Syllabus
- Discrete Probability
- Joint/Conditional probabilities
- Independence
- Bayes’ theorem
- Discrete random variables
- Continuous Random Variables
- Cumulative distribution functions (CDFs) and probability density functions (PDFs)
- Gaussian random variables, standardized Gaussian integrals
- Conditional distribution and density functions
- Expected values, moments and conditional expected values
- Transformations of random variables
- Characteristic functions and moment generating functions
- Chernoff Bounds
- Multiple random variables
- Joint and conditional CDFs and PDFs
- Independence
- Jointly Gaussian random variables
- Transformations of multiple random variables
- Random sequences – definitions of convergence modes and relationships between various modes
- Law of large numbers
- Central limit theorem