This 4-credit postgraduate course introduces students to stochastic methods. It covers probability theory, probability distributions, Markov chains, birth and death processes, queueing networks, and correlation and regression analysis. The course aims to provide a comprehensive understanding of stochastic processes for applications in communication engineering. It is taught using theory and case-based methods, and students are assessed through mid-term and end-term exams, assignments, viva, and attendance.

1. Course Title: Stochastic Methods
Course Code: ECE604
Credit Units: 4
Level: PG
Course Objectives: This course deals with the comprehensive knowledge of Probability theory, probability distributions, transition probabilities, Markov
Chains, birth and death processes, Network of queues, correlation and regression analysis and Analysis of variance. The course objective aims at giving
comprehensive understanding of stochastic process for application in communication engineering.
Prerequisites: Basics of Probability theory & Statistics
Weightage
(%)
Module I Random Variables 25%
Probability Bay’s rule, Distribution function, discrete random vectors, different distributions, jointly distributed random variables. Order
statistics, Distribution of sums, expectations, moments, transform methods mean time to failure, Inequalities and limit theorems, Mixture
distribution, Conditional expectations, Imperfect fault coverage & reliability, Random sums.
Module II: Stochastic Processes 25%
Classification Bernoulli process, Poisson process, Renewal processes, available analysis, Random incidence, renewal model of program
behavior
Module III: Markov Chains 25%
N-step transition probabilities, limiting distribution, distribution of times between state changes, irreducible finite chains with a periodic
states, the m/g/I, queuing system discrete parameter, Birth Data Processes, Markov chains with absorbing states, Birth and death Processes,
Non – Birth Death Processes.
Module IV: Network of Queues 25%
Open and close queuing networks, Non exponential service item distributions and multiple job type, non product form networks. Correlation
& Regression: Introduction, least squares curve fitting, Coefficient of determination, Confidence of intervals in linear regression,
concatenation analysis, non linear regression, Analysis of variance.
L T P/
S
SW/F
W
TOTAL CREDIT
UNITS
3 1 0 0 4

2. Student Learning Outcomes:
Analyze the effects of noise in the performance of practical communication systems.
Apply the theory of Stochastic Processes in comprehensive representation of noise, clutter and interference.
Develop insight into the methods suited for modeling continuous and discrete time systems.
Pedagogy for Course Delivery: The class will be taught using theory and case-based method. In addition to assigning the case studies, the course instructor
will spend considerable time in emphasizing the approach to the analysis, design and evaluation of communication systems in the presence of noise.
Assessment/ Examination Scheme:
Theory L/T (%) Lab/Practical/Studio (%) Total
100% NA 100%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment End Term
Examination
Components
(Drop down)
Mid-Term
Exam
Assignment Viva Attendance
Weightage (%)
10% 7% 8% 5% 70%
Text & References:
Papoulis,A., Probability, Random Variables and Stochastic Processes, Third Edition, McGraw-Hill
K.S.Trivedi: Probability and Statistics, PHI, 3rd
Ed.
S.P.Gupta, Statistical Methods, Sultan Chand Sons
V.K. Kapoor and S. C. Gupta Fundamentals of Statistics, Sultan Chand and Sons