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L ESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date: 12.12.2011

Page 1 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: I Branch: EC Semester : IV


Unit syllabus:


UNIT I RANDOM VARIABLES

Discrete and continuous random variables – Moments - Moment generating functions and their properties. Binomial, Poisson ,Geometric, Uniform, Exponential, Gamma and normal distributions – Function of Random Variable.


Objective: To enable the students to have a fundamental knowledge of the basic probability concepts and to have a well-founded knowledge of standard distributions which can describe real life phenomena



Session

No



Topics to be covered


Time


Ref

Teaching Method

1

Introduction, Random variables, discrete and continuous random variables, cumulative distribution function

50




1





Black Board and Chalk

2

Probability mass/density function Moments, moment generating function, probability generating function.

50

3

Moments, moment generating function, probability generating function

50


4,5

Examples of discrete random variables- Binomial Poisson variates . Poisson Distribution

100

6,7

Poisson , Geometric distributions.

100


8,9

Continuous distributions - Uniform, Exponential distributions.


100


10

Gamma distribution, Normal distribution

50

11

Normal Distribution

50

12

Function of Random Variable – discrete, continuous

50

13

Function of Random Variable, Revision

50


14

CAT 1

40











LESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date: 12.12.2011

Page 2 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: II Branch: EC Semester : IV


Unit syllabus:


UNIT II TWO DIMENSIONAL RANDOM VARIBLES

Joint distributions - Marginal and conditional distributions – Covariance - Correlation and Regression - Transformation of random variables - Central limit theorem (for iid random variables)


Objective: To acquire skills in handling situations involving more than one random variable and functions of random variables



Session

No



Topics to be covered


Time


Ref

Teaching Method

15

Two- dimensional random variables, Joint distribution functions, joint density functions.

50




1



Black Board and Chalk

16

Marginal distribution/density functions, conditional density functions, independent random variables

50


17

Correlation, covariance, Spearman’s rank correlation.

100


18

Regression curves

50

19

Regression curves

50

20

Regression lines, Rank correlation

50

21

Regression lines, Rank correlation

50

22

Tranformation of random variables

50

23

Tranformation of random variables

50

24

Central limit theorem

50

25

CAT 2

40





LESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date: 12.12.2011

Page 3 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: III Branch: EC Semester : IV


Unit syllabus:


UNIT III CLASSIFICATION OF RANDOM PROCESSES

Definition and examples - first order, second order, strictly stationary, wide-sense stationary and ergodic processes - Markov process - Binomial, Poisson and Normal processes - Sine wave process – Random telegraph process.


Objective:


Understand and characterize phenomena which evolve with respect to time in probabilistic manner.



Session

No



Topics to be covered


Time


Ref

Teaching Method

26

Random processes- Introduction, classification.

50



2



Black Board and Chalk

27

Stationary processes- first order, second order, autocorrelation function, autocovariance function , WSS

50

28,29

WSS processes, Problems, Ergodic Processes


100


30

Markov process, Bernoulli process

50


31

Binomial process

50


32

Poisson process

50


33


Poisson process

50


34

Normal process

50

35

Normal process

50

36

Sine-wave process

50

37

Random Telegraph process

50

38

CAT 3

40





LESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date: 12.12.2011

Page 4 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: IV Branch: EC Semester : IV


Unit syllabus:


UNIT IV CORRELATION AND SPECTRAL DENSITIES

Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density - Properties – Wiener-Khintchine relation – Relationship between cross power spectrum and cross correlation function .


Objective:

To understand the relationship within and between random processes


Session

No



Topics to be covered


Time


Ref

Teaching Method

39

Properties of Auto-correlation, auto-covariance functions

50




2



Black Board and Chalk

40

Cross correlation function –properties.

50


46

Power spectral density, cross Power spectral density, properties

50


47

Problems

50


48

Wiener –Khintchine theorem

50

49

Problems

50

50

Relationship between cross power spectrum and cross correlation function

50

51

Problems

50

52

Revision

50

53

CAT 4

40





LESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date: 12.12.2011

Page 5 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: V Branch: EC Semester : IV


Unit syllabus:


UNIT V LINEAR SYSTEMS WITH RANDOM INPUTS

Linear time invariant system - System transfer function – Linear systems with random inputs – Auto correlation and cross correlation functions of input and output – white noise.

Objective:

To be able to analyze the response of random inputs to linear time invariant systems.



Session

No



Topics to be covered


Time


Ref

Teaching Method

54

Linear systems with random inputs - LTI systems- System transfer function

50




2



Black Board and Chalk

55

Causal system, stable system, Autocorrelation and cross correlation functions of input and output

50


56


Autocorrelation and cross correlation functions of input and output

50


57

Problems

50

58

Problems

50


59

White Noise

50


60

Problems, Revision

50

61

Cat 5

40





LESSON PLAN

LP-EC-181403

LP Rev. No: 00

Date:12.12.2011

Page 6 of 6
Sub Code & Name : 181403 PROBABILITY AND RANDOM PROCESSES

Unit: Branch: EC Semester : IV


Course Delivery Plan:



Week

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

I II

Units

 




 




 




 




 CAT I




 




 CAT II 




 




 CAT III









 




 




 




CAT IV






CAT V


TEXT BOOKS


1. Oliver C. Ibe, “Fundamentals of Applied probability and Random processes”, Elsevier, First Indian Reprint ( 2007) (For units 1 and 2)


2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, Tata McGraw-Hill Publishers, Fourth Edition, New Delhi, 2002. (For units 3, 4 and 5).


REFERENCES


1. Miller,S.L and Childers, S.L, “Probability and Random Processes with applications to Signal Processing and Communications”, Elsevier Inc., First Indian Reprint 2007.


2. H. Stark and J.W. Woods, “Probability and Random Processes with Applications to Signal Processing”, Pearson Education (Asia), 3rd Edition, 2002.


3. Hwei Hsu, “Schaum’s Outline of Theory and Problems of Probability, Random Variables and Random Processes”, Tata McGraw-Hill edition, New Delhi, 2004.


4. Leon-Garcia,A, “Probability and Random Processes for Electrical Engineering”, Pearson Education Asia, Second Edition, 2007.


5. Yates and D.J. Goodman, “Probability and Stochastic Processes”, John Wiley and Sons, Second edition, 2005.




Prepared by

Approved by

Signature







Name

Dr. B. Thilaka

Dr. R. Muthucumarasamy

Designation

Associate Professor

HOD,AM

Date

12.12.2011

12.12.2011

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