Maths 320: Mathematical Statistics - I (4)

Syllabus

1.  Prerequisite:  Maths 166, 215. 

2.  Course Description: Probability theory for discrete and continuous sample spaces, random variables, density functions, distribution functions, marginal and conditional distributions, mathematical expectation, moment-generating functions, common distributions, sampling distribution theory, central limit theorem, and t, chi-square, and F distributions.

3.  Course Objectives: this course will provide a solid foundation in probability theory at the undergraduate level.  This is the beginning course that will prepare students for a wide variety of courses in mathematical statistics and statistical inference.

4.  Course Rationale: The concepts of probability are of great importance in a wide variety of applications.  The theory of probability, as the foundation upon which the methods of statistics are based, should command the attention of those who what to understand as well as apply statistical techniques.  This course, therefore, is a required course for those who want to major in statistics or actuarial science and is an excellent course for those who are in mathematics, business, and other allied fields.   

5.  Course Content:

            Probability

                        Random Experiments

                        Random Variables

                        Properties of Probability

                        Methods of Enumeration

                        Conditional Probability

                        Bayes’ theorem

                        Independent Events

            Distributions of Discrete Type

                        Random Variables of Discrete Type

                        Mathematical Expectation

                        Mean and Variance

                        Moment Generating functions

                        Bernoulli and Binomial Distributions

                        Geometric and Negative Binomial Distributions

                        Multivariate Distributions of Discrete Type

                        Correlation Coefficient

                        Conditional Distributions

                        Multinomial Distribution

            Distributions of Continuous Type

                        Samples, Histograms, and Ogives

                        Exploratory Data Analysis

                        Random Variables of continuous Type

                        Uniform Distribution

                        Exponential and Gamma Distributions

                        Normal Distribution

                        Multivariate Distributions of Continuous Type

                        Bivariate Normal Distribution

                        Sampling from Bivariate Distributions

                        Mixed Distributions and Censoring

            Sampling Distribution Theory

                        Distributions of functions of Random Variables

                        Sums of Independent Random Variables

                        Chi-square Distribution

                        The t and F Distributions

                        Central Limit theorem

                        Approximations for Discrete Distributions

                        Limiting Moment generating Functions

                        Transformations of Random Variables

6.  Course Format: Lecture/discussion.  The amount of material to be covered may not allow for a complete treatment in class of all topics listed in the Course Content, so students may need to supplement overviews in class with individual reading.      

7.  Methods of Evaluating Student Performance: Course grades are determined primarily on student performance of tests and the final examination, augmented by evaluation of performance on homework.  

8.  Evaluation of the Course: The instruction of the course is evaluated by departmental student evaluations and peer evaluation.  The course is reviewed and revised periodically by the Departmental Graduate Programs Committee.  

Ali/ rev. Nelson 2002

M. Begum 10/17/05