ECE 331 Introduction to Random Signal Analysis and Statistics, Lec. 1, Fall 2001

9/5	Wednesday. Course overview.  Section 1.1 of course notes.
	Assigned HW #1 Ch. 1: 1, 2, 3, 4, 5, 6, 7 DUE WED 9/12.

9/7	Covered Section 1.2 Probability Models.  Skipped Examples 1.2, 1.3.
	Worked Examples 1.4, 1.5, 1.6, 1.8, 1.9.  You may wish to read
	Examples 1.7 and 1.10 on your own.

9/10	Covered Section 1.3 Axioms and Properties of Probability.
	Started Section 1.4 Independence through p. 14.

9/12	Finished Section 1.4. Started Section 1.5 Conditional Probability.
	Assigned HW #2 Ch. 1: 16, 17, 18, 21, 22, 23, 24 DUE WED 9/19.
	Due Date Extended to FRI 9/21.

9/14	Class Canceled.

9/17	Finished Section 1.5, Law of Total Probability & Bayes' Rule.
	Started Chapter 2, through Discrete Random Variables on p. 32.

9/19	Covered Integer-Valued RVs, Pairs of RVs, Multiple Independent RVs,
	Example 2.5, pp. 32-35.

9/21	Finished Section 2.1, pp. 36-40, Pr(max<=z), Pr(min<=z), geometric RVs,
	pmfs, Poisson pmf, joint pmfs, joint pmfs and independence.
	Assigned HW #3 Ch. 2: 1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 20 DUE FRI 9/28.

9/24	Covered Section 2.2 Expectation, pp. 40-45 thru eq. (2.6), but
	skipped derivation of Law Of The Unconscious Statistician (LOTUS).

9/26	Finished Section 2.2 Expectation, pp. 45-48.

9/28	Section 2.3 Conditional Probability, Law of Total Probability, pp. 48-51.
	Assigned HW #4 Ch. 2: 14, 16, 17, 18, 26, 27, 29 DUE FRI 10/5.

10/1	The Substitution Law, pp. 52-54, Section 2.4 Conditional Expectation,
	through Example 2.23 on p. 55.

10/3	Finished Chapter 2.  Started Chapter 3.
	In addition to going over old HW, it may be helpful to solve
        the following problems.  Ch 1: 25, 26.
        Ch 2: 4, 10, 15, 19, 30, 31, 35, 36.

10/5	Finished Section 3.1.

10/8	Answered review questions.  Convered Section 3.2, Expectation of
	a Single RV, pp. 69-71.  Worked first part of Example 3.5.

10/10	Exam 1 - in class, covers only Chapters 1 and 2.
	Assigned HW #5 Ch. 3: 3, 4, 5, 6, 10(a), 11(a)(b) DUE WED 10/17.

10/12	Went over exam.  Finished Example 3.5.  Worked Example 3.6, moments
	of the standard normal density.  Skipped subsection, "When Expectation
	is Not Defined."  Skipped Example 3.7.  Introduced Moment Generating
	Functions, worked Examples 3.8, 3.9, and 3.10.

10/15	Characteristic functions: Examples 3.11, 3.13, 3.14, 3.15.
	Started Markov's and Chebyshev's inequalities in Section 3.4.

10/17	Derived Markov's and Chebyshev's inequalities.  Showed that
	if the X_i are uncorrelated with common mean m and variance sigma², then
	E[|M_n -m|²] converges to zero, and by Chebyshev's inequality,
	so does P(|M_n-m| >= epsilon).  Started Chapter 4, pp. 94-97, cdfs
	for continuous random variables.
	Assigned HW #6 Ch. 3: 19, 20, 21, 30, 38, 42, 44 DUE WED 10/24.

10/19	Conditional cdfs and the law of total probability, pp. 97-98.
	Jumped to Examples 4.9 and 4.10, pp. 104-105.  Jumped back to
	Cdfs for Discrete RVs, pp. 98-100.  Covered Section 4.2,
	Mixed RVs, pp. 101-103.

10/22	Section 4.3 Functions of RVs and Their CDFs, Examples 4.11 and 4.12.
	Section 4.4 Properties of CDFs.  Covered derivations only of
	properties (i), (ii), (iii), (vii), and (viii).

10/24	Started Chapter 5, pp. 124-128.
	Assigned HW #7 Ch. 4: 5, 7, 10, 17, 25, 26 DUE WED 10/31.

10/26	NO CLASS.

10/29	Worked Problem 24(a) in Chapter 4.  Worked Examples 5.4 and 5.5.

10/31	Formula for E[g(X,Y)] on p. 131.  Skipped bivariate characteristic
	functions.  Covered Specifying joint densities on p. 132, Example 5.6.
	Section 5.3 Conditional Probability and Expectation.  Definition of
	E[g(X,Y)|X=x], laws of total probability for jointly continuous RVs.
	Examples 5.7, 5.8, and 5.9.
	Assigned HW #8 Ch. 5: 6, 7, 14, 15(a)(b), 16(a)(b), 19(b)(c) DUE WED 11/7.

11/2	Worked Examples 5.13, 5.14, and 5.15.

11/5	Discussed Problems 19(a) and 19(b).  Started Chapter 6: mean,
	correlation, and covariance functions.  Skipped beginning of Section
	6.2 until definition of WSS.  Covered definition of WSS, Example 6.1,
	definition of power spectral density.

11/7	Derived Cauchy-Schwarz inequality as suggested in Problem 1.  Worked
	Examples 6.2-6.6.  Started Section 6.3 WSS processes thru LTI systems
	thru top half of p. 160.
	Primary Review Problems for Exam 2:
	Ch 3:  1, 23, 28, 33, 45, 43
	Ch 4: 18, 21, 23(c)
	Ch 5: 16(c), 17, 18, 29.
	Secondary Review Problems:
	Ch 3: 29, 27, 26
	Ch 4: 19, 12
	Ch 5: 32, 33.
	Click here for solutions to all review problems.

11/9	Derived formulas for cross correlation and cross power spectral
	density, output correlation and power spectral density.  Examples 6.8
	and 6.8.  Section 6.4: The Matched Filter.

11/12	Section 6.5: The Wiener Filter.

11/13	5pm, TUES. evening exam-review session in 2349 Engr. Hall.

11/14	Exam 2 - in class.
	Assigned HW #9: Ch. 6: 4(b)(d), 5, 6(b)(c), 7(d)(f), 13, 14 DUE WED 11/21.

11/16	Go over Exam 2.  Worked sample problems from Ch. 6.

11/19	Worked Problem 15 in Chapter 6.  Started Section 8.1, The Poisson Process, pp. 200-203.

11/21	Worked Example 8.2.  Started Chapter 11, pp. 249-250.
	Assigned HW #10: Ch. 6: 12, 16, 20, Ch. 8: 1, 2, 4, 7 DUE WED 11/28.

11/23	Thanksgiving Recess - NO CLASS.

11/26	Examples 11.1 and 11.2, Central Limit Theorem, Example 11.3.

11/28	Derived Central Limit Theorem (CLT), Example 11.4 (Stirling's Formula),
	Section 11.2 Confidence Intervals When the Variance Is Known.
	Assigned HW #11: Ch. 11:  1, 3, 4, 5, 7 DUE WED 12/5.

11/30	Section 11.3, The Sample Variance, Section 11.4, Confidence Intervals
	When the Variance Is Known.

12/3	Began discussion of Markov Chains.

12/5	Solved for the stationary distribution of the infinite-buffer queue.
	Assigned HW #11: Ch. 11:  9, 10, 11;
	also two Markov chain problems on board DUE WED 12/12.

12/7	Worked two examples of finding the stationary distribution of a
	finite-state Markov chain.  Derived the Chapman-Kolmogorov Eq.
	Distributed teaching evaluations.

12/10	Worked two Markov chain examples.  Started talking about first
	entrance and first return times (you are not responsible for
	this material).  Distributed updated version of Chapter 10.
	Copies are outside my office.

12/12	Finished discussion of first entrance and first return times.
	You are not responsible for this material.
	Suggested Review Problems:
	Ch. 2: 4, 21, 37, 41
	Ch. 3: 29
	Ch. 4: 28
	Ch. 5: 16(c)(d), 18, 34
	Ch. 6: 11, 15, 18
	Ch. 8: 5, 8
	Ch. 11: 2, 6, 12, 13
	Also some MC problems on the board.

12/14	Last Class Day.

12/17   MONDAY, Final Exam, 7:45 am.