define (i) An Ergodic Markov Chain, (ii) Stationary Markov Chain.
2. Find the probability distribution of interarrival time for a Poisson process.
3. Let C1 and C2 be two communicative classes of a Markov chain and “S” be a state, which belongs to C1 but not C2. Prove that C1 and C2 are disjoint.
4. Prove that if a Poisson process has occurred once in time interval (0,a], then the point at which it occurs is distributed uniformly over interval (0,a].
5. Define gambler’s ruin problem.