Probability & Statistics
- learn about probability axioms and (conditional) probability distributions
- study moments of random variables and Chebychev's inequality
- learn about law of large numbers and central limit theorem
- study estimation methods and ways to evaluate estimators
- develop hypothesis testing
- study linear regression
Probability theory is a deductive science describing the axioms for calculating the probability of some event given some known state of the world. In the first part of the course, we define the probability axioms, introduce the concept of events, random variables, and probability distributions. In inductive practice we are interested to learn about the state of the world given some event, i.e., the data. Statistics is probability theory turned upside down. In this course we will learn about estimation procedures, in particular, maximum likelihood and the method of moments. We will introduce hypothesis testing and linear regression analysis.
Combination of lectures and tutorials
- Prasanna Sahoo, Probability and Mathematical Statistics, 2013.