Foundations of Mathematical Statistics

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.

COURSE LAYOUT

Week 1First day: module 1 - Meaning and Scope of StatisticsThird day: module 2 – Classification and TabulationFifth day: Module 3- Diagrammatic and Graphic Representation of Data – I: DiagramsSixth day: Interaction based on the three modules covered.Seventh day: deadline for submitting assignments.
Week 2First day: module 4 – Diagrammatic and Graphic Representation of Data – II: GraphsThird day:module 5-Diagrammatic and Graphic Representation of Data – III: GraphsFifth day: Module6- Measures of Central Tendency - Arithmetic MeanSixth day: Interaction based on the three modules covered.Seventh day: deadline for submitting assignments.
Week 3First day: module 7 - Measures of Central Tendency – Median and ModeThird day: module 8 –Partition valuesFfth day: module 9- Measures of dispersion-I: Quartile Deviation and Standard deviationSixth day: Interaction based on the three modules covered.Seventh day: deadline for submitting assignments.
Week 4First day: module 10 – Measures of dispersion-I: Quartile Deviation and Standard deviationThird day: module 11 – Skewness and Kurtosis Fifth day: Interaction based on the two modules covered.Seventh day: deadline for submitting assignments.
Week 5First day: module 12 – Correlation and Regression – Part I: CorrelationThird day: module 13 – Correlation and Regression – Part II :RegressionFifth day: Interaction based on the two modules covered.Seventh day: deadline for submitting assignments.
Week 6First day: module 14 – Random Experiment, Sample Space and Events and ProbabilityThird day: module 15 – Conditional Probability and Independence of eventsFifth day: Interaction based on the two modules covered.Seventh day: deadline for submitting assignments.
Week 7First day: module 16 – Bayes’ TheoremThird day: module 17 – Random variable-Discrete type Fifth day: Interaction based on the two modules covered.Seventh day: deadline for submitting assignments.
Week 8First day: module 18 – Random variable-Continuous typeThird day: module 19 – Mathematical ExpectationFifth day: Interaction based on the two modules covered.Seventh day: deadline for submitting assignments.
Week 9First day: module 20 – Moments and Moment Generating FunctionThird 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 10First 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 11First 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 12First 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.