 # JNTUA B.TECH R 20 2-1 Syllabus For Probability theory and stochastic processes PDF 2022

### Get Complete Lecture Notes for Probability theory and stochastic processes on Cynohub APP  You will be able to find information about Probability theory and stochastic processes along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Probability theory and stochastic processes after reading this blog. Probability theory and stochastic processes has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Probability theory and stochastic processes can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.

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### Probability theory and stochastic processes Unit One

#### Probability & Random Variable

Probabilitythrough Sets and Relative Frequency: Experiments and Sample Spaces, Discrete and Continuous Sample Spaces, Events, Probability Definitions and Axioms, Mathematical Model of Experiments, Probability as aRelative Frequency, Joint Probability, Conditional Probability, Total Probability, Bayes’ Theorem, Independent Events, Problem Solving.Random Variable: Definition of a Random Variable, Conditions for a Function to be a Random Variable, Discrete, 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, Problem Solving.

### Probability theory and stochastic processes Unit Two

#### Operations on Random variable

Operations on Single Random Variable: Introduction, Expectation of a random variable, moments-moments aboutthe origin, Central moments, Variance and Skew, Chebyshev’s inequality, moment generating function, characteristic function, transformations of random variable.Multiple Random Variables: Vector Random Variables, Joint Distribution Function, Properties ofJoint Distribution, Marginal Distribution Functions, Conditional Distribution and Density –Point Conditioning, Interval conditioning, Statistical Independence, Sum of Two Random Variables, Sum of Several Random Variables, Central Limit Theorem, (Proof not expected), Unequal Distribution, Equal Distributions.

### Get Complete Lecture Notes for Probability theory and stochastic processes on Cynohub APP  ### Probability theory and stochastic processes Unit Three

#### Operations on Multiple Random variables

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 of Gaussian random variables, Transformations of Multiple Random Variables, Linear Transformations of Gaussian Random Variables.

### Probability theory and stochastic processes Unit Four

#### Random Processes

Random Processes-Temporal Characteristics:The Random 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 Functions, Gaussian Random Processes, Poisson Random Process.Random Processes-Spectral Characteristics:The Power Density Spectrum and its Properties, Relationship between Power Spectrum and Autocorrelation Function, The Cross-Power Density Spectrum and its Properties, Relationship between Cross-Power Spectrum and Cross-Correlation Function.

### Probability theory and stochastic processes Unit Five

#### Random Signal Response of Linear Systems

Random Signal Response of Linear Systems:System Response –Convolution, Mean and Mean squared Value of System Response, autocorrelation Function of Response, Cross-Correlation Functions of Input and Output, Spectral Characteristics of System Response: Power Density Spectrum of Response, Cross-Power Density Spectrums of Input and Output, Band pass, Band Limited and Narrowband Processes, Properties. Noise Definitions: White Noise, colored noise and their statistical characteristics, Ideal low pass filtered white noise, RC filtered white noise.

### Probability theory and stochastic processes Course Objectives

•To gain the knowledge of the basic probability concepts and acquire skills in handling situations involving more than one random variable and functions of random variables.
•To understand the principles of random signals and random processes.
•To be acquainted with systems involving random signals.
•To gain knowledge of standard distributions that can describe real life phenomena

### Probability theory and stochastic processes Course Outcomes

CO1:Understanding the concepts of Probability, Random Variables, Random Processes and their characteristics learn how to deal with multiple random variables, conditional probability, joint distribution and statistical independence. (L1)
CO2:Formulate and solve the engineering problems involving random variables and random processes. (L2)
CO3:Analyze various probability density functions of random variables. (L3)
CO4:Derive the response of linear system for Gaussian noise and random signals as inputs. (L3)

### Probability theory and stochastic processes Text Books

1.Peyton Z. Peebles, “Probability, Random Variables & Random Signal Principles”, 4th Edition, TMH, 2002.
2.Athanasios Papoulis and S. UnnikrishnaPillai, “Probability, Random Variables and Stochastic Processes”, 4thEdition, PHI, 2002

### Probability theory and stochastic processes Reference Books

1.Simon Haykin, “Communication Systems”, 3rdEdition, Wiley, 2010.
2.Henry Stark and John W.Woods, “Probability and Random Processes with Application to Signal Processing,” 3rdEdition, Pearson Education, 2002.
3.George R. Cooper, Clave D. MC Gillem, “Probability Methods of Signal and System Analysis,” 3rd Edition, Oxford, 1999.

### Scoring Marks in Probability theory and stochastic processes

Information about JNTUA B.Tech R 20 Probability theory and stochastic processes was provided in detail in this article. To know more about the syllabus of other Engineering Subjects of JNTUH check out the official CynoHub application. Click below to download the CynoHub application.

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