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

SYLLABUS

Semester IV - Major IV - Statistical Inference I

UNIT - 1:

Sampling distributions - concept - distributions of mean and variance from Normal population. Sampling distributions of Chi-Square, t and F statistics.

UNIT - 2:

Point Estimation - Problem of Point estimation - Properties of estimators- Consistency and Efficiency of an estimator. Sufficiency of a statistic - Neyman- Fisher factorization theorem (discrete case) - Simple problems.

UNIT - 3:

Unbiasedness - Properties, MVUE, BLUE, Rao - Blackwell theorem-Sufficiency and completeness, Lehman- Scheffe theorem, Cramer- Rao inequality - simple problems.

UNIT - 4:

Methods of estimation: Method of Moments, Method of Maximum Likelihood, Method of minimum chi-square, Method of modified minimum chi-square, method of least squares- properties of estimators obtained by these methods -simple problems.

UNIT - 5:

Interval Estimation - Confidence Interval for proportions, mean(s), variance, and variance ratio based on chi square, student's t, F and Normal distributions. Tests of significance: concepts - tests based on normal, t, F, and Chi Square.

Books for Study:

Mood, AM. Graybill , F.A. and Boes, D.C. (1974) : Introduction to the theory of Statistics, McGraw Hill.

Hogg R.V. and Craig, A.T. (1972): Introduction to mathematical statistics, 3^rd edition, Academic Press, USA.

Goon, A.M. Gupta, M.K., and Das Gupta, B. (1980): An outline of statistical theory, Vol.I, 6^th revised ed. World Press limited, Calcutta.

BOOKS FOR REFERENCE:

Hoel, P.G. (1971) : Introduction to mathematical Statistic, Asia publishing house.
Rohatgi, V.K. (1984) An introduction to probability theory and mathematical statistics, Wiley Eastern.
Degroot, M.H. (1975): Probability and Statistics, Addison - Wesley
Marek Fisz (1961): Probability theory and Mathematical statistics, John Wiley.
Spiegal, M.R. (1982): Theory and problems of probability and statistics, Schaum's outline series, McGraw Hill
Snedecor, G.W. and Cochran, W.G. (1967): Statistical methods 6^th edition, Oxford IBH Publishing Co.
Wilk, S.S. (1962): Mathematical statistics - John Wiley & Sons.