Part I: Probability spaces, random variables, probability distributions and probability densities, conditional probability, Bayes' formula, mathematical expectation, moments. Part II: Sampling distributions, decision theory, estimation (theory and applications), hypothesis testing (theory and applications), regression and correlation, analysis of variance, non-parametric tests.
For further information see the academic catalog: IAM530 - Elements of Probability and Statistics
Course Objectives
The objective 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. This course initiate students to Probability Calculus and statistical methods used in current application problems.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
- apply the conditional probability concepts and Bayes' theorem to the problems in finance and actuarial mathematics
- do mathematical modelling using the distributions of continuous and discrete random variables
- apply the concepts learn in the second part of the course to do statistical inference
Instructional Methods
The following instructional methods will be used to achieve the course objectives: lecture, questioning, discussion, group work, simulation.
Tentative Weekly Outline
- Probability
- Random Variables and Their Distributions
- Special Probability Distributions
- Joint Distributions
- Properties of Random Variables
- Functions of Random Variables
- Limiting Distributions
- Statistics and Sampling Distributions
- Point Estimation
- Sufficiency and Completeness
- Interval Estimation
- Tests of Hypotheses
- Contingency Tables and Goodness-of-Fit
- Nonparametric Methods
- Regression and Linear Models
Course Textbook(s)
- Introduction to Probability and Mathematical Statistics, L. J. Bain and M. Engelhardt, 2nd edition, 1992.
- Statistical Inference, Second Edition, Casella, G. and Berger, R.L., Thomson Learning, 2002.
Course Material(s) and Reading(s)
Reading(s)
- Introduction to Probability and Statistics Using R, G. Jay Kerns, First Edition, 2010.
- Probability and Statistical Inference, Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman, 9th edition, 2015.
- All of Statistics - A Concise Course in Statistical Inference, Larry Wasserman, 2004.
- An Introduction to R - Notes on R: A Programming Environment for Data Analysis and Graphics, W. N. Venables, D. M. Smith, and the R Core Team, Version 3.4.2 (2017-09-28).
Supplementary Readings / Resources / E-Resources
Resources
Those who do not have R on their PCs can download it from the site http://www.r-project.org.
A very nice Quick-R website is located on http://www.statmethods.net.
Other
Related to the textbook, check the site http://www.stat.pitt.edu/stoffer/tsa3/R_toot.htm.