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You are here:Open notes-->VTU-->STOCHASTIC-MODELS-AND-APPLICATIONS-10CS665-

# How to study this subject

Subject Code: 10CS665 I.A. Marks : 25
Hours/Week : 04 Exam Hours: 03
Total Hours : 52 Exam Marks: 100
PART � A
UNIT � 1 6 Hours
Introduction � 1: Axioms of probability; Conditional probability and
independence; Random variables; Expected value and variance; MomentGenerating
Functions and Laplace Transforms; conditional expectation;
Exponential random variables.
UNIT � 2 6 Hours
Introduction � 2: Limit theorems; Examples: A random graph; The
Quicksort and Find algorithms; A self-organizing list model; Random
permutations.
UNIT � 3 7 Hours
Probability Bounds, Approximations, and Computations: Tail probability
inequalities; The second moment and conditional expectation inequality;
probability bounds via the Importance sampling identity; Poisson random
variables and the Poisson paradigm; Compound Poisson random variables.
UNIT � 4 7 Hours
Markov Chains: Introduction; Chapman-Kologorov Equations;
Classification of states; Limiting and stationary probabilities; some 62
applications; Time-Reversible Markov Chains; Markov Chain Monte Carlo
methods.
PART � B
UNIT � 5 6 Hours
The Probabilistic Method: Introduction; Using probability to prove
existence; Obtaining bounds from expectations; The maximum weighted
independent set problem: A bound and a ranom algorithm; The set covering
problem; Antichains; The Lovasz Local lemma; A random algorithm for
finding the minimal cut in a graph.
UNIT � 6 6 Hours
Martingales: Martingales: Definitions and examples; The martingale
stopping theorem; The Hoeffding-Azuma inequality; Sub-martingales.
UNIT � 7 7 Hours
Poisson Processes, Queuing Theory � 1: The non-stationary Poisson
process; The stationary Poisson process; Some Poisson process
computations; Classifying the events of a non-stationary Poisson process;
Conditional distribution of the arrival times
Queuing Theory: Introduction; Preliminaries; Exponential models
UNIT � 8 7 Hours
Queuing Theory � 2: Birth-and-Death exponential queuing systems; The
backwards approach in exponential queues; A closed queuing network; An
open queuing network; The M/G/1 queue; Priority queues.
Text Books:
1. Sheldon M. Ross: Probability Models for Computer Science,
Elsevier, 2002.
Reference Books:
1. B. R. Bhat: Stochastic Models Analysis and Applications, New Age
International, 2000.
2. Scott L. Miller, Donald G. Childers: Probability and Random
Processes with Applications to Signal Processing and
Communications, Elsevier, 2004.

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