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

### 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

1. Probability
2. Random Variables and Their Distributions
3. Special Probability Distributions
4. Joint Distributions
5. Properties of Random Variables
6. Functions of Random Variables
7. Limiting Distributions
8. Statistics and Sampling Distributions
9. Point Estimation
10. Sufficiency and Completeness
11. Interval Estimation
12. Tests of Hypotheses
13. Contingency Tables and Goodness-of-Fit
14. Nonparametric Methods
15. 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)

• 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.