Course

Unit I

Review of probability concepts-Conditional probability –Bayes Theorem, Introduction to Random variables: Discrete and Continuous random variables and its distribution –mathematical expectations.

Unit II

Some standard distributions –Binomial, Multinomial, Poisson, Uniform, exponential, Weibull, Gamma, Beta, Normal, Mean, variance, properties and application of these distributions.

Unit III

Introduction to multivariate random variables and distribution functions, variance-covariance matrix, correlation matrix, Bivariate normal distribution, Multivariate normal density.

Unit IV

Principal component Analysis, Dimensionality Reduction, Cluster Analysis: Hierarchical clustering and divisive clustering methods.

Unit V

Simple linear regression, properties, least squares estimation of parameters, Hypothesis test in simple linear regression.

Course Description  

The course will provide basic understanding of the multivariate statistics used in many areas. The course introduces some very powerful statistics behind solving real world problems from data reduction to forecasting. 

Course Objectives 

• To understand the concept of multivariate distributions  

• To understand the computations of multivariate calculus. 

• To explore the use of multivariate calculus in real life.  

Course Outcomes 

CO-PO Mapping 

• S.C Gupta and V.K Kapoor Fundamentals of Mathematical Statistics
• Anderson T.W (1983): An introduction to multivariate statistical analysis, #rd Ed, Wiley
• Ronald E.Walpole, Raymond H Myers, Sheron L Myers and Kreying Ye. Probability and Statistics for Engineers and Scientists, Eighth Edition, Pearson Education Asia 2007
• Douglas C. Montgomery and Elizabeth A Peck and G Geoffrey Vining. “Introduction to linear regression Analysis”, Third Edition, John Wiley and Sons, I