Revision on probability theory, order statistics, limiting distribution and stochastic convergence.



Point estimation: estimation using maximum likelihood method, method of moments and minimum chi-square method.



Properties of estimators: consistency, unbiasedness, efficiency and sufficiency. Completeness property for a family of distributions. Unbiased estimators with minimum variance.



Interval estimation: confident interval for small and large samples, pivotal quantity.

Hypothesis testing: basic properties of hypothesis testing, Neyman Pearson theory, critical region, Type I and Type II error, power of a test, fundamental lemma of Neyman-Pearson, the most powerful test, likelihood ratio tests for testing the mean, variance, equality of two means and equality of two variances for normal populations.



References:

1. Bain, L.J., & Engelhardt, M. (2000). Introduction To Probability and Mathematical Statistics (2nd Edition). Duxbury Press.

2. Hogg, R.V., Craig, A., & Mcken, J.W. (2004). Introduction to Mathematical Statistics (6th Edition). Prentice Hall.

3. Rice, J. (1995). Mathematical Statistics and Data Analysis (2nd Edition). Duxbury Press.