Download Probability Theory and Stochastic Processes

GR15 Regulations (2015-16)
GOKARAJU RANGARAJU
INSTITUTE OF ENGINEERING AND TECHNOLOGY
PROBABILITY THEORY AND STOCHASTIC PROCESSES
Course Code: GR15A2050
II Year I Semester
L:3 T:1 P:0 C:4
Prerequisites
•
Fundamentals of Probability theory
•
Basics of Fourier series, transforms
Course Objectives
•
To understand the fundamentals of probability
•
To understand the principles of random signals and random processes
•
To be acquainted with systems involving random signals, Noise concepts
and data coding
•
To know random phenomena which occur in engineering applications
Course Outcomes
•
Interpret probability by modeling sample spaces.
•
Construct the probability distribution of a random variable, based on
a real-world situation, and use it to compute expectation and variance
•
Evaluate response of a linear system to Random Process
Unit-I
PROBABILITY & RANDOM VARIABLES
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,
Baye’s Theorem, Independent Events, Random Variable, Functions of random
variable, Discrete and Continuous, Mixed Random Variable, Distribution and
Density functions, Binomial, Poisson, Uniform, Gaussian Distribution.
Unit-II
OPERATIONS ON SINGLE VARIABLE – EXPECTATIONS
Introduction, Expected Value of a Random Variable, Function of a Random
Variable, Moments about the Origin, Central Moments, Variance and Skew,
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. Vector Random Variables
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GR15 Regulations (2015-16)
Unit-III
OPERATIONS ON & MULTIPLE RANDOM– EXPECTATIONS
Joint Distribution Function, Properties of Joint Distribution, Marginal Distribution
Functions, Conditional Distribution and Density - Point Conditioning, Conditional
Distribution and Density -Statistical Independence, Sum of Two Random
Variables, Sum of Several Random Variables, Central Limit Theorem, Expected
Value of a Function of Random Variables: Joint Moments about the Origin, Joint
Central Moments, Joint Characteristic Functions.
Unit-IV
RANDOM PROCESSES -TEMPORAL CHARACTERISTICS
The Random process, classification, deterministic and no ndeterministic
processes, distribution and density Functions, stationarity and statistical
independence, first-order stationary processes, second-order and wide-sense
stationarity, auto correlation function and its properties, cross-correlation
function and its properties, covariance functions, Gaussian random processes,
random signal response of linear systems, autocorrelation and cross-correlation
functions of input and output.
Unit-V
RANDOM PROCESSES-SPECTRAL CHARACTERISTICS AND NOISE
The Power Spectrum: Properties, Relationship between Power Spectrum and
Autocorrelation Function, Cross-Power Density Spectrum, Properties,
Relationship between Cross-Power Spectrum and Cross-Correlation Function.
Spectral Characteristics of System Response: Power Density Spectrum of
Response, Cross-Power Density Spectrums of Input and Output.
MODELLING OF NOISE
Introduction to noise, types and sources of noises, noise in communication
system, Arbitrary Noise Sources, Resistive and Thermal Noise Source, Effective
Noise Temperature, Average Noise Figures, Average Noise Figure of cascaded
networks.
Teaching methodologies
•
Power Point presentations
•
Tutorial Sheets
•
Assignments
•
Experiments with Matlab software
Text Books
1.
Probability, Random Variables and Stochastic Processes - Athanasios
Papoulis and S. Unnikrishna Pillai, PHI, 4th Edition, 2002.
2.
Probability, Random Variables & Random Signal Principles - Peyton Z.
Peebles, TMH, 4th Edition, 2001
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GR15 Regulations (2015-16)
Reference Books
1.
Probabilistic Methods of Signals and System Analysis-George R. Cooper
and Clare D. McGillem, oxford, 3rd Edition, 2007.
2.
R.P. Singh and S.D. Sapre, “Communication Systems Analog & Digital”,
1995,TMH.
Web Resources
1.
Http://walrandpc.eecs.berkeley.edu/126notes.pdf
2.
http://nptel.iitm.ac.in/courses/Webcoursecontents/IIT%20Guwahati/
Probability_rp/index.htm
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