UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN STATISTICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Major III - Probability and Distributions II

UNIT - 1:

Standard univariate distributions - Point distribution, Power series, Uniform, Binomial, Poisson, Geometric, Hypergeometric, Multinomial, Negative Binomial distributions and their properties, moment generating functions, characteristic functions for the above distributions - simple problems.

UNIT - 2:

Standard continuous distributions - Uniform, Exponential, Gamma, Weibull, Beta Pareto, Cauchy, Laplace, Lognormal distributions and their properties, moment generating function, characteristic function for the above distributions - simple problems.

UNIT - 3:

Normal, and Bivariate Normal distributions and their properties, moment generating function, characteristic function for the above distributions - concepts and simple problems.

UNIT - 4:

Limit Laws - Chebychev's inequality - convergence in probability - Weak Law of Large Numbers (W.L.L.N.), Definition of almost sure convergence, Strong Law of Large Numbers (S.L.L.N. )(Statement only) and applications.

UNIT - 5:

Convergence of distributions - Binomial to Poisson, De-moivre's - Lajilace theorems, Central Limit Theorem due to Lindeberg - Levy for iid Statements of continuity theorem, uniqueness theorem and inversion theorem.

Books for Study:

A.M.Mood, F.A. Graybill and D.C. Boes (1974): Introduction to the theory of statistics, International student ed. McGraw Hill.

Hogg, R.V. and Craig, A.T. (1998): Introduction to Mathematical Statistics, 4^th ed. Acadmic Press.

A.M.Goon, M.K.Gupta & B. Dasgupta (1980): An outline of Statistical theory, Vol.I, 6^th revised ed., World Press

BOOKS FOR REFERENCE:

Rohatgi, V.K. (1984): An introduction to probability theory and mathematical statistics.
P. G.Hoel (1971): Introduction to Mathematical Statistics, Asia publishing house.
Murry R. Spiegal (1982): Theory and problems of Probability and Statistics, Schaum's outline series, McGraw Hill.
Seymour Lipshutz (1982): Theory and problems of probability, Schaum's outline series, McGraw Hill.
Marek Fisz (1961): Probability theory and Mathematical Statistics, John Wiley.
K.L.Chung (1983): Elementary probability theory with stochastic processes, Springer International student edition.
W.Feller (1968): An introduction to probability theory and its applications, Vol.I, 3^rd ed., John Wiley.