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| ECE 2-1 RVSP | ||
|---|---|---|
| S.No | Chapters / Units | Download Link |
| 1 | Unit 1 | Download |
| 2 | Unit 2 | Download |
| 3 | Unit 3 | Download |
| 4 | Unit 4 | Download |
| 5 | Unit 5 | Download |
ECE 2-1 RVSP Important Topics Questions
UNIT I
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.
UNIT II
OPERATION ON ONE RANDOM VARIABLE-EXPECTATIONS: Introduction,
Expected Value of a Random Variable, Function of a Random Variable, Moments about
theOrigin, Central Moments, Variance and Skew, Chebychev’s Inequality, Characteristic
Function,Moment Generating Function,Transformations of a Random Variable:Monotonic Transf
ormations for a Continuous Random Variable,Non-
monotonic Transformations of Continuous Random Variable.
UNIT III
MULTIPLE RANDOM VARIABLES: 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.
UNIT IV
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.
UNIT V
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.
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