Basic ideas of probability theory and statistics, Random variable, probability density functions, probability distributions, mean, variance, correlation, laws of large numbers estimation and testing. Here is a tentative schedule of our course. Please note that this schedule may change as we proceed.
1. History of probability (1 lecture)
2. Axioms of probability (4 lectures)
3. Conditional probability (3 lectures)
4. Discrete random variables, probability distributions, expectation and variance (5.5 lectures)
5. Continuous random variables (3 lectures)
6. Multiple random variables and joint distributions (4 lectures)
7. Point estimation, the principle of maximum likelihood, and linear regression (5 lectures)
8 . Confidence interval (2 lectures)
9. The law of large numbers and central limit theorem (0.5 lectures)