# Foundations of Mathematical Statistics

By Dr.Aneesh Kumar.K   |   Mahatma Gandhi College, Iritty, Kannur, Kerala
Learners enrolled: 851
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.
The course contents starts with the meaning and scope of statistics.  The course develops through the following topics:
Various types of data and basics of data collection
Classification and tabulation
Diagrams and graphs
Central tendency, dispersion, skewness, kurtosis, moments
Correlation and regression
Various approaches to probability, Independence and conditional probability
Bayes’ theorem
Random variables – Discrete and Continuous
Mathematical Expectation
Some special discrete and continuous probability distributions.
With these foundation modules, one can take off to the  areas of interest in Statistics.
Summary
 Course Status : Completed Course Type : Core Duration : Category : Credit Points : 4 Level : Undergraduate Start Date : 18 Jan 2021 End Date : 11 Apr 2021 Exam Date :

### Course layout

Week 1
First day: module 1 - Meaning and Scope of Statistics
Third day: module 2 – Classification and Tabulation
Fifth day: Module 3- Diagrammatic and Graphic Representation of Data – I: Diagrams
Sixth day: Interaction based on the three modules covered.
Seventh day: deadline for submitting assignments.

Week 2
First day: module 4 – Diagrammatic and Graphic Representation of Data – II: Graphs
Third day:module 5-Diagrammatic and Graphic Representation of Data – III: Graphs
Fifth day: Module6- Measures of Central Tendency - Arithmetic Mean
Sixth day: Interaction based on the three modules covered.
Seventh day: deadline for submitting assignments.

Week 3
First day:  module 7 - Measures of Central Tendency – Median and Mode
Third day: module 8 –Partition values
Ffth day: module 9- Measures of dispersion-I: Quartile Deviation and Standard deviation
Sixth day: Interaction based on the three modules covered.
Seventh day: deadline for submitting assignments.

Week 4
First day:  module 10 – Measures of dispersion-I: Quartile Deviation and Standard deviation
Third day: module 11 – Skewness and Kurtosis
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 5
First day:  module 12 – Correlation and Regression – Part I: Correlation
Third day: module 13 – Correlation and Regression – Part II :Regression
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 6
First day:  module 14 – Random Experiment, Sample Space and Events and Probability
Third day: module 15 – Conditional Probability and Independence of events
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 7
First day:  module 16 – Bayes’ Theorem
Third day: module 17 – Random variable-Discrete type
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 8
First day:  module 18 – Random variable-Continuous type
Third day: module 19 – Mathematical Expectation
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 9
First day:  module 20 – Moments and Moment Generating Function
Third day: module 21 – Discrete Random variables – I (Bernoulli and Binomial random variables)
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 10
First day:  module 22 – Discrete Random variables – II (Geometric random variable)
Third day: module 23 – Discrete Random variables – III (Poisson random variable)
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 11
First day:  module 24 – Continuous Random variables – I (Uniform random variable)
Third day: module 25 – Continuous Random variables – II (Exponential and Gamma random variable)
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

Week 12
First day:  module 26 – Continuous Random variables – III (Normal distribution)
Third day: module 27 – Continuous Random variables – IV (Standard normal distribution)
Fifth day: Interaction based on the two modules covered.
Seventh day: deadline for submitting assignments.

### Books and references

1.Medhi 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.S.C.Gupta, V.K.Kapoor, Introduction to Mathematical Statistics (Sulthan Chand  and Sons),  2003.
4.T.K.Chandra , D.Chatterjee , A first course in Probability (Narosa), 2003.
5.Sheldon M Ross, A first course in Probability (Pearson Education), 2007.
6.Marcello Pagano and Kimberlee Gauvreau, Principles of Biostatistics (Cenage Learning).

### 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.