## ECE 6960 Schedule

Readings preceded by "LG" are in Alberto Leon-Garcia, "Probability, Statistics, and Random Processes for Electrical Engineers", 3rd edition, 2008. Other readings will be made available as handouts or on WebCT under the "Resources" tab. Homework questions are numbered and lettered, so the problem "(5a)" refers to homework five, problem "a". All problems for homework # are due on Thursday at the start of lecture, on the day when the HW # is listed under the "Due" column.

NOTE: the International 3rd edition of the Leon-Garcia book does not have the same problems at the end of the chapter as the national (what is the opposite of international?) 3rd edition. I am going to scan the problem sections from each chapter and put them on WebCT so that we are all solving the same problems.

 No. Date Topics Reading Homework Q's Due 1 08/24/10 Random variables (r.v.s): discrete and continuous, distributions (pmf, CDF, pdf, conditional) LG 4.1, 4.2, 4.4 1a: LG 4.17; 1b: LG 4.15; 1c: LG 4.29, but just do the first four properties on page 144 (assuming that F_X(x) satisfies the eight properties of the CDF) 2 08/26/10 Expectation of r.v.s, Functions of an r.v., Markov Inequality LG 4.3, 4.5 1d: LG 4.49; 1e: LG 4.51; 1f: LG 4.64; 1g: LG 4.77; 1h: LG 4.85; 1i: LG 4.96 3 08/31/10 Probability bounds LG 4.6 2a: LG 4.99 (a) and (b) (Compare by plotting both functions). 2b: LG 4.108. 2c: LG 4.113. 4 09/02/10 Transform methods, entropy & differential entropy (See letter entropy code) LG 4.7, 4.10 2d: LG 4.102. 2e: LG 4.112. 2f: LG 4.149. 2g: LG 4.154. 2h: LG 4.160. HW 1 5 09/07/10 Random Vectors (R.V.s), functions of R.V.s, Expectation, iterated expectation LG 6.1-6.3, 5.7.2 3a: LG 6.24. 3b: LG 6.29. 3c: LG 6.39(a). 3d: LG 5.88 6 09/09/10 Gaussian R.V.s, Linear transforms of R.V.s LG 6.4, 6.3.2, 6.3.4, 6.4.1, 6.6 3e: LG 6.55. 3f: Find $A$ in $\mathbf{Y} = A \mathbf{X}$ that makes $C_\mathbf{Y} = I$, given arbitrary covariance matrix $C_\mathbf{X} =$ Cov$\{\mathbf{X}\}$, and prove that your choice makes $C_\mathbf{Y} = I$. 3g: Let X_1 and X_2 be independent with the same variance sigma^2 and mean mu. Show that the average, Y_1 = (X_1 + X_2)/2, and the difference, Y_2 = X_1 - X_2, are uncorrelated. HW 2 7 09/14/10 Estimation theory intro LG 6.5, 8.2, 8.3 8 09/16/10 Estimation examples, Performance of estimators The complete HW 4 assignment as pdf HW 3 9 09/21/10 Detection theory: unknown parameters LG 8.5 11 09/23/10 Review for Exam 1 HW 4 10 09/28/10 Detection theory: test of correlation, test of distribution LG 8.7; Milton & Arnold Section 11.5 (on WebCT) The complete HW 5 assignment as pdf 09/30/10 Exam 1 (solutions on WebCT) 12 10/05/10 Random processes review; including indep. Increments, autocovariance, stationarity LG 9.1-9.3 13 10/07/10 Poisson r.p. LG 9.4 The complete HW 6 assignment as pdf HW 5 10/12/10 Fall Break 10/14/10 Fall Break 14 10/19/10 Poisson: telegraph wave, spatial, non-stationary, compound handout: Ross_Generalizations_ Poisson_Process.pdf on WebCT: Resources: Ross Book 15 10/21/10 Gaussian r.p.s and finance applications LG 9.5, handout: Ross_Pricing_ Stock_Options.pdf on WebCT: Resources: Ross Book The complete HW 7 assignment as pdf HW 6 16 10/26/10 Markov Processes, Markov chains, Multi-step MC dynamics LG 11.1, 11.2 17 10/28/10 State classification, MC limiting probabilities LG 11.3 The complete HW 8 assignment as pdf HW 7 18 11/02/10 Networking applications of MCs G. Bianchi, Performance Analysis of the IEEE 802.11 Distributed Coordination Function, IEEE J. Sel. Areas in Communications, 2000. 19 11/04/10 Hidden Markov Chains. Matlab code: hmm_example.m, SimHMC.m, ForwardSolveHMC.m handout: Ross_Hidden_Markov_Models.pdf on WebCT: Resources: Ross Book The complete HW 9 assignment as pdf HW 8 20 11/09/10 Continuous-time MCs LG 11.4 21 11/11/10 Sums of r.v.s, weak law of large numbers, CLT LG 7.1, 7.2, 7.3 HW 9 22 11/16/10 Review 11/18/10 Exam 2 After the exam, complete HW 10, the "Plagiarism Assignment". Turn in your answers to questions 2-5, which will be graded. 23 11/23/10 Convergence of sequences of r.v.s LG 7.4 11/25/10 Thanksgiving Break 24 11/30/10 Project work time HW 10 25 12/02/10 Project work time 26 12/07/10 Presentation Session I 27 12/09/10 Presentation Session II Written project report