Broadly, this course is focused on mathematical statistics. We will most likely cover the following topics:
1) Basics of probability: expectations, conditional expectations, probability distributions, moments, tranformations of random variables, moment generating functions.
2) Concentration inequalities: Markov, Chebyshev, Hoeffding inequalities, and their uses in statistics.
3) Central limit theorem, delta method.
4) Point estimation and its properties: likelihood, MLE, Fisher Information, Cramer-Rao bound, decision theory.