Academic year

SRI RAMAKRISHNA 2022-2023

COLLEGE OF ENGINEERING Year/Semester
Sri Saradha Nagar, PERAMBALUR - 621 113.
II/IV

Name of the Course Instructor : Ms J.JAYASRI

Course Code :MA3355

Course Name : RANDOM PROCESSES AND LINEAR ALGEBRA

Class : BME
: IV
Semester : IV

Total number of students :

PART – I
VISION OF SRCE : MISSION OF SRCE :
1.To provide valuable resources for society 1.To offer state-of-the-art undergraduate
through excellence in technical education and programmes
research 2.To generate new knowledge
3.To undertake collaborative projects with
academic and industry
4.To develop human intellectual capacity to
its fullest potential

DEPARTMENT OF BIO MEDICAL ENGINEERING

DEPARTMENT VISION : DEPARTMENT MISSION :

1. To develop an innovative and multi-disciplinary 1. To enrich the learning skills and to
skills relating the fundamentals of Biomedical emphasize the usage of technical knowledge
engineering with other disciplines to improve the health
care and to increase life expectancy.
to improve the quality and betterment of life.

2. To practice excellence in Biomedical

Engineering by relating engineering and
medicine through education

B.E-Biomedical Engineering-C211/22-23 1
PROGRAM EDUCATIONAL OBJECTIVES (PEOs)
The Program Educational Objectifies of the biomedical Engineering degree program is
to mold graduates so that, during the first few years after graduations, they will
To enable the graduates to demonstrate their skills in solving challenges in their chosen field
through the core foundation and knowledge acquired in engineering and biology.
PEO -1
To enable the graduates to exhibit leadership, make decisions with societal and ethical
responsibilities, function and communicate effectively in multidisciplinary settings.
PEO -2
To ensure that graduates will recognize the need for sustaining and expanding their technical
competence and engage in learning opportunities throughout their careers.
PEO -3
To Carryout multidisciplinary research, addressing human healthcare problems and
Sustain technical competence with ethics, safety and standards.
PEO -4

PROGRAM OUTCOMES:
PO1: Engineering knowledge: Apply the knowledge of mathematics, science, engineering
fundamentals, and an engineering specialization to the solution of complex engineering problems.
PO2:Problem analysis: Identify, formulate, review research literature, and analyze complex
engineering problems reaching substantiated conclusions using first principles of mathematics, natural
sciences, and engineering sciences.
PO3:Design/development of solutions: Design solutions for complex engineering problems and
design system components or processes that meet the specified needs with appropriate consideration for
the public health and safety, and the cultural, societal, and environmental considerations.
PO4: Conduct investigations of complex problems: Use research-based knowledge and research
methods including design of experiments, analysis and interpretation of data, and synthesis of the
information to provide valid conclusions.
PO5: Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern
engineering and IT tools including prediction and modeling to complex engineering activities with an
understanding of the limitations.
PO6:The engineer and society: Apply reasoning informed by the contextual knowledge to assess
societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the
professional engineering practice.

B.E-Biomedical Engineering-C211/22-23 2
PO7: Environment and sustainability: Understand the impact of the professional engineering
solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for
sustainable development.
PO8: Ethics: Apply ethical principles and commit to professional ethics and responsibilities and norms
of the engineering practice.
PO9: Individual and team work: Function effectively as an individual, and as a member or leader in
diverse teams, and in multidisciplinary settings.
PO10: Communication: Communicate effectively on complex engineering activities with the
engineering community and with society at large, such as, being able to comprehend and write effective
reports and design documentation, make effective presentations, and give and receive clear instructions.
PO11: Project management and finance: Demonstrate knowledge and understanding of the
engineering and management principles and apply these to one’s own work, as a member and leader in
a team, to manage projects and in multidisciplinary environments.
PO12: Life-long learning: Recognize the need for, and have the preparation and ability to engage in
independent and life-long learning in the broadest context of technological change.
Program Specific Outcomes (PSOs)
To design and develop diagnostic and therapeutic devices that reduces physician burnout
PSO1 and enhances the quality of life for the end user by applying fundamentals of Biomedical
Engineering.
To apply software skills in developing algorithms for solving healthcare related problems
PSO2
in various fields of Medical sector.
To adapt to emerging information and communication technologies (ICT) to innovate ideas and
PSO3 solutions for current societal and scientific issues thereby developing indigenous medical
instruments that are on par with the existing technology

B.E-Biomedical Engineering-C211/22-23 3
 PART – II
SYLLABUS AS PER ANNA UNIVERSITY REGULATION 2021

MA3355 RANDOM PROCESSES AND LINEAR ALGEBRA LTPC

3104
COURSE OBJECTIVES
 To introduce the basic notions of vector spaces which will then be used to solve related
problems.
 To understand the concepts of vector space, linear transformations , inner product
spaces and orthogonalization..
 To provide necessary basic concepts in probability and random processes for
applications such as random signals, linear systems in communication engineering.
 To provide necessary basics in probability that are relevant in applications such as
random signals, linear systems in communication engineering.
 To understand the basic concepts of probability, one and two dimensional random
 variables and to introduce some standard distributions applicable to engineering which
can describe real life phenomenon.
UNIT - I PROBABILITY AND RANDOM VARIABLES 9+3
Axioms of probability – Conditional probability – Baye’s theorem - Discrete and continuous
random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric,
Uniform,Exponential and Normal distributions - Functions of a random variable.
UNIT - II TWO - DIMENSIONAL RANDOM VARIABLES 9+3
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear
regression – Transformation of random variables – Central limit theorem (for independent and
identically distributed random variables).
UNIT-III RANDOM PROCESSES 9+3
Classification – Stationary process – Markov process - Poisson process - Discrete parameter
Markov chain – Chapman Kolmogorov equations (Statement only) - Limiting distributions
UNIT – IV VECTOR SPACES 9+3
Vector spaces – Subspaces – Linear combinations and linear system of equations – Linear
independence and linear dependence – Bases and dimensions.
UNIT - V LINEAR TRANSFORMATION AND INNER PRODUCT SPACES 9+3
Linear transformation - Null spaces and ranges - Dimension theorem - Matrix representation of a
linear transformations - Inner product - Norms - Gram Schmidt orthogonalization process – Adjoint
of linear operations - Least square approximation.
TOTAL :60 PERIODS

B.E-Biomedical Engineering-C211/22-23 4
COURSE OUTCOMES:
After the course, the student should be able to:

Explain the fundamental concepts of advanced algebra and their role in modern
CO-1
mathematics and applied contexts.
CO-2 Demonstrate accurate and efficient use of advanced algebraic techniques.

CO-3 Apply the concept of random processes in engineering disciplines

Understand the fundamental concepts of probability with a thorough knowledge of
CO-4
standard distributions that can describe certain real-life phenomenon.
Understand the basic concepts of one and two dimensional random variables and
CO-5
apply them to model engineering problems.

B.E-Biomedical Engineering-C211/22-23 5
 PART – II
SRI RAMAKRISHNA COLLEGE OF ENGINEERING
DEPARTMENT OF BIO MEDICAL ENGINEERING
(CONTENT BEYOND SYLLABUS ADDED)
YEAR : II SEMESTER :III
MA3355 RANDOM PROCESSES AND LINEAR ALGEBRA LTPC
3104
COURSE OBJECTIVES
 To introduce the basic notions of vector spaces which will then be used to solve related
problems.
 To understand the concepts of vector space, linear transformations , inner product
spaces and orthogonalization..
 To provide necessary basic concepts in probability and random processes for
applications such as random signals, linear systems in communication engineering.
 To provide necessary basics in probability that are relevant in applications such as
random signals, linear systems in communication engineering.
 To understand the basic concepts of probability, one and two dimensional random
 variables and to introduce some standard distributions applicable to engineering which
can describe real life phenomenon.
UNIT - I PROBABILITY AND RANDOM VARIABLES
12
Axioms of probability – Conditional probability – Baye’s theorem - Discrete and continuous
random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric,
Uniform,Exponential and Normal distributions - Functions of a random variable.
CONTENT BEYOND : Understand and apply basic probability concepts, Identify and analyze
different types of random variables.
UNIT - II TWO - DIMENSIONAL RANDOM VARIABLES
12
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear
regression – Transformation of random variables – Central limit theorem (for independent and
identically distributed random variables).
UNIT-III RANDOM PROCESSES 12
Classification – Stationary process – Markov process - Poisson process - Discrete parameter
Markov chain – Chapman Kolmogorov equations (Statement only) - Limiting distributions
UNIT – IV VECTOR SPACES
12
Vector spaces – Subspaces – Linear combinations and linear system of equations – Linear
independence and linear dependence – Bases and dimensions.
CONTENT BEYOND : Understand the definition and properties of vector spaces and subspaces,
Apply vector space theory to solve problems in various contexts.
UNIT - V LINEAR TRANSFORMATION AND INNER PRODUCT SPACES 12
Linear transformation - Null spaces and ranges - Dimension theorem - Matrix representation of a
linear transformations - Inner product - Norms - Gram Schmidt orthogonalization process – Adjoint
B.E-Biomedical Engineering-C211/22-23 6
of linear operations - Least square approximation.
TOTAL : 60 PERIODS

TEXT BOOKS:
1.Gross, D., Shortle, J.F, Thompson, J.M and Harris. C.M., “Fundamentals of Queueing
Theory", Wiley Student 4th Edition, 2014.
2. Ibe, O.C., “Fundamentals of Applied Probability and Random Processes", Elsevier,1st
Indian Reprint, 2007.
3. Friedberg. A.H., Insel. A.J. and Spence. L., “Linear Algebra”, Prentice Hall of India, New
Delhi, 4th Edition, 2004.
REFERENCES:
1.Hsu, "Schaum’s Outline of Theory and Problems of Probability, Random Variables and
Random Processes", Tata McGraw Hill Edition, New Delhi, 2004.
2. Trivedi, K.S., "Probability and Statistics with Reliability, Queueing and Computer Science
Applications", 2nd Edition, John Wiley and Sons, 2002.
3. Yates, R.D. and Goodman. D. J., "Probability and Stochastic Processes", 2nd Edition,
Wiley India Pvt. Ltd., Bangalore, 2012.
4 Dr.A.Singaravelu .,Random processes and linear algebra ,First edition, sep 22 Meenakshi
agency.
5. Kolman. B. Hill. D.R., “Introductory Linear Algebra”, Pearson Education, New Delhi, First
Reprint, 2009.
6. Kumaresan. S., “Linear Algebra – A Geometric Approach”, Prentice – Hall of India, New
Delhi, Reprint, 2010.
7. Strang. G., “Linear Algebra and its applications”, Thomson (Brooks/Cole), New Delhi,
2005.
Referred Journals
1.www.researchgate.net/publication/2800633_Linear_Approximation_Of_Random_Processes
2. www.sciencedirect.com/journal/linear-algebra-and-its-applications
Video / Online Links :
1." Random processes" by 4G Silver Academy
2." Linear transformations" by Mathematics Kala
3. "Bay’s theorem" by Engineering mathematics

Online Certification Courses :

1.NTPEL Courseon Probability and Random Processes.
2. NTPEL Courseon Linear Algebra

B.E-Biomedical Engineering-C211/22-23 7
 PART – III
Teaching
Planned Actual
Methodology Text Book PO
Hr. No. Syllabus Topic CO
Date Date
and Teaching / Ref Book
Aid Used
UNIT – I PROBABILITY AND RANDOM VARIABLES
1 IntroductionProbability 1,2 T1 / R4 1 2, 12
2 Axioms of probability 1,2 T1 / R4 1 2, 12
3 Conditional probability 1,2 T1 / R4 1 2, 12
4 Baye’s theorem 1,4 T1 / R4 1 2, 12
Discrete random 1,3 T1 / R4 2, 12
5 1
variables
Discrete random 1,3 T1 / R4 2, 12
6 1
variables
Continuous random 1,2 T1 / R4 2, 12
7 1
variables
Moment generating 1,2 T1 / R4 2, 12
8 functions-Binomial 1
distribution
Poisson ,Geometric 1,3 T1 / R4 2, 12
9
distribution
Uniform,Exponential 1,3 T1 / R4 2, 12
10
distribution
11 Normal distribution 1,2 T1 / R4 1 2, 12
12 Revision -Unit-I 5 T1 / R4 1
13 Student Seminar 6 T1 / R4 1
UNIT – II TWO DIMENSIONAL RANDOM VARIABLES
14 Joint distributions 1,2 T1 / R4 2 2, 12
15 Marginal distributions 1,2 T1 / R4 2 2, 12
16 Conditional distributions 1,3 T1 / R4 2 2, 12
17 Covariance 1,4 T1 / R4 2 2, 12
18 Correlation 1,3 T1 / R4 2 2, 12
19 Linear regression 1,2 T1 / R4 2 2, 12
Transform of random 1,2 T1 / R4 2, 12
20 2
variables
21 Central limit theorem 1,2 T1 / R4 2 2, 12
Independent distributed 1,3 T1 / R4 2, 12
22 2
random variables.
Identically distributed 1,3 T1 / R4 2, 12
23 random variables. 2
24 Revision -Unit-II 5 2
25 Student Seminar 6 2
UNIT – III RANDOM PROCESSES
Basics concepts of 1,2 T1 / R4 2, 12
26 3
random process
27 Classifications 1,3 T1 / R4 3 2, 12
28 Stationary process 1,2 T1 / R4 3 2, 12
29 Markov process 1,4 T1 / R4 3 2, 12
30 Poisson process 1,3 T1 / R4 3 2, 12
31 Discrete parameters 1,2 T1 / R4 3 2, 12
32 Markov chain process 1,3 T1 / R4 3 2, 12
33 Markov chain problems 1,2 T1 / R4 3 2, 12

B.E-Biomedical Engineering-C211/22-23 8
 Chapman Kolmogorov 1,3 T1 / R4 3 2, 12
34
equations
Chapman Kolmogorov 1,2 T1 / R4 3 2, 12
35 equations related
problems
36 Limiting distribution 1,4 T1 / R4 3 2, 12
37 Limiting distribution 1,4 T1 / R4 3 2, 12
38 Revision -Unit-III 5 3
39 Student Seminar 6 3
UNIT – IV VECTOR SPACES
Introduction of Vector 1,2 T1 / R4 2, 12
40 4
space
41 Definition of basics 1,3 T1 / R4 4 2, 12
42 Vector spaces 1,2 T1 / R4 4 2, 12
43 Subspaces 1,3 T1 / R4 4 2, 12
44 Linear combinations 1,2 T1 / R4 4 2, 12
Linear system of 1,3 T1 / R4 2, 12
45 4
equations
46 Linear independence 1,2 T1 / R4 4 2, 12
47 Bases 1,3 T1 / R4 4 2, 12
48 dimensions 1,2 T1 / R4 4 2, 12
49 Problems and theorem 1,3 T1 / R4 4 2, 12
50 applications 1,4 T1 / R4 4 2, 12
51 Revision -Unit-IV 5
52 Student Seminar 6
UNIT – V LINEAR TRANSFORMATION AND INNER PRODUCT SPACES
Basic concepts of linear 1,2 T1 / R4 2, 12
53 5
transformation
54 Linear transformations 1,3 T1 / R4 5 2, 12
55 Null spaces 1,2 T1 / R4 5 2, 12
56 Ranges 1,3 T1 / R4 5 2, 12
57 Dimension theorem 1,2 T1 / R4 5 2, 12
58 Matrix representation 1,3 T1 / R4 5 2, 12
Inner product space, 1,2 T1 / R4 2, 12
59 5
norms
Gram Schmidt 1,3 T1 / R4 2, 12
60 5
orthogonalization
Adjoint of linear 1,2 T1 / R4 2, 12
61 5
operations
Least square 1,3 T1 / R4 2, 12
62 5
approximation
63 Applications 1,4 T1 / R4 2, 12
64 Revision -Unit-I 5 5
65 Student Seminar 6 5
NO. OF HOURS ALLOTTED IN SYLLABUS : 60
NO. OF HOURS REQUIRED AS PER PLAN : 60

Delivery / Instructional Methodologies:

B.E-Biomedical Engineering-C211/22-23 9
1 Chalk & Talk / Demonstration
2 Power Point Presentation
3 Video Presentation
4 ICT Mode(eg:NPTEL videos)
5 Tutorial / Seminar
6 Collaborative learning activities
· Think-pair-share,
· Problem-based learning
· Group Discussion
· Four Corners collaborative learning
· Inside-outside circle
· Quiz, etc.

Course Instructor Head of the Department

B.E-Biomedical Engineering-C211/22-23 10
 Academic year

SRI RAMAKRISHNA 2022-2023

COLLEGE OF ENGINEERING Year/Semester II/IV

Sri Saradha Nagar, NH-45, PERAMBALUR - 621 113.

PART IV
A. COURSE OUTCOMES
Sl. No. KL DESCRIPTION
Explain the fundamental concepts of advanced algebra and their
C211.1 K2
role in modern mathematics and applied contexts.
Demonstrate accurate and efficient use of advanced algebraic
C211.2 K3
techniques.
Apply the concept of random processes in engineering
C211.3 K3
disciplines.
Understand the fundamental concepts of probability with a
C211.4 K2 thorough knowledge of standard distributions that can describe
certain real-life phenomena.
Understand the basic concepts of one and two-dimensional
C211.5 K2,K3
random variables and apply them to model engineering problems.

B. COURSE ASSESSMENT MATRIX

PO PO PO PO PO PO PO PO PO PO PO PO PSO PSO PSO

CO’s
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3

CO1 3 3 1 1 0 0 0 0 2 0 2 3 - - -
CO2 3 3 1 1 0 0 0 0 2 0 2 3 - - -
CO3 3 3 1 1 0 0 0 0 2 0 2 3 - - -
CO4 3 3 1 1 0 0 0 0 2 0 2 3 - - -
CO5 3 3 1 1 0 0 0 0 2 0 2 3 - - -

Competency address outcome: - 1=Low; 2=Medium; 3=High

B.E-Biomedical Engineering-C211/22-23 11
 C. JUSTIFICATION FOR MAPPING

Sl.No. PO/PSO MAPPED JUSTIFICATION

Strongly mapped as students will apply engineering knowledge to solve

PO1 (High)
complex problems in biomedical contexts.
PO2 (Moderate) Moderately mapped as students will analyze and interpret data relevant
to biomedical engineering challenges.
C211.1 Strongly mapped as students will design devices that enhance quality of
PSO1 (High)
life using biomedical engineering principles.
Moderately mapped as students will adapt to ICT for developing
PSO3 (Moderate)
solutions in healthcare.
Strongly mapped as students will design solutions considering societal
PO3 (High)
and ethical impacts in biomedical applications.
PO5 (Moderate) Moderately mapped as students will use modern tools for the
C211.2 development of biomedical devices.

Strongly mapped as students will apply software skills to develop

PSO2 (High)
algorithms for healthcare problems.

Strongly mapped as students will conduct investigations and analyze data

PO4 (High)
to address complex biomedical problems.
PO9 (Moderate) Moderately mapped as students will work effectively in teams to develop
C211.3 innovative biomedical solutions.
Strongly mapped as students will design diagnostic and therapeutic
PSO1 (High)
devices that address user needs.
Strongly mapped as students will apply contextual knowledge to assess
PO6 (High) health and safety issues in biomedical projects.
PO7 (Moderate) Moderately mapped as students will understand the environmental
C211.4 impacts of biomedical engineering solutions.
Strongly mapped as students will innovate solutions for societal issues
PSO3 (High)
using ICT.
Strongly mapped as students will apply ethical principles in their
PO8 (High)
engineering practice in healthcare settings.
PO10 (Moderate) Moderately mapped as students will communicate effectively about their
C211.5 biomedical engineering projects.
Strongly mapped as students will formulate solutions to healthcare
PSO2 (High) problems using modern technologies.

A. JUSTIFICATION FOR CONTENT BEYOND SYLLABUS ADDED

B.E-Biomedical Engineering-C211/22-23 12
Unit PS PS
Topic PO JUSTIFICATION
No. O1 O3
Students will apply engineering
Understand and apply basic knowledge to solve complex
I 1 3 2
probability concepts problems and utilize probability in
developing healthcare solutions.
Students will analyze data relevant
Identify and analyze
to biomedical engineering, aiding
I different types of random 2 2 3
in the development of diagnostic
variables
devices.

Unit PO PO PSO
Topic JUSTIFICATION
No. 4 7 2
Understand the definition
Enhances problem-solving skills
and properties of vector
for engineering challenges and
spaces and subspaces,
IV 3 2 2 evaluates societal impacts, while
Apply vector space theory
improving algorithm
to solve problems in various
development for healthcare .
contexts.

Course Instructor Head of the Department

B.E-Biomedical Engineering-C211/22-23 13