Descriptive Statistics, Graphical representation of data, Curve fittings, Simple correlation and regression, Multiple and partial correlations and regressions, Sampling, Sampling distributions, Standard error. Normal distribution and its properties, The distribution of X and S 2 in sampling from a normal distribution, Exact sampling distributions: χ 2 , t, F . Theory and Methods of Estimation: Point estimation, Criteria for a good estimator, Properties of estimators: Unbiasedness, Efficiency, Consistency, Sufficiency, Robustness. A lower bound for a variance of an estimate, Method of estimation: The method of moment, Least square method, Maximum likelihood estimation and its properties, UMVU Estimator, Interval estimation. Test of Hypothesis: Elements of hypothesis testing, Unbiased test, Neyman-Pearson Theory, MP and UMP tests, Likelihood ratio and related tests, Large sample tests, Test based on χ 2 , t, F .
- H. J. Larson, “Introduction to Probability Theory and Statistical Inference”, John Wiley & Sons, 1982.
- V. K. Rohatgi, “Introduction to Probability Theory and Mathematical Statistics”, John Wiley & Sons, 1976.
- I. Miller, M. Miller, “John E. Freund’s Mathematical Statistics with Applications”, Pearson, 2013.