Contents |
Course Code
IAM 530 (9700530)
Credit
(3-0) 3
Prerequisites
Consent of the instructor
Content/ Aims
The goal of this course is to introduce students to the basic probability theory and mathematical statistics and help them in establishing a good theoretical background for their future professions. This course provides a comprehensive introduction to probability, statistical theory and methodology. Lectures will explain the theoretical origins and practical implications of statistical formulae.
Content of this course: Probability, combinatorics, random variables, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, limit theorems, exponential families, sufficiency and completeness, point estimation, hypothesis testing, interval estimation, linear regression.
Learning Outcomes
Suggested Textbooks
- Probability and Statistical Inference,Hogg, R. V. and Tanis, E. A., Prentice Hall, 2006
- Statistical Inference, Casella, G. and Berger, R.L., Thomson Learning, 2nd Edition, 2002
- Mathematical Statistics with Applications, Wackerly, D.D., Mendelhall, W.III and Scheaffer, R.L., 7th ed., Thomson, 2008.
- Introduction to Probability and Mathematical Statistics, 2nd edition, Bain and Engelhardt, 1992
- Introduction to Probability and Statistical Inference, Roussas, G.G., Academic Press. (2003)
- Introduction to Probability and Statistics, Milton, J. S. and Arnold, J. C., McGraw-Hill, 1995
- Introduction to Mathematical Statistics, 6th edition, Hogg, McKean and Craig, Prentice Hall, 2005
- John E. Freund’s Mathematical Statistics with Applications, 7th edition, Miller, I. and Miller, M., Prentice Hall, 2004
- Mathematical Statistics, 2nd edition, Bickel, P.J. and Doksum, K. A., Prentice Hall, 2001
- An Introduction to Mathematical Statistics and Its Applications, 4th ed.,Larsen, R. J. and Marx, M. L., Prentice Hall, 2005.
Outline
- Week 1: Probability Axioms, Combinatorics.
- Week 2: Conditional Probability, Bayes Theorem.
- Week 3: Random variables, Discrete distributions and their properties.
- Week 4: Continuous distributions and their properties.
- Week 5: Expectations of random variables, Joint distribution functions, Conditional distributions.
- Week 6: Distribution functions and their properties, Transformations of variables.
- Week 7: Moment generating functions, Limit theorems.
- Week 8: Statistics, Sampling Distributions, Point Estimation, Maximum likelihood estimation, Method of moments.
- Week 9: Unbiased estimators, Consistent estimators, , Mean-square error, Sufficiency; Completeness
- Week 10: Rao-Blackwell Theorem, Complete sufficient statistics, Lehmann-Scheffe theorem, Minimum variance unbiased estimators,
- Week 11: Exponential families, Fisher information, Rao-Cramer inequality, Efficient estimators, Asymptotic efficiency.
- Week 12: Testing hypotheses: concepts of hypothesis testing, Neyman-Pearson lemma
- Week 13: Likelihood ratio test, Confidence intervals
- Week 14: Linear Regression