MA 5313 Introduction to Mathematical Statistics
Unit I: Distributions of Random Variables: The probability set function; random variables; probability density function; distribution function; certain probability models; mathematical expectation; Chebyshev�s inequality; conditional probability; marginal and conditional distributions; correlation coefficient; stochastic independence.
Unit II: Special Discrete and Continuous Distributions and the Distributions of Functions of Random Variables. Sampling Theory; Transformation of variables: Discrete and Continuous; Distribution of order statistics; moment generating function technique; Distribution of X̄ and S2 and expectations.
Unit III: Limiting Distributions and Estimation: Limiting distributions; stochastic convergence; limiting moment-generating functions; central limit theorem; point estimation, measures of quality of estimators; Confidence intervals: mean, differences of means; variances; Bayesian estimators.
Unit IV: Statistical Hypotheses and other Statistical Tests: Testing of hypotheses, Neyman-Pearson lemma, tests for one sample and two sample problems; chi-squared tests; analysis of variance; regression problem; test for stochastic independence.
1. Hogg R. V. and Craig, A. T., Introduction to Mathematical Statistics, Macmillan Publishing Co., Fourth Edition, (1989).
1. G. Casella and R. L. Berger. Statistical Inference. Duxbury Press, (2001).
2. V. K. Rohtagi and A. K. Md. E. Saleh. An Introduction to Probability and Statistics. Wiley Eastern, Second Edition (2002).