MATH 4751/6751– Learning Outcomes

Title: Mathematical Statistics I

Students will understand the basic probability theory.
Students will understand the concepts of probability distributions and distribution functions.
Students will understand how the most commonly used discrete as well as continuous distributions arise in the real world.
Students will understand the random variables and their distributions.
Students will understand the concept of joint distributions.
Students will understand the mathematical expectations of random variables.
Students will understand the moments, joint moments and moment generating functions of the random variables.
Students will be able to apply the various techniques they learned in calculus to the field of Statistics.
Students will be able to derive the marginal and conditional distributions from the joint distributions.
Students will be able to derive the distributions of the functions of random variables by various different methods.

Problems based on the learning objectives will be assigned on a regular basis and may appear in variety of contexts:

Homework problems serve as both learning and assessment tools for understanding and getting familiar with the topics covered. Working on the homework problems is very important in order to mastering the material.
Classroom discussion of the problems provides an indication of students’ understanding of the topics covered previously. It also can stimulate students’ thinking on the new topics.
Classroom questions are designed to assess the students’ ability of theoretical thinking and concept understanding.
Giving in-class exams is one of the most powerful methods of encouraging students to study the material covered in class. The exams are used to determine whether the students understand the concepts of chance mechanism and other important materials.