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Foundations of Mathematical Statistics

By Dr.Aneesh Kumar.K   |   Mahatma Gandhi College, Iritty, Kannur, Kerala
Learners enrolled: 93
The course entitled “Foundations of Mathematical Statistics” deals with the basic aspects of Mathematical Statistics.  The contents of this course are inevitable for any students who wish to study Statistical concepts.  The students of Statistics, Mathematics, Economics, Commerce, Bioinformatics, Computer Science etc., are equally benefited with this course as a stepping stone to the broad area of Statistical science.  The course aims to provide foundations in descriptive statistics and probability.
Summary
Course Status : Upcoming
Course Type : Elective
Language for course content : English
Duration : 15 weeks
Category :
  • Mathematics
Credit Points : 4
Level : Undergraduate
Start Date : 12 Jan 2026
End Date : 21 Apr 2026
Enrollment Ends : 28 Feb 2026
Exam Date :
Translation Languages : English
NCrF Level   : 5.0

Page Visits



Course layout

Weeks         Lecture Topics (Module Titles)

1 Day 1 Module 1: Meaning and Scope of Statistics  
Day 2 Module 2: Collection of Data    
Day 3 Module 3: Classification and Tabulation
Day 4 Discussion
Day 5 Assignment

2 Day 1 Module 4: Diagrammatic and Graphic Representation of Data – I:  Diagrams
Day 2 Module 5: Diagrammatic and Graphic Representation of Data – II: Graphs
Day 3 Module 6: Diagrammatic and Graphic Representation of Data – III: Graphs 
Day 4 Discussion
Day 5 Assignment

3 Day 1 Module 7: Measures of Central Tendency– Arithmetic Mean
Day 2 Module 8: Measures of Central Tendency– Median and Mode
Day 3 Module 9: Partition values
Day 4 Discussion
Day 5 Assignments

4 Day 1 Module 10: Harmonic Mean and Geometric Mean
Day 2 Module 11: Measures of dispersion-I: Quartile Deviation and Standard deviation type 
Day 3 Module 12: Measures of Dispersion – II - Range, Mean Deviation, Relative Measures and Coefficient of Variation
Day 4 Discussion
Day 5 Assignment

5 Day 1 Module 13: Skewness and Kurtosis 
Day 2 Module 14: Correlation and Regression – Part I: Correlation
Day 3 Module 15: Correlation and Regression – Part II: Regression
Day 4 Discussion
Day 5 Assignment

6 Day 1 Module 16: Random Experiment, Sample Space and Events and Probability 
Day 2 Module 17: Conditional Probability and Independence of events 
Day 3 Module 18: Bayes’ Theorem 
Day 4 Discussion
Day 5 Assignment

7 Day 1 Module 19: Random variable-Discrete type 
Day 2 Module 20: Random variable-Continuous type 
Day 3 Module 21: Mathematical Expectation    
Day 4 Discussion
Day 5 Assignment

8 Day 1 Module 22: Moments and mgf 
Day 2 Module 23: Discrete Random variables – I (Bernoulli and Binomial random variables)
Day 3 Module 24: Discrete Random variables – II (Geometric random variable)
Day 4 Discussion
Day 5 Assignment
9 Day 1 Module 25: Discrete Random variables – III (Poisson random variable)
Day 2 Module 26: Discrete Random variables – III (Discrete Uniform and Negative Binomial random variables)
Day 3 Module 27: Continuous Random variables – I (Uniform random variable)
Day 4 Discussion
Day 5 Assignment

10 Day 1 Module 28: Continuous Random variables – II (Exponential and Gamma random variable)
Day 2 Module 29: Continuous Random variables – III (Normal distribution)
Day 3 Module 30: Continuous Random variables – IV (Standard normal distribution)
Day 4 Discussion
Day 5 Assignment

11 Day 1 Module 31: Law of Large Numbers
Day 2 Module 32: Sampling Distributions and Chi-square Distribution
Day 3 Module 33: Student’s t- Distribution Snedecor’ s F-Distribution
Day 4 Discussion
Day 5 Assignment

12 Day 1 Module 34: Estimation of Parameters – Point Estimation 
Day 2 Module 35: Estimation of Parameters –Interval Estimation 
Day 3 Module 36: Methods of Estimation-Methods of MLE and Moments 
Day 4 Discussion
Day 5   Assignment

13 Day 1 Module 37: Testing of Hypothesis
Day 2 Module 38: Testing of Hypothesis – More Problems
Day 3 Module 39: Large sample tests
Day 4 Discussion
Day 5 Assignment

 15 Day 1 Module 40 : Small sample tests
Day 2
Day 3 Assignment
Day 4 Final Discussion
Day 5

Books and references

1. Methi J, Statistical Methods- an Introductory Text (New Age international (p) Ltd).
2. Bhat. B. R. ,Srivenkatramana T. & Madhav Rao K. S., Statistics A beginner’s text (New Age international (p) Ltd).
3. Gupta S. C. And V. K. Kapoor, Fundamentals of Mathematical Statistics (Sulthan Chand & sons).

Instructor bio

Dr.Aneesh Kumar.K

Mahatma Gandhi College, Iritty, Kannur, Kerala
20 years of experience in teaching Undergraduate level Statistics, Operations Research etc.  Developed study material for many Univeristies in Kerala for their School of Distance Education.  Awarded Ph.D. from the University of Calicut in 2007 for the works under Dr. M. Manoharan- University of Calicut. Published research articles in various journals.

Course certificate

1.       End-Term Examination:
  • Weightage: 70% of the final result
  • Minimum Passing Criteria: 40%
2.       Internal Assessment:
  • Weightage: 30% of the final result
  • Minimum Passing Criteria: 40%
Calculation of IA Marks:
  • Out of all graded weekly assessments/assignments, the top 50% of assignments shall be considered for the calculation of the final Internal Assessment marks.
All students who obtain 40% marks in the internal assessment and 40% marks in the end-term proctored exam separately will be eligible for the SWAYAM Credit Certificate.
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