Info
References:
- Introduction to Probability Theory (Paul G. Hoel, Sidney C. Port, Charles J. Stone)
- Lecture recordings
Lecture notes
These notes have been reorganized because I lost count of the lectures at some point, and do not reflect the exact sequence or breadth of topics covered in class.
- PROB_L1 ✅
- Probability spaces, some properties of the probability measure
- PROB_L2 ✅
- More properties of the probability measure, Conditional probability
- PROB_L3 ✅
- Independent events, discrete random variables, binomial distribution, the distribution function
- PROB_L4 ✅
- Examples of probability mass distributions: Geometric, hypergeometric, negative binomial, poisson
- PROB_L5 ✅
- Random vectors, independent random variables
- PROB_L6
- Infinite sequences of Bernoulli trials, Sums of independent random variables, The probability generating function
- PROB_L7
- Expectation: Properties of expectation, moments, variance, correlation coefficient, Schwarz inequality, Chebyshev’s inequality, Weak and Strong laws of large numbers, conditional expectation
- PROB_L8 ✅
- Continuous random variables, symmetric, uniform, normal, exponential, and gamma densities.
- PROB_L9 ✅
- Expectation and moments of continuous random variables
- PROB_L10 ✅
- Distributions of sums and quotients, Characteristic functions
- PROB_L11