ECE 1500 Lecture Schedule (Fall 2009)


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
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
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
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
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
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

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
Nov 23
Random Sum, Branching Processes, Extinction Probability
C-T MC, State Sojourn Time, C-T MC Construction, Kolmogorov Equations
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