ECE 331 Introduction to Random Signal Analysis and Statistics, Lec. 1, Spring 2000

1/24	Monday.  Course overview.  Section 1.1 of course notes.
	Assigned HW Ch. 1: 1, 2, 3, 4, 5, 6, 7, 16, 17, 18 DUE WED 2/2.

1/26	Covered Section 1.2, examples.

1/28	Covered Section 1.3, Axioms and properties of probability.

1/31	Covered Section 1.4, Independence.  Started Section 1.5 on
	Conditional Probability up to Law of Total Probability.

2/2	Finished Section 1.5 and started Chapter 2.
	Assigned HW Ch. 1: 21, 23, 24, 25; Ch 2: 1, 2, 5, 6, 7 DUE WED 2/9.

2/4	Finished Section 2.1.  Covered Section 2.2 through Example 2.3.

2/7	Discussed Bernoulli(p), uniform, binomial, geometric, and Poisson
	random variables.  Started Section 2.3 on Multiple Random Variables.

2/9	Worked Examples 2.6 and 2.7.  Probability mass functions,
	conditional probability for random variables.
	Assigned HW Ch 2: 8, 9, 10, 11, 12, 13, 14 DUE WED 2/16.

2/11	Discussed conditional probability, conditional pmfs, Example 2.9.
	Started Section 2.4 on The Law of Total Probability, Example 2.10.

2/14	Finished Example 2.10.  Skipped Example 2.11.  Started the
	Substitution Law.  Worked Examples 2.12 and first half of
	Example 2.13.

2/16	Finished Example 2.13.  Worked out Example 2.14 and part of 2.15.
	Began discussion of Expectation, Section 2.5.
	Assigned HW Ch 2: 17, 21(a) 25, 26, 30, 31, 32 DUE WED 2/23.

2/18	Worked Example 2.17.  LOTUS (Eqs. (2.16) and (2.17); skip derivation
	between (2.16) and (2.17)), Example 2.18, Moments, Example 2.19,
	Example 2.21.
	Exam 1 is scheduled for Wed. Mar. 1 in class.  It will cover
	Chapters 1 and 2.

2/21	Covered Probability Generating Functions (p. 26).  Started
	Section 2.6, Conditional Expectation, laws of total probability
	and substitution for conditional expectation.

2/23	Worked Example 2.24 and Problem 35 in Ch. 2.
	Distributed Exam 1 Review (PostScript).
	The table of discrete random variables from the notes will be
	included on the exam.  Also various formulas will be included
	on the Exam Cover Page (PostScript).

2/25	Covered Section 3.1 and Example 3.4 in Section 3.2.

2/28	Review for Exam 1.

3/1	Exam 1 in class, covers Chapters 1 and 2.
	Assigned HW Ch 3: 1, 2, 3, 7, 8(a)(b)(d), 15, 16 DUE WED 3/8.

3/3	Covered Example 3.5.  Skipped eq. (3.3) through Example 3.6.
	Started Moment Generating Functions.  Worked Example 3.7.

3/6	Worked Examples 3.8, 3.9.  Covered characteristic functions,
	worked Examples 3.13 and 3.14.  Derived Markov's Inequality.

3/8	Derived Chebyshev's Inequality.  Worked Example 3.17 and
	discussed the weak law of large numbers.  Started Chapter 4, p. 44.
	Assigned HW Ch 3: 24, 29(a), 30, 31, 33, 34, 35 DUE WED 3/22.

3/10	For fun we discussed Problems 23, 24, and 27 in Chapter 2.

3/13	NO CLASS - Spring Break
3/15	NO CLASS - Spring Break
3/17	NO CLASS - Spring Break

3/20	Reviewed Section 4.1.  Covered Section 4.2.

3/22	Section 4.3.
	Assigned HW Ch 4: 4, 5, 6, 8, 9, 11 DUE WED 3/29.

3/24	Worked Example 4.10 and Example 4.13.

3/27	For motivation, I discussed a digital communications scenario
	(noncoherent detection) in which one is interested in finding the
	pdf of sqrt(X^2+Y^2).  This pdf turns out to be Rayleigh or Rice.
	Related this to the chi-squared and noncentral chi-squared RVs.
	Went over Section 4.4 on properties of cdfs.  Started Section 4.5
	on reliability.

3/29	Finished Section 4.5.  Started Ch. 5, Section 5.1.  Worked
	Example 5.1.
	Assigned HW Ch 4: 16, 17, 19, 21, 28(c), 29(b) DUE WED 4/5.

3/31	Finished Example 5.1.  Worked Example 5.2.  Started Section 5.2.
	Skipped Examples 5.3 and 5.4.

4/3	Discussed conditional densities, independence, and expectation
	E[g(X,Y)] (pp. 61-62).  Section 5.3 Conditional Probability and
	Expectation.

4/5	Worked Examples 5.3 and 5.4 using conditional probability - not
	the way it is in the notes.  Started Section 5.4 The Bivariate Normal.
	Assigned HW Ch 4: 32, 34.  Ch 5: 5, 7, 8, 11 DUE WED 4/12.

4/7	Finish Section 5.4.  NOTE: The purpose of Section 5.4 is mostly
	informational.  That way, when you see it in another course, it
	won't be totally new.  Started Section 5.5.  Emphasized Example 5.13.

4/10	Finished Section 5.5, Examples 5.14, 5.15.  Talked about motivation
	for material in Ch. 7.

4/12	Went over Problem 27 in Chapter 5.
	Assigned HW Ch 5: 16, 18(a)(b)(c)(d), 31 DUE WED 4/19.

4/14	Covered Section 7.1.  Covered Section 7.2 through Example 7.1.

4/17	Finished Section 7.2.  Started Section 7.3; got up to eq. (7.2).

4/19	Made some comments about the HW and worked an example.
	Derived eqs. (7.2)-(7.4).
	Exam 2 Review: Ch 3: 21, 23; Ch 4: 12, 27(c), 28(d), 33;
	Ch 5: 26, 29, 30.

4/21	Worked Example 7.7.  Discussed the application of (7.4) to the
	design of digital communication systems in additive white Gaussian
	noise.  Showed that minimizing the probability of a decision error
	is equivalent to maximizing the output signal-to-noise ratio (SNR).
	Showed that this is accomplished by the matched filter.
	This material is not in the notes.  You are not responsible for it.

4/24	Review for Exam 2.
	Solution of Chapter 5 Problem 31.

4/26	Exam 2 - in class.
	Assigned HW Ch 7: 4, 6(a)(c)(e), 10, 13, 15  DUE WED 5/3.

4/28	Went over Exam 2.  Worked Example 7.8.  Briefly went over the
	interpretation of the Wiener fileter.

5/1	Start Chapter 8 on the Poisson process.
	Worked Problems 1 and 3 in Ch. 8.

5/3	Talked about HW Problem 10 in Ch 7.  Worked Problem 11 in Ch 7.
	Discussed arrival times and interarrival times of the Poisson
	process.  Skipped material from "Derivation of the Poisson
	Probabilities" to end of chapter.
	Recommended Problems: Ch 8: 2, 4, 5, 7.

5/5	Briefly discussed material in Ch 10 (not on final).
	Distributed Final Exam Review.  Also distributed handout with
	discrete RVS, Fourier Transforms and continuous RVs.  
        Extra copies outside my office.
	Also recommend:  Old exam reviews and old HWs, and problems
	Ch 2: 18
	Ch 3: 2, 36(a)(b)(c)
	Ch 4: 26, 35, 36
	Ch 5: 4, 9, 10, 12, 13, 17
	Ch 7: 12, 14

5/8	Answered questions from Ch 8 and Ch 7.

5/10	Reviewed for final exam.

5/14	SUNDAY, Final Exam at 2:45 pm in 2535 Engr. Hall.
	You may bring to the exam one 8.5in x 11in paper with any
	formulas you think are necessary.