Probability Theory and Stochastic Processes Detailed Syllabus for B.Tech second year second sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.
The detailed syllabus for Probability Theory and Stochastic Processes B.Tech 2016-2017 (R16) second year second sem is as follows.
B.Tech. II Year II Sem. L/T/P/C
Course Code: EI401ES 4/0/0/4
Pre-requisites: Nil.
Course Objectives: The primary objective of this course is:
- To provide mathematical background and sufficient experience so that the student can read, write, and understand sentences in the language of probability theory, as well as solve probabilistic problems in signal processing and Communication Engineering.
- To introduce students to the basic methodology of “probabilistic thinking” and to apply it to problems;
- To understand basic concepts of probability theory and random variables, how to deal with multiple random variables, Conditional probability and conditional expectation, joint distribution and independence, mean square estimation.
- To understand the difference between time averages and statistical averages
- Analysis of random process and application to the signal processing in the communication system.
- To teach students how to apply sums and integrals to compute probabilities, means, and expectations.
Course Outcomes: Upon completion of the subject, students will be able to compute:
- Simple probabilities using an appropriate sample space.
- Simple probabilities and expectations from probability density functions (pdfs)
- Likelihood ratio tests from pdfs for statistical engineering problems.
- Least -square & maximum likelihood estimators for engineering problems.
- Mean and covariance functions for simple random processes.
UNIT – I Probability: Probability introduced through Sets and Relative Frequency, Experiments and
Sample Spaces, Discrete and Continuous Sample Spaces, Events, Probability Definitions and Axioms, Mathematical Model of Experiments, Probability as a Relative Frequency, Joint Probability, Conditional Probability, Total Probability, Baye’s Theorem, Independent Events. Random Variable: Definition of a Random Variable, Conditions for a Function to be a Random Variable, Discrete, Continuous, and Mixed Random Variables
UNIT – II Distribution & Density Functions: Distribution and Density functions and their Properties – Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh and Conditional Distribution, Methods of defining Conditional Event, Conditional Density, and Properties. Operation on One Random Variable – Expectations: Introduction, Expected Value of a Random Variable, Function of a Random Variable, Moments about the Origin, Central Moments, Variance and Skew, Chebychev’s Inequality, Characteristic Function, Moment Generating Function, Transformations of a Random Variable: Monotonic Transformations for a Continuous Random Variable, Non-monotonic Transformations of Continuous Random Variable, Transformation of a Discrete Random Variable.
UNIT – III Multiple Random Variables: Vector Random Variables, Joint Distribution Function, Properties of Joint Distribution, Marginal Distribution Functions, Conditional Distribution and Density – Point Conditioning, Conditional Distribution and Density – Interval conditioning, Statistical Independence, Sum of Two Random Variables, Sum of Several Random Variables, Central Limit Theorem (Proof not expected), Unequal Distribution, Equal Distributions. Operations on Multiple Random Variables: Expected Value of a Function of Random Variables: Joint Moments about the Origin, Joint Central Moments, Joint Characteristic Functions, Jointly Gaussian Random Variables: Two Random Variables case, N Random Variable case, Properties, Transformations of Multiple Random Variables, Linear Transformations of Gaussian Random Variables.
TEXT BOOKS:
- Probability, Random Variables & Random Signal Principles – Peyton Z. Peebles, 4Ed., 2001, TMH.
- Probability and Random Processes – Scott Miller, Donald Childers, 2 Ed, Elsevier, 2012.
REFERENCE BOOKS:
- Probability, Random Variables and Stochastic Processes – Athanasios Papoulis and S. Unnikrishna Pillai, 4 Ed., TMH.
- Theory of Probability and Stochastic Processes- Pradip Kumar Gosh, UniversityPress
- Probability and Random Processes with Application to Signal Processing – Henry Stark and John W. Woods, 3 Ed., PE
- Probability Methods of Signal and System Analysis – George R. Cooper, Clave D. MC Gillem, 3 Ed., 1999, Oxford.
- Statistical Theory of Communication – S.P. Eugene Xavier, 1997, New Age Publications.
For all other B.Tech 2nd Year 2nd Sem syllabus go to JNTUH B.Tech Electronics and Instrumentation Engineering 2nd Year 2nd Sem Course Structure for (R16) Batch.
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