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

SYLLABUS

Semester II - Major II - Probability and Distributions I

UNIT - 1:

Random experiment, sample point, sample space, event, algebra of events, operations on events. Classical and relative frequency approach to probability - discrete probability space, axiomatic approach to probability.

UNIT - 2:

Addition theorem of probability, conditional probability, independence of events multiplication theorem - Bayes theorem and its applications.

UNIT - 3:

Definition of discrete and continuous random variables - probability mass function, distribution functions and probability density functions their properties. Expectation of random variables and its properties.

UNIT - 4:

Moment generating function, characteristic function, cumulant generating, function - their properties, moments, measures of locations, dispersion, Skewness and Kurtosis for discrete and continuous variates.

UNIT - 5:

Bivariate distributions - discrete and continuous type, cumulative distribution function (c,d.f.), and probability mass function (p.m.f) and probability density function (p.d.f.) Marginal and Conditional expectation. Covariance, Correlation, Regression.

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. Academic 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.
William.Feller (1968): An introduction to probability theory and its applications, Vol. I, 3^rd ed., John Wiley & Sons.