# JNTUK B.TECH R20 2-1 Syllabus For Random variables and stochastic processes PDF 2022

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### Random variables and stochastic processes Unit One

#### THE RANDOM VARIABLE

Introduction, Review of Probability Theory, Definition of a Random Variable, Conditions for a Function to be a Random Variable, Discrete, Continuous andMixed Random Variables, Distribution and Density functions, Properties, Binomial, Poisson, Uniform, Gaussian, Exponential, Rayleigh, Conditional Distribution, Conditional Density, Properties

### Random variables and stochastic processes Unit Two

#### OPERATIONONONERANDOMVARIABLE-EXPECTATIONS

Expected Value of a Random Variable, Function of a Random Variable, Moments about theOrigin, Central Moments, Variance and Skew, Chebychev’s Inequality, Characteristic Function,MomentGeneratingFunction,TransformationsofaRandomVariable:MonotonicTransf ormationsforaContinuousRandomVariable,Non- monotonicTransformationsofContinuousRandom Variable.

### Random variables and stochastic processes Unit Three

MULTIPLERANDOMVARIABLES: Vector Random Variables, 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: Unequal Distribution,Equal Distributions.

OPERATIONS ON MULTIPLE RANDOM VARIABLES: Joint Moments about the Origin, Joint Central Moments, Joint Characteristic Functions, Jointly Gaussian Random Variables: TwoRandom Variables case, N Random Variables case, Properties, Transformations of Multiple RandomVariables, Linear Transformations of Gaussian Random Variables.

### Random variables and stochastic processes Unit Four

#### RANDOM PROCESSES –TEMPORAL CHARACTERISTICS

The Random Process Concept,

Classification of Processes, Deterministic and Non deterministic Processes, Distribution and Density Functions, Concept of Stationarity and Statistical Independence. First-Order

Stationary Processes, Second-orderand Wide-Sense Stationarity, Nth-orderandStrict- Sense Stationarity, Time Averages and Ergodicity, Autocorrelation Function and its Properties, Cross-Correlation Function and its Properties, Covariance Functions, Gaussian Random Processes, Poisson Random Process.

### Random variables and stochastic processes Unit Five

RANDOM PROCESSES -SPECTRAL CHARACTERISTICS: The Power Density

Spectrum: Properties, Relationship between Power Density Spectrum and Auto correlation Function, The Cross-Power Density Spectrum, Properties, Relationship between Cross-Power Density Spectrum and Cross-Correlation Function.

LINEAR SYSTEMS WITH RANDOM INPUTS: Random Signal Response of Linear Systems: System Response – Convolution, Mean and Mean-squared Value of System Response, Auto correlation Function of Response, Cross-Correlation Functions of Input and Output, Spectral Characteristics of System Response: Power Density Spectrum of Response, Cross-Power Density Spectra of Input and Output, Bandpass, Band-Limited and Narrow band Processes, Properties.

### Random variables and stochastic processes Course Objectives

To give students an introduction to elementary probability theory, in preparation to learn the concepts of statistical analysis, random variables and stochastic processes.

To mathematically model therand omphenomena with the help of probability theory Concepts.

To introduce the important concepts of random variables and stochastic processes.

To analyze the LTI systems with stationary random process as input.

### Random variables and stochastic processes Course Outcomes

After completion of the course, the student will be able to

Mathematically modelther and omphenomena and solve simple probabilistic problems.

Identify different types of random variables and compute statistical averages of the serandom variables.

Characterize the random processes in the time and frequency domains.

Analyze the LTI systems with random inputs.

### Random variables and stochastic processes Text Books

Probability, Random Variables & Random SignalPrinciples, Peyton Z.Peebles, TMH, 4thEdition, 2001.

Probability, Random Variables and Stochastic Processes, Athanasios Papoulis and

S.Unnikrisha, PHI,4th Edition, 2002.

Probability and Random Processes with Applications to Signal Processing, Henry Starkand John W.Woods, Pearson Education, 3rdEdition, 2001.

### Random variables and stochastic processes Reference Books

Schaum’s Outline of Probability, Random Variables, and Random Processes, 1997.

An Introduction to Random Signals and Communication Theory, B.P.Lathi, International Textbook, 1968.

Probability Theory and Random Processes, P. Ramesh Babu, McGrawHill,2015.

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