Probability Theory and Stochastic Process
UNIT-I
INTRODUCTION TO PROBABILITY
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. Simulation of Baye’s Theorem in MATLAB.
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. Simulation of Moments in MATLAB
UNIT-III
OPERATIONS ON & MULTIPLE RANDOM– EXPECTATIONS
Joint Distribution Function, Properties of Joint Distribution, Marginal Distribution Functions, 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. Simulation of Central Limit Theorem in MATLAB.
UNIT-IV
RANDOM PROCESSES -TEMPORAL and SPECTRAL CHARACTERISTICS
The Random process, classification, deterministic and non-deterministic 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.
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. Simulation of Gaussian random process in MATLAB.
UNIT-V
MODELLING OF NOISE:
Classification of Noise, types and sources of noises, Thermal Noise Source, Effective Noise Temperature, Average Noise Figures. Simulation and analysis of White Noise in MATLAB.
👉👉👉Probability and stochastic process
UNIT - 1
Download from Here 👉👉 unit1.pdf
UNIT - 2
Download from Here👉👉 unit2.pdf
Model paper 👉👉 model_paper_pdf
PROBABILITY THEORY AND STOCHASTIC PROCESS TEXTBOOK
👉👉👉Probability and stochastic process
