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DOC/LP/01/28.02.02
LP-EC-MA6451
LESSON PLAN
LP Rev. No: 01
Sub Code & Name: MA6451 PROBABILITY AND
Date: 27.12.2014
RANDOM PROCESSES
Unit: I
Branch(Student): EC
Semester : IV
Page 1 of 6
Unit syllabus: RANDOM VARIABLES
Discrete and continuous random variables – Moments - Moment generating functions -- Binomial,
Poisson ,Geometric, Uniform, Exponential, Gamma and normal distributions.
Objective: At the end of the unit, the students would have a fundamental knowledge of the
concept of random variables. Have a well – founded knowledge of standard
distributions which can describe real life phenomena.
Session
No
1.
Time
(mm)
Topics to be covered
Introduction to unit I. Discrete and continuous random
variables, Probability mass function, probability density
Ref
Teaching
Method
50
function.
2.
Cumulative distribution function and their properties
50
3.
Moments, Moment generating functions, properties
50
4.
Binomial distribution.
50
5.
Problems solved
50
6.
Tutorial class
50
7.
Poisson distribution.
50
8.
Problems solved
50
9.
Geometric distribution
50
10.
Uniform distribution, Exponential distribution.
50
11.
Problems solved
50
12.
Gamma distribution.
50
13.
Normal distribution.
50
14.
Tutorial class
50
1,2,3 BB/PPT
1
DOC/LP/01/28.02.02
LP-EC-MA6451
LESSON PLAN
LP Rev. No: 00
Sub Code & Name: MA6451 PROBABILITY AND
Date:27.12.2014
RANDOM PROCESSES
Unit: II
Branch(Student): EC
Semester : IV
Page 2 of 6
Unit syllabus: TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and
Regression –-Transformation of random variables - Central limit theorem.
Objective: At the end of the unit, the students would acquire skills in handling situations involving
more than one random variable and functions of random variables.
Session
No
Topics to be covered
Time
(mm)
15
Introduction - Unit Syllabus - Joint distributions.
50
16
Problems solved
50
17
Marginal and conditional distributions.
18
CAT-I
19
Problems solved
20
Problems on Marginal and conditional distributions.
21
Tutorial
22
Covariance.
23
Properties and problems on Correlation coefficients.
24
Properties and problems on Regression.
25
Problems on function of a random variable.
Ref
Teaching
Method
1,2,3
BB/PPT
50
90
50
50
50
50
2
50
50
50
DOC/LP/01/28.02.02
LP-EC-MA6451
LESSON PLAN
LP Rev. No: 00
Sub Code & Name: MA6451 PROBABILITY AND
Date:27.12.2014
RANDOM PROCESSES
Unit: III
Branch(Student): EC
Semester : IV
Page 3 of 6
Unit syllabus: RANDOM PROCESSES
Classification of random process - Stationary processes - Markov process - Poisson processes –
Random telegraph process.
Objective: Understand and characterize phenomena which evolve with respect to time in
probabilistic manner.
Session
No
Time
(mm)
Topics to be covered
Introduction-Random process.
27
Classification of random process with examples
28
Classification of random process with examples
29
Stationary processes-first and second order, auto correlation
function, auto covariance function
30
Problems solved
31
Wide-sense stationary processes(WSS), Ergodic processes
32
Tutorial
CAT - II
35
Poisson processes
36
Poisson processes-problems solved
37
Normal processes
38
50
50
50
50
50
50
50
Markov process
34
Teaching
Method
50
26
33
Ref
50
50
50
50
Sine wave process – Random telegraph process.
3
50
1,2,3
BB/PPT
DOC/LP/01/28.02.02
LESSON PLAN
LP-EC-MA6451
Sub Code & Name: MA6451 PROBABILITY AND
Date:27.12.2014
RANDOM PROCESSES
Unit: IV
Branch(Student): EC
Page 4 of 6
Semester : IV
Unit syllabus: CORRELATION AND SPECTRAL DENSITIES
Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density
– Properties.
Objective: To understand the relationship within and between random processes
Session
No
Time
(mm)
Topics to be covered
39
Unit IV introduction, Auto-correlation, auto-covariance
functions-properties
40
Problems solved
41
Cross correlation function and properties.
42
Tutorial class
43
Power spectral density, Cross spectral density, Properties
44
Problems solved
45
Wiener-Khintchine relation
46
Tutorial class
47
Relationship between cross power spectrum and cross
correlation function
48
Problems solved
49
Cross correlation function and properties.
50
Problems solved
Ref
Teaching
Method
50
50
50
50
50
50
1,2,3 BB/PPT
50
50
50
50
4
50
DOC/LP/01/28.02.02
LP-EC-MA6451
LESSON PLAN
LP Rev. No: 00
Sub Code & Name: MA6451 PROBABILITY AND
Date:27.12.2014
RANDOM PROCESSES
Unit: V
Branch(Student): EC
Semester : IV
Page 5 of 6
Unit syllabus: 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.
Objective: To be able to analyze the response of random inputs to linear time invariant systems.
Session
No
Time
(mm)
Topics to be covered
51
Linear time invariant system - System transfer function
52
Problems solved
53
Causal system, stable system
54
Linear systems with random inputs
55
Tutorial
56
Auto correlation and cross correlation functions of input and
output
57
Problems solved
58
White noise
59
Problems solved
60
CAT III
Ref
Teaching
Method
50
50
50
50
50
50
50
50
50
90
5
1,2,3 BB/PPT
DOC/LP/01/28.02.02
LP-EC-MA6451
LESSON PLAN
LP Rev. No: 00
Sub Code & Name: MA6451 PROBABILITY AND
Date: 27.12.2014
RANDOM PROCESSES
Branch(Student): EC
Page 6 of 6
Semester : IV
Course Delivery Plan:
1
Week
I
II
2
3
4
I II
I II
I II
5
6
7
9
I II I II I II I II I II
10
I II
11
I
II
12
I
II
13
14
15
I II I II I II
CAT-III
C
A
T
II
CAT-I
Units
8
BOOKS FOR REFERENCES:
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).
3. T.Veerarajan, Probability,Statistics and Random processes, TataMcGraw-Hill Education Private
Limited, Fifth Edition, New Delhi,2008
Prepared by
Approved by
Name
T.KULANDAIVEL
Dr R MUTHUCUMARASWAMY
Designation
Assistant Professor
Signature
Date
Professor & Head
02.01.2015
02.01.2015
6