23UMATE35 Mathematical Statistics Syllabus:

23UMATE35 Mathematical Statistics Syllabus – Annamalai University UG Syllabus Regulation 2023-24

Objectives of the Course

To Learn Statistical Methods Probability theory, Random variables, Distribution functions, Mathematical expectations, Generating functions, Correlation , Regression,  and some  standard Distributions. Students should be given practice on Statistical methods so that he could apply the techniques to solve real world problems in the field of  Science, Technology and Business Management.

UNIT-I: Probability Theory

Axiomatic approach to probability – Some theorems on Probability – Conditional Probability – Multiplication theorem of probability – Independent events – Baye’s Theorem – Simple Problems.

UNIT-II: Random Variables, Distribution Functions and Mathematical Expectation

Random Variables (Discrete and Continuous) – Distribution Function – Mathematical Expectation – Expected value of function of a random variable – properties of expectation – properties of variance – covariance.

UNIT-III: Generating Functions

Moment generating function – Characteristic Function – Uniqueness and Inversion Theorem (Statement only) – Chebychev’s Inequality – Simple Problems.

UNIT-IV: Correlation and Regression

Concept of Bivariate Distribution – Correlation – Karl Pearson’s Coefficient of Correlation – Rank Correlation – Linear Regression.

UNIT-V: Standard Distributions

Discrete distributions – Binomial, Poisson, Hyper Geometric and Negative Binomial Distributions – Continuous Distributions Normal, Uniform, Exponential.

Recommended Text

  • S.C. Gupta & V.K. Kapoor: Fundamentals of Mathematical Statistics, Sultan & sons , (11th edition, June 2002).

Reference Books

  • Hogg, R.V. & Craig.A.T.(1998): Introduction to Mathematical Statistics, Macmillan.
  • A.M. Graybill. F.A.& Boes.D.G.(1974): Introduction to theory of Statistics, McGraw Hill.
  • G.W. &Cochran.W.G.(1967): Statistical Methods, Oxford and IBH
  • Hoel, P.G (1971): Introduction to Mathematical Statistics, Wiley.
  •  Wilks S.S. Elementary Statistical Analysis, Oxford and IBH