Probability Theory and Stochastic processing (EC-703 (C)) - Official Syllabus

1 min read 0 words

Unit 1

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
Bayese28099 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 2

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, Properties
Operation on One Random Variable e28093 Expectations: Introduction, Expected Value of a Random Variable, Function of a Random Variable
Moments about the Origin, Central Moments, Variance and Skew
Chebycheve28099s 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 3

Multiple Random Variables: Vector Random Variables, Joint Distribution Function, Properties of Joint Distribution, Marginal Distribution Functions
Conditional Distribution and Density e28093 Point Conditioning, Conditional Distribution and Density e28093 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

Unit 4

The Stochastic Process Concept, Classification of Processes, Deterministic and Nondeterministic Processes, Distribution and Density Functions
Concept of Stationarity and Statistical Independence, First-Order Stationary Processes, Second-Order and Wide-Sense Stationarity, Nth Order and Strict-Sense Stationarity
Time Averages and Ergodicity, Mean-Ergodic Processes, Correlation-Ergodic Processes
Autocorrelation Function and its Properties, Cross-Correlation Function and its Properties, Covariance and its Properties
Linear System Response of Mean and Mean-squared Value, Autocorrelation Function, Cross-Correlation Functions
Gaussian Random Processes, Poisson Random Process

Unit 5

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 Spectral Density of Input and Output of a Linear System

Reference Books

Probability, Random Variables and Stochastic Processes — Athanasios Papoulis, S. Unnikrishna Pillai — TMH
Theory of Probability and Stochastic Processes — Pradip Kumar Gosh — University Press
Probability and Random Processes with Application to Signal Processing — Henry Stark, John W. Woods
Probability Methods of Signal and System Analysis — George R. Cooper, Clave D. McGillem — Oxford
Statistical Theory of Communication — S.P. Eugene Xavier
Probability, Random Variables & Random Signal Principles — Peyton Z. Peebles — TMH
Probability and Random Processes — Scott Miller, Donald Childers — Elsevier

Go to where you left off?

Quick Add to Notes

Save questions, your own notes and screenshots into notes filed by unit. It takes a free account.

Have an account? Log in