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DEPARTMENT OF MATHEMATICS
NATIONAL INSTITUTE OF TECHNOLOGY, TIRUCHIRAPPALLI
COURSE PLAN – PART I Course Title Probability and Statistics
Course Code MAIR45 No. of Credits 4
Course Code of Pre-
requisite subject(s) 10 + 2 Mathematics
Session January 2021 Section
(if, applicable) IV Sem. PROD-A (UG) Name of Faculty V. Kumaran Department Mathematics
Email [email protected] Telephone No. 2503670/6383276625 Name of Course
Coordinator(s) (if, applicable)
E-mail Telephone No.
Course Type Core course Elective course
COURSE OBJECTIVES Objective of the course is to
1. To understand fundamentals and application of statistics to engineering problems.
2. To use statistical concepts in their research work.
3. To form hypothesis and able to test their hypothesis with various statistical tests.
4. To compute multiple and partial correlation coefficients.
5. To identify the significant factors using ANOVA.
COURSE OUTCOMES (CO)
Course Outcomes Aligned Programme Outcomes
(PO) After the completion of the course, student will be able to:
1. Understand random variables and various distributions.
2. Form hypothesis & test it with various statistical tests.
3. Find correlation and perform regression analysis.
4. Understand random process, Markov chain and applications.
5. Perform time series analysis.
1, 2 & 4 X
Page 2 of 4 Reference Books:
1. Gupta, S.C. and Kapoor, V.K., Fundamentals of Mathematical Statistics, Sultan Chand and Sons, Eleventh Revised Editions, June 2002.
2. Gupta, S.C. Fundamentals of Statistics, Himalaya Publishing House, Sixth Revised Edition, April 2004.
3. Medhi, J., Stochastic Processes, New Age International (P) Ltd., Publishers, 2nd Edition, 2004.
4. Kishor, S. Trivedi, Probability and Statistics with Reliability, Queuing and Computer Science Applications, Wiley-India, Edition 2008.
5. Papoulis, A. Probability, Random Variables and Stochastic Processes, McGraw Hill, 2006.
Syllabus (approved in BoS)
Random variable -Two dimensional random variables –standard probability distributions –Binomial, Poisson and normal distributions -moment generating function.
Sampling distributions –testing of hypotheses – Large sample tests for mean and proportion –t- test, F-test and Chi-square test –Independence of Attributes-Analysis of Variance.
Point Estimation-Interval estimation –Measures of quality of Estimators-Confidence intervals for means and variance - Correlation -rank correlation –multiple and partial correlation –Regression Analysis.
Random process –Markov Dependence, Markov Chains, definition, examples –Ergodicity-Finite Markov Chain-Various States –Limiting Probability –Application of Markov Chain to Simple Problems.
Time Series Analysis-Introduction-Probability models for Time Series-moving average-method of least squares-auto regressive models-Application to simple problems.
COURSE PLAN – PART II COURSE OVERVIEW
The course develops the basic concepts of random variables, various distributions, hypothesis & test it with various statistical tests, correlation and perform regression analysis, random processes, Markov chains & applications of Markov Chain and time series analysis.
Page 3 of 4 COURSE TEACHING AND LEARNING ACTIVITIES
S.No. Week/Contact Hours
Topic Deliv.
Mode
1
1st Week 2nd Week 3rd Week (9-12 hrs)
Probability and Random variables.
Two dimensional random variables.
Standard probability distributions –Binomial, Poisson,
normal distributions and Moment generating function.
Online
2
4th Week 5th Week
6th Week (9-12 hrs)
Sampling distributions, testing of hypotheses and large sample tests for mean and proportion.
t-test, F-test and Chi-square test –Independence of
Attributes.
Analysis of Variance.
Online
3
7th week 87h week
9th week (9-12 hrs)
Point Estimation and measures of quality of Estimators.
Interval estimation and confidence intervals for mean &
variance.
Correlation, rank correlation, multiple & partial correlation and Regression analysis.
Online
4
10th week
117h week 12th week (9-12 hrs)
Random process and Markov Dependence, Markov
Chains, definition, examples.
Ergodicity-Finite Markov Chain-Various States.
Limiting Probability and application of Markov chain to Simple Problems.
Online
5
13th week 147h week
15th week (9-12 hrs)
Time Series Analysis introduction.
Probability models for Time series, moving average,
method of least squares, auto regressive models.
Application to simple problems.
Online
COURSE ASSESSMENT METHODS (all online mode, shall range from 4 to 6)
S.No. Mode of Assessment Week/Date Duration % Weightage 1 Assessment-I (Test) Feb. 4th week
/Mar 1st week 1½ hrs 25%
2 Assessment-II (Test) Apr. 1st week
/Apr. 2nd week 1½ hrs 25%
3 Assignments/Quiz Every 3 weeks Next 1 week 20%
CPA Compensation Assessment* May 1st week 1½ hrs 25%
5 Final Assessment * May 2nd week 2 hrs 30%
*mandatory; refer to guidelines on page 4
Page 4 of 4 COURSE EXIT SURVEY (mention the ways in which the feedback about the course shall be assessed)
Twice in a semester student can give oral (recorded by student)/anonymous written feedback about the content, content delivery and valuation.
COURSE POLICY (preferred mode of correspondence with students, policy on attendance, compensation assessment, academic honesty and plagiarism etc.)
MODE OF CORRESPONDENCE (email/ phone etc)
Email : [email protected] Phone 0431-2503670/6383276625
ATTENDANCE
3. Permitted to write Semester Exam if a) attendance in online is >= 75%
b) exceptional case (with valid reasons and proofs)>=60%
(if approved by the faculty and PAC Chair)
COMPENSATION ASSESSMENT . Absent for tests: 1. If reason is genuine and informed his inability to write the test in time with a written request, the student may be permitted for CPA.
ACADEMIC HONESTY & PLAGIARISM. If found copying in any form in tests/semester exam will get zero marks.
ADDITIONAL INFORMATION
At least 20% of marks in the final assessment and overall 35% of marks is essential for a Pass in the course.
FOR APPROVAL
(2-2-2021) (V.Kumaran)
Course Faculty CC-Chairperson ________________ HOD _______________
(Dr. D. Lenin Singaravelu)
