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EC-703 (C) Probability Theory and Stochastic processing Notes

5 notes for Probability Theory and Stochastic processing, unit by unit.

Unit 1 · Short notes Probability and Random Variable 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
Unit 2 · Short notes Distribution & Density Functions and Operation on One Random Variable 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
Unit 3 · Short notes Multiple Random Variables and Operations 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
Unit 4 · Short notes Stochastic Processes – Temporal Characteristics 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
Unit 5 · Short notes Stochastic Processes – Spectral Characteristics 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

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