<h3>MA 5313 Introduction to Mathematical Statistics</h3>
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<h4>Course Details</h4>
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.<br> 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.<br> 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.<br> 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.
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<h4>Course References:</h4>
Text Books:<br>
1.      Hogg R. V. and Craig, A. T., Introduction to Mathematical Statistics, Macmillan Publishing Co., Fourth Edition, (1989).<br>
References:<br>
1.      G. Casella and R. L. Berger. Statistical Inference. Duxbury Press, (2001).<br>
2.      V. K. Rohtagi and A. K. Md. E. Saleh. An Introduction to Probability and Statistics. Wiley Eastern, Second Edition (2002).