| Lecture 1 | Introduction,
Probability spaces, properties of probability measures,
conditional probability.
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| Lecture 2 | Statistical independence, Conditional independence, repeated trials,
random variables, CDFs, PMFs, PDFs, mixed and singular random variables.
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| Lecture 3 | Multiple random variables, joint
distributions, stochastic processes, the Bernoulli process.
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| Lecture 4 | Expected Values, Moments, Moment generating
functions, sums of random variables, conditional expectation. |
| Lecture 5 | Markov's inequality, Chebyshev's inequality,
Chernov bounds. |
| Lecture 6 | Mean-squared convergence, convergence in
probability, almost sure convergence, convergence in distribution,
laws of large numbers. |
| Lecture 7 | The Central Limit theorem, Poisson
Processes. |
| Lecture 8 | More on Poisson Processes. |
| Lecture 9 | Markov Chains: transistion matrices/graphs,
first-step analysis. |
| Lecture 10 | Markov Chains: state classifications,
stationary distributions. |
| MID-TERM EXAM |
| Lecture 11 | Markov Chains: Balance equations;
Introduction to Gaussian Random Vectors. |
| Lecture 12 | More on Gaussian random vectors. |
| Lecture 13 | Conditioning and Gaussian random vectors;
introduction to Gaussian Processes. |
| Lecture 14 | Stationary processes, Properties of
covariance functions, Weiner processes. |
| Lecture 15 | Orthonormal expansions, Gaussian sinc
processes, filtered Gaussian sinc processes. |
| Lecture 16 | Second-order characterizations of
filtered random processes, Spectral
densities; introduction to estimation. |
| Lecture 17 | MMSE estimation, estimation and Gaussian
random vectors, LLSE estimation, optimal filtering.
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