# 13A04304 PROBABILITY THEORY & STOCHASTIC PROCESSES

 Course Code : 13A04304 Author : uLektz University : Jawaharlal Nehru Technological University, Anantapur (JNTUA) Regulation : 2013 Categories : Electronics & Communication Format : ePUB3 (DRM Protected) Type : eBook

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Description :13A04304 PROBABILITY THEORY & STOCHASTIC PROCESSES of 13A04304 covers the latest syllabus prescribed by Jawaharlal Nehru Technological University, Anantapur (JNTUA) for regulation 2013. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT I: PROBABILITY

1.1 Probability Introduced Through Sets And Relative Frequency: Experiments And Sample Spaces,Discrete And Continuous Sample Spaces.Events

1.2 Probability Definitions And Axioms,Mathematical Model Of Experiments,Probability As a Relative Frequency

1.3 Joint Probability,Conditional Probability,Total Probability,Bays Theorem,Independent Events

1.4 The Random Variable : Definition Of a Random Variable,Conditions For a Function To Be a Random Variable,Discrete And Continuous,Mixed Random Variable

1.5 Distribution And Density Functions,Properties,Binomial, Poisson, Uniform, Gaussian, Exponential, Raleigh, Conditional Distribution

1.6 Methods Of Defining Conditioning Event, Conditional Density, Properties

###### UNIT II:MULTIPLE RANDOM VARIABLES

2.1 Vector Random Variables,Joint Distribution Function,Properties Of Joint Distribution,Marginal Distribution Functions,Conditional Distribution And Density – Point Conditioning

2.2 Conditional Distribution And Density – Interval Conditioning,Statistical Independence,Sum Of Two Random Variables,Sum Of Several Random Variables

2.3 Central Limit Theorem, (Proof Not Expected),Unequal Distribution,Equal Distributions

2.4 Operations On Multiple Random Variables: Expected Value Of a Function Of Random Variables,Joint Moments About The Origin,Joint Central Moments,Joint Characteristic Functions

2.5 Jointly Gaussian Random Variables: Two Random Variables Case,n Random Variable Case,Properties,Transformations Of Multiple Random Variables,Linear Transformations Of Gaussian Random Variables

###### UNIT III:RANDOM PROCESSES – TEMPORAL CHARACTERISTICS

3.1 The Random Process Concept,Classification Of Processes,Deterministic And Nondeterministic Processes

3.2 Distribution And Density Functions,Concept Of Stationarity And Statistical Independence

3.3 First-Order Stationary Processes, Second- Order And Wide-Sense Stationarity,(n-Order) And Strict-Sense Stationarity,Time Averages And Ergodicity,Mean-Ergodic Processes

3.4 Correlation-Ergodic Processes,Autocorrelation Function And Its Properties,Cross-Correlation Function And Its Properties

3.5 Covariance Functions,Gaussian Random Processes,Poisson Random Process

###### UNIT IV: RANDOM PROCESSES – SPECTRAL CHARACTERISTICS

4.1 The Power Spectrum: Properties,Relationship Between Power Spectrum And Autocorrelation Function

4.2 The Cross-Power Density Spectrum,Properties,Relationship Between Cross-Power Spectrum And Cross-Correlation Function

###### UNIT V:LINEAR SYSTEMS WITH RANDOM INPUTS

5.1 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

5.2 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