EC-703 (C) RGPV B.Tech
Probability Theory and Stochastic processing (PTSP)
Previous year papers and the official syllabus are free to read, no account needed.
Previous Year Papers
1 paper, latest Nov 2023
Syllabus, notes and important questions for EC-703 (C)
Syllabus units
Topics as the official RGPV syllabus lists them.
Unit 1 Probability and Random Variable 15 topics
- 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
- Bayes’ Theorem
- Independent Events
- 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 and Operation on One Random Variable 14 topics
- Distribution and Density functions and their Properties (Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh)
- Conditional Distribution and Conditional Density
- Methods of defining Conditional Event
- Conditional Density Properties
- Expectations – Introduction and 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
- 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 and Operations 18 topics
- Vector Random Variables
- Joint Distribution Function and its Properties
- 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
- 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
- Jointly Gaussian Random Variables – N Random Variables case and Properties
- Transformations of Multiple Random Variables
- Linear Transformations of Gaussian Random Variables
Unit 4 Stochastic Processes – Temporal Characteristics 17 topics
- Stochastic Process Concept
- Classification of Processes
- Deterministic and Nondeterministic Processes
- Distribution and Density Functions of Processes
- 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
- Gaussian Random Processes
- Poisson Random Process
Unit 5 Stochastic Processes – Spectral Characteristics 7 topics
- Power Spectrum and its Properties
- Relationship between Power Spectrum and Autocorrelation Function
- Cross‑Power Density Spectrum and its 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