PROBABILITY THEORY AND STOCHASTIC PROCESSES Notes pdf – PTSP pdf notes
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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, Bayes’ Theorem, Independent Events:
THE RANDOM VARIABLE : Definition of a Random Variable, Conditions for a Function to be a Random Variable, Discrete and Continuous, Mixed Random Variable, Distribution and Density functions, Properties, Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh, Conditional Distribution, Methods of defining Conditioning Event, Conditional Density, Properties.
OPERATION ON ONE RANDOM VARIABLE – EXPECTATIONS : Introduction, 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, Transformations of a Random Variable: Monotonic Transformations for a Continuous Random Variable, Nonmonotonic Transformations of Continuous Random Variable, Transformation of a Discrete Random Variable.
MULTIPLE RANDOM VARIABLES : Vector Random Variables, Joint Distribution Function, Properties of Joint Distribution, 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.
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.
STOCHASTIC PROCESSES – TEMPORAL CHARACTERISTICS : 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, (N-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 reponse of mean and mean squared value, Auto Correlation function, Cross Correlation Function, Gaussian Random Processes, Poisson Random Process.
STOCHASTIC PROCESSES – SPECTRAL CHARACTERISTICS : The Power Spectrum: Properties, Relationship between Power Spectrum and Autocorrelation Function, The Cross-Power Density Spectrum, Properties, Relationship between Cross-Power Spectrum and Cross-Correlation Function. Spectral characteistics of system response: Power density spectrum of response, cross power spectral density of input and output of a linear system.
Noise : Resistive (Thermal) Noise Source, Arbitrary Noise Sources, White noise, narrowband noise: In phase and quadrature phase components and its properties, modelling of noise sources, average noise bandwidth, Effective Noise Temperature, Average Noise Figures, Average Noise Figure of cascaded networks.
TEXT BOOKS : [ Ptsp pdf notes | PROBABILITY THEORY AND STOCHASTIC PROCESSES Notes Pdf | PROBABILITY THEORY AND STOCHASTIC PROCESSES Notes | ptsp notes | ptsp pdf ]
1. Probability, Random Variables & Random Signal Principles – Peyton Z. Peebles, TMH, 4th Edition, 2001.
2. Probability, Random Variables and Stochastic Processes – Athanasios Papoulis and S. Unnikrishna Pillai, PHI, 4th Edition, 2002.
REFERENCES : [ Ptsp pdf notes | PROBABILITY THEORY AND STOCHASTIC PROCESSES Notes Pdf | PROBABILITY THEORY AND STOCHASTIC PROCESSES Notes | ptsp notes | ptsp pdf ]
1. Communication Systems Analog & Digital – R.P. Singh and S.D. Sapre, TMH, 1995.
2. Probability and Random Processes with Application to Signal Processing – Henry Stark and John W. Woods, Pearson Education, 3rd Edition.
3. Probability Methods of Signal and System Analysis. George R. Cooper, Clave D. MC Gillem, Oxford, 3rd Edition, 1999.
4. Statistical Theory of Communication – S.P. Eugene Xavier, New Age Publications, 2003.
5. Signals, Systems & Communications – B.P. Lathi, B.S. Publications, 2003.