This course aims to provide a solid foundation in statistical theory and an indication 
of the relevance and importance of the theory in solving practical problems in the real 
world. Students will learn how to use specific statistical distributions and general 
modes of statistical thinking to make inferences from data, and to support an argument 
with quantitative information. Students will learn the mathematical and probabilistic 
underpinnings of statistical theory, which is essential for understanding and properly 
applying statistical techniques used in other fields such as economics, biology, 
engineering, social science, and so on. By the end of the course, students will be able 
to apply a wide variety of probability distributions, and approach and solve practical 
problems through statistical and probabilistic reasoning. In addition, they will be 
able to prove theorems relating to the content of the course, provide written
explanations of the ideas behind statistical concepts, and will have improved 
their skills at solving complex and multi-step problems.

Set operations; laws of probability; conditional probability and Bayes' theorem; 
discrete distributions; continuous distributions; bivariate and multivariate 
distributions; distributions of functions of random variables; sampling distributions; 
moment generating functions; laws of large numbers and central limit theorems.