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
|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
| Lecture 8|| Poisson Processes cont'd. |
| Lecture 9|| Markov Chains, transistion
matrices/graphs, first step analysis. |
| MIDTERM EXAM |