Probability and Random Process
S. Y. B. Tech. Semester III (CSE and ECE)
Credits: 03 Examination Scheme:
Continuous Evaluation: 20 marks
Teaching Scheme: (L-T-P: 3-0-0) Mid Sem Exam: 30 marks
End Sem Exam: 50 marks
Course Outcomes: Students will be able to
CO1: Solve problems related to basic concepts and commonly used techniques of statistics,
conditional probability, and Bayes’ rule, estimation of intervals, and testing of hypothesis.
CO2: Model a given scenario using continuous and discrete distributions appropriately and
estimate the required probability of a set of events.
CO3: Apply theory of probability and statistics to solve problems in domains such as
machine learning, data mining, computer networks etc.
CO4: Understand Basic concepts of random variables and stochastic processes.
CO5: Interpret moment analysis including linear systems applied to stochastic and random
processes.
Unit I: Basic Probability Theory: Probability axioms, sample space, event space,
conditional probability, independence of events, Bayes’ rule [02 Hrs]
Unit II: Random Variables: Discrete and continuous random variables; distribution of a
random variable (cdf and pdf); Discrete Distributions such as Binomial, Poisson, Geometric
etc.; Continuous Distributions such as Exponential, Normal etc.; Expectation: Moments;
Central Limit theorem, Some sampling distributions like chi-square, t, F; Markov inequality,
Chebyshev inequality, and Chernoffbound, Introduction to Multidimensional Random
variables, Joint distribution function [12 Hrs]
Unit III: Statistical Inference: Estimation - introduction, classical methods of estimation,
single sample: estimating the mean and variance, two samples: estimating the difference
between two means and ratio of two variances; Tests of hypotheses - introduction, testing a
statistical hypothesis, tests on single sample and two samples concerning means and
variances; ANOVA (One–way, Two–way); Covariance, correlation coefficient [12 Hrs]
Unit IV: Discrete-time Markov Chains: Definitions, examples, Time-homogenous
Markov Chains, Transition probability matrix. Recurrence time, transient and recurrent states,
classification of states (open, closed). Period of a state, stationary distributions, irreducible
and reducible Markov chains, ergodicity. [08 Hrs]
Unit V: Random Processes: Strict Sense Stationarity, Wide Sense Stationarity. Cross-
correlation and cross-covariance, Cyclo-stationary processes, Random processes in
linear systems. WSS processes in LTI systems. [03 Hrs]
Unit VI: Introduction to Queuing Theory: Stochastic Processes, Markov Processes and
Markov Chains, Birth-Death Process, basic queuing theory (M/M/-/-) Type Queues [05 Hrs]
Text Books:
Ronald E, Walpole, Sharon L. Myers, Keying Ye, “Probability and Statistics for
Engineers and Scientists”, Pearson, 9th edition, ISBN-13: 978-9332519084
V. Sundarapandian, “Probability, Statistics and Queuing Theory”, PHI, 1st edition,
ISBN13: 978-8120338449
Papoulis, S. U. Pillai, Probability, Random Variables, and Stochastic Processes.2001.
Reference Books:
Sheldon M. Ross, “Introduction to Probability and Statistics for Engineers and
Scientists”, Elsevier, 4th edition, ISBN-13: 978-8190935685
KishorTrivedi, “Probability and Statistics with Reliability, Queuing, and Computer
Science Applications”, John Wiley and Sons, New York, 2001, ISBN number 0-471-
33341-7
R. Gallager, Stochastic Processes: Theory for Applications.
Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed.,
Prentice Hall, 1993.
C.W. Helstrom, Probability and Stochastic Processes for Engineers, 2nd ed., Prentice
Hall,1990.
