16EC404

**UNIT I****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, Bays’ 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,

Raleigh, Conditional Distribution, Methods of defining Conditioning Event, Conditional

Density, Properties.

**UNIT II****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.

**UNIT III****RANDOM PROCESSES – TEMPORAL CHARACTERISTICS:** The Random Process

Concept, Classification of Processes, Deterministic and Nondeterministic Processes,

Distribution and Density Functions, concept of Stationary and Statistical Independence. FirstOrder Stationary Processes, Second- Order and Wide-Sense Stationary, (N-Order) and StrictSense Stationary, Time Averages and Ergodicity, Mean-Ergodic Processes, CorrelationErgodic Processes, Autocorrelation Function and Its Properties, Cross-Correlation Function and its Properties, Covariance Functions, Gaussian Random Processes, Poisson Random Process.

**UNIT IV**

RANDOM PROCESSES – SPECTRAL CHARACTERISTICS: The Power Spectrum:

Properties, Relationship between Power Spectrum and Autocorrelation Function, the CrossPower Density Spectrum, Properties, Relationship between Cross-Power Spectrum and

Cross-Correlation Function.

**UNIT V**

LINEAR SYSTEMS WITH RANDOM INPUTS: 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.

**TEXT BOOKS:**

1. Random Variables & Random Signal Principles Peyton Z. Peebles,“Probability,”, TMH,

4th Edition,

2. Probability, Random Variables and Stochastic Processes, Athanasios Papoulis and

Unnikrishna Pillai, PHI, 4th Edition, 2002.

**REFERENCES:**

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, Statistical Theory of

Communication, New Age Publications, 2003.

5. Signals, Systems & Communications B.P. Lathi, , B.S. Publications, 2003.

**UNIT -1: View/Download**

**UNIT -2: View/Download**

**UNIT-3 part 1: View/Download**

**UNIT-3 part 2: View/Download**

**UNIT -4: View/Download**

**UNIT -5: View/Download**

- Regulation-16
- Regulation-17
- Regulation-18
- Compliant Box

- Discussion Forums
- Quiz
- PPT'S
- Blog

© All rights reserved by creativestellars-2018

Designed by team- creativestellars