| Lecture 1 | Introduction,
Probability spaces, properties of probability measures,
conditional probability, statistical independence.
|
| Lecture 2 | Conditional independence, repeated trials,
random variables, CDFs, PMFs, PDFs, mixed and singular random variables.
|
| Lecture 3 | Multiple random variables, independent
RVs, conditioning and RVs, stochastic processes, the Bernoulli
process.
|
| Lecture 4 | Expectations, functions of random
variables, moment generating functions, conditional expectation.
|
| Lecture 5 | Markov Inequality, Chebyshev's inequality,
Chernoff Bounds. |
| Lecture 6 | Convergence of random variables, laws of
large numbers, central limit theorem. |
| Lecture 7 | Central Limit theorem cont'd., Poisson
Processes. |
| Lecture 8 | Poisson Processes cont'd. |
| Lecture 9 | Markov Chains, transistion
matrices/graphs, first step analysis. |
| MIDTERM EXAM |