Week |
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Sep 14 |
Course Introduction, Subtlety of Probability,
Probability Space, Probability Definitions |
(review) Probability over Real Line, Conditional
Probability, Total Probability, Bayes Theorem, Combined Experiments, Bernoulli
Trials HW #1 assigned |
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Sep 21 | (review) Random Variables, CDF, PDF, Poisson Theorem, Expected Value, Moments, Moment Generating Function, Characteristic Function | (review) Complex RVs, Two RVs, Independence,
Correlation, Orthogonality, Vector Space of RVs, Conditional Density, Conditional
Expectation |
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Sep 29 |
(review) Random Vectors, Independence,
Group/Pairwise/Linear Independence, Correlation Matrix, Characteristic Function,
Gaussian Vector, Transformation, Order Statistics |
Sample Mean and Variance, Convergence
of Random Sequence, Laws of Large Numbers, Central Limit Theorem |
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Oct 5 |
Stochastic Processes, Classical Examples,
Mean, Autocorrelation, Autocovariance, Poisson and Gaussian Processes HW #1 due; HW #2 assigned |
Stationarity, Wide-Sense
Stationarity, Two Stochastic Processes |
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Oct 12 |
Systems with Stochastic Input, Memoryless Systems, Linear Systems, LTI Systems with Stationary Input | Power Spectrum, Wiener-Khinchin Theorem,
Cross-Power Spectrum, LTI
Systems, Brownian Motion |
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Oct 19 |
Mean Ergodicity, Necessary and Sufficient
Conditions, Higher-Order Ergodicity HW #2 due; HW #3 assigned |
Spectral Interpretation of Ergodicity, MS Periodicity, Fourier Series | |
Oct 26 |
Karhunen-Loève Expansion,
Discrete-Time Analogy |
MS Estimation, Linear MS Estimation, Orthogonality Principle | |
Nov 2 |
Midterm Exam HW #4 assigned |
Prediction, Interpolation, Smoothing, Wiener Filtering |
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Nov 9 |
Markov Chains | D-T MC, Chapman-Kolmogorov Equation, Limiting and Steady State Distributions, Irreducibility | |
Nov 16 |
Recurrence, Periodicity, Ergodicity HW#4 due; HW #5 assigned |
Absorption Probability, Mean Time to
Absorption |
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Nov 23 |
Random Sum, Branching Processes, Extinction
Probability |
C-T MC, State Sojourn Time, C-T MC
Construction, Kolmogorov Equations |
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Nov 30 |
Limiting and Steady State Distributions,
State Classification, Birth-Death Processes, Markovian Queues HW #5 due; HW #6 assigned |
Time Reversibility, Balance Equations, Markovian Queues in Tandem | |
Dec 7 |