Week 

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, WideSense
Stationarity, Two Stochastic Processes 

Oct 12 
Systems with Stochastic Input, Memoryless Systems, Linear Systems, LTI Systems with Stationary Input  Power Spectrum, WienerKhinchin Theorem,
CrossPower Spectrum, LTI
Systems, Brownian Motion 

Oct 19 
Mean Ergodicity, Necessary and Sufficient
Conditions, HigherOrder Ergodicity HW #2 due; HW #3 assigned 
Spectral Interpretation of Ergodicity, MS Periodicity, Fourier Series  
Oct 26 
KarhunenLoève Expansion,
DiscreteTime Analogy 
MS Estimation, Linear MS Estimation, Orthogonality Principle  
Nov 2 
Midterm Exam HW #4 assigned 
Prediction, Interpolation, Smoothing, Wiener Filtering 

Nov 9 
Markov Chains  DT MC, ChapmanKolmogorov 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 
CT MC, State Sojourn Time, CT MC
Construction, Kolmogorov Equations 

Nov 30 
Limiting and Steady State Distributions,
State Classification, BirthDeath Processes, Markovian Queues HW #5 due; HW #6 assigned 
Time Reversibility, Balance Equations, Markovian Queues in Tandem  
Dec 7 