ECE 331 Introduction to Random Signal Analysis and Statistics, Lec. 1, Spring 2002


Last Modified: Tue 15 Oct 2019, 01:45 PM, CDT

Clock Icon  Instructor Office Hours: Fri 9:00-10:30, or by appointment.
Eye Icon See what we did in Fall 2001. Spring 2002 will be quite similar.
Teacher Icon TA: Manoj Kulkarni, mdkulkar@cae.wisc.edu
          Office hours: Thurs. 5pm-7pm in B632.
          Discussion Thursdays at 3:30 in Room 2341 EH.
PC Icon Java Demos for Probability and Statistics (by Prof. Stanton, Cal. State Univ., San Bernardino)
Papers Icon Syllabus
Papers Icon Homework Solutions
Tacked Note Icon Class Schedule for Spring 2002
1/23	Wednesday.  Course overview.  Section 1.1 of course notes.
	Started Section 1.2.
	Assigned HW #1 Ch 1: 1, 2, 3, 4, 5, 6, 7 DUE FRI 2/1.

1/25	Continued Section 1.2.  Skipped Example 1.2 through Example 1.3.
	Worked Examples 1.4, 1.5, 1.6.  You should work Example 1.7 on your
	own.  Worked Example 1.8.  You should work Example 1.9 on your own.
	Worked Example 1.10.

1/28 Section 1.3 Axioms and Properties of Probability, pp. 10-14. Started Section 1.4 Independence, pp. 14-15. 1/30 Independence for More Than Two Events pp. 15-17. 2/1 Covered Section 1.5 Conditional Probability. Started Chatper 2, through Example 2.2. Assigned HW #2 Ch 1: 16, 17, 18, 20, 23, 24, 25 DUE FRI 2/8.
2/4 Indicator functions p. 31. Discrete and integer-valued RVs Example 2.3, pp. 32-33. Pairs of RVs and independent RVs, started Example 2.5 pp. 34-35. 2/6 Finished Example 2.5. Covered pp. 35 through eq. (2.3) on p. 39. 2/8 Covered pp. 35 - top of 44: joint pmfs, expectation, LOTUS, moments. Skip derivation of (2.5) on pp. 42-43. Assigned HW #3 Ch 2: 2, 3, 4, 7, 9, 10, 11, 13, 14, 15, 24 DUE FRI 2/15.
2/11 Worked Examples 2.13 & 2.14 on p. 44. Covered probability generating functions, pp. 45-47. 2/13 Derived binomial theorem on p. 48. Skip "Poisson Approximation of Binomial Probabilities" on pp. 48-49. Started Section 2.3 on Conditional Probability, covered pp. 49-51. 2/15 Covered pp. 52-54, emphasis on substitution law. Assigned HW #4 Ch 2: 16, 19, 21, 23, 28, 35, 36, 38 FRI 2/22. Announced Exam 1 will be on Friday, Mar. 1, in class.
2/18 Covered pp. 55-57: Example 2.22, Section 2.4: Conditional Expectation, Substitution Law for Conditional Expectation, Law of Total Probability for Expectation. 2/20 Finished Chapter 2, p. 58. Worked Problems 48 and 46 in Chapter 2. 2/22 Started Chapter 3. Covered Section 3.1, pp. 68-72. Exam Review Suggestions: Solve old HW again without looking at the answers. Additional Problems: Ch 1: 21, 26, 27; Ch 2: 6, 8, 12, 17, 22, 39, 40, 41, 49, 50.
2/25 Covered Section 3.2, pp. 72-77 through eq. (3.4). Skip subsection, "When Expectation Is Not Defined" on p. 75. 2/27 Covered pp. 77-81, moment generating functions, characteristic functions, expection for multiple random variables, especially Examples 3.14 and 3.15. 3/1 Exam 1 -- in class. Assigned HW #5 Ch 3: 3, 5, 6, 7, 11(a), 12(a)(b) DUE FRI 3/8.
3/4 Went over Exam 1. Derived Markov's inequality; skipped Example 3.16. Derived Chebyshev's inequality; skipped Example 3.17. 3/6 Worked Example 3.18. Started Chapter 4, pp. 98-top of p. 102. 3/8 Worked Examples 4.4, 4.5. Skip subsection on Normal CDF and the Error Function. Skip Section 4.2. Covered Section 4.3 Cdfs for Discrete RVs, Section 4.4 Mixed RVs. Assigned HW #6 Ch 3: 20, 21, 22, 31, 39(a), 45, 47 DUE FRI 3/15.
3/11 Lectured on material from Section 4.5, Functions of RVs and Their Cdfs. Worked three examples not in the notes. You should read the material in Section 4.5 on your own. 3/13 From Ch 3: Reviewed gamma function (Problem 11(a)). Problem 12: The Erlang and chi-squared RVs. Problem 40. Also worked Problems 7 and 38 in Chapter 4. 3/15 Reviewed fact that if X is N(0,1), then X^2 is chi-squared with one degree of freedom. Worked and discussed Problem 12 in Ch 4 (generalized Rayleigh: Rayleigh, Maxwell, Nakagami densities). Worked and discussed Problem 13 in Ch 4 (asymptotic expansion of normal complementary cumulative distribution). Students filled out TA evaluations. Assigned HW #7 Ch 4: 8, 9, 10, 26, 36, 37 DUE FRI 3/22.
3/18 Started Ch 5. Covered Section 5.1, Joint CDFs, but skipped Eample 5.1. Started Section 5.2, Jointly Continuous RVs, worked Example 5.3. 3/20 Worked Example 5.3, discussed marginal densities. Worked Example 5.4, discussed more about marginal densities. Worked Example 5.5. Showed that jointly continuous RVs are independent if and only if f_{XY}(x,y)=f_X(x) f_Y(y). Talked about conditional densities. Worked Example 5.6 in reverse. 3/22 Recalled formula for E[g(X,Y)] on p. 135. Covered Section 5.3 on Conditional Probability and Expectation. Assigned HW #8 Ch 5: 6, 7, 13, 15(a)(b), 16(a)(b), 19(b)(c) DUE FRI 4/5.
3/25 NO CLASS - Spring Break 3/27 NO CLASS - Spring Break 3/29 NO CLASS - Spring Break
4/1 Went over Example 5.13, Problem 29 in Ch. 5. Suggested Problem 17 in Ch. 5 as an optional problem. 4/3 Worked Problems 17 and 19(d). Started Chapter 6, Sections 6.1, Section 6.2 through Example 6.1 on p. 159. 4/5 Covered Section 4.6 Properties of CDFs. Worked Problem 31 in Ch. 5. Had students work on Problem 4 in Ch. 3. Primary Review Problems for Exam 2: Ch 3: 1, 29, 34, 46, 48, 49 Ch 4: 5, 6, 8, 28, 32, 34(c) Ch 5: 17, 18, 29, 32, 33. Secondary Review Problems: Ch 3: 24, 27, 28, 30 Ch 4: 30 Ch 5: 16(c)(d).
4/8 Worked Example 4.11, Problem 44 in Ch. 3 two different ways - one using moment generating functions, the other using the law of total probability. 4/10 Worked Problem 34 in Ch. 3 and Problem 5 in Ch. 4. In Chapter 6: Introduced power spectral density on p. 160. Worked Examples 6.2, 6.3, 6.4. Covered Properties of Correlation Functions on p. 162. Worked Examples 6.5 and 6.6. Started Section 6.3 on Wide-Sense Stationary Processes through LTI Systems. 4/12 Exam 2 -- in class. Assigned HW #9: Ch 6: 4(b)(d), 5, 6(b)(c), 7(d)(f), 13, 14 DUE FRI 4/19.
4/15 Returned and reviewed Exam 2. Covered Section 6.3 through eq. (6.5). 4/17 Worked Examples 6.7 and 6.8. Worked Problem 12. Covered Section 6.4 on the Matched Filter. 4/19 Worked Problem 18 in Ch 6. Covered Section 6.5 The Wiener Filter. Assigned HW #10: Ch 6: 17, 23 Ch 8: 1, 2, 4, 7, 8 DUE FRI 4/26.
4/22 Covered Section 8.1 on the Poisson process. Focus on Examples 8.1 and 8.2. 4/24 Worked Poisson process example. Started Chapter 10, Section 10.1 on Discrete-Time Markov Chains. Worked Examples 10.1 and 10.2. Introduced transition probabilities, state transition diagram, transition matrix. Discussed state transition diagrams of several examples. 4/26 Discussed general random walk, walk with barrier (absorbing, reflecting), birth-death process, pure birth process. Introduced n-step transition probabilities, Chapman-Kolmogorov equation and its interpretation, stationary/equillibrium distributions. Assigned HW #11: Ch 10: 2, 4, 5, 7, 8 DUE FRI 5/3.
4/29 Worked Example 10.3. Worked Problem 3 in Ch. 10. Derived the Chapman-Kolmogorov equation. 5/1 Started Chapter 11. Covered Section 11.1. 5/3 Reviewed CLT. Worked Examples 11.3 and 11.4. Covered Section 11.2. Started Section 11.3, the Sample Variance. Suggested Problems for Ch 11: 1, 4, 5, 6, 11, 12 Review Problems for Final: Ch 2: 6, 26, 49, 53 Ch 3: 30, 46 Ch 4: 6 Ch 5: 16(a)(e), 17, 18, 34 Ch 6: 11, 16, 19(Use R(tau)=(1-|tau|)I_[-1,1](tau)) Ch 8: 5, 9 Ch 10: 6 Ch 11: 2, 6, 13, 14, 15.
5/6 Distributed teaching evaluations. Worked Examples 11.5 and 11.6. Discussed Sampling with and without Replacement. 5/8 Worked Problem 16(e) in Ch 5, Problem 19 in Ch 6, and Problem 9 in Ch 8. Distributed ABET evaluations. 5/10 Worked Problems 8 and 9 in Ch 5, Problem 21 in Ch 6, Problem 15 in Ch 11. Talked about Problem 18 in Ch 11.
5/16 THURSDAY, Final Exam, 2:45 pm in 2534 Engr. Hall.

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