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

9/6     Wednesday.  Course overview.  Section 1.1 of course notes.
	Assigned HW #1 Ch. 1: 1, 2, 3, 4, 5, 6, 7 DUE WED 9/13.

9/8     Covered Section 1.2.  Skipped Examples 1.2 and 1.3.  Carefully
	went over Examples 1.5, 1.6 and 1.8.  You should also go over
	Examples 1.7, 1.9, and 1.10 on your own.

9/11	Covered Section 1.3, Axioms and properties of probability.
	Covered Section 1.4, Independence.

9/13	Covered Section 1.5, Conditional Probability.  Started Ch. 2:
	pages 31-32.
	Assigned HW #2 Ch. 1: 16, 17, 18, 22, 23, 24; Ch 2: 1, 2, 3 DUE WED 9/20.

9/15	Covered pages 33-35: Discrete RVs, Integer-valued RVs, pairs of RVs,
	independent RVs.

9/18	Covered pp. 36-38, Examples 2.5-2.8.  Had class work Problem 6 in
	Ch. 2; then went over it in class.

9/20	Pages 39-45: Probability mass functions (pmfs), the Poisson RV, joint
	pmfs, marginal pmfs, expectation, law of the unconscious statistician
	(LOTUS) [but skip derivation below (2.5)], moments, variance,
	standard deviation.
	Assigned HW #3 Ch 2: 5, 7, 8, 9, 11, 12, 13, 20 DUE WED 9/27.

9/22	Finish Example 2.14, probability generating functions (pgfs).
	Binomial random variable.  pp. 45-49.

9/25	Section 2.3 Conditional Probability, pp. 49-53, Examples 2.17-2.20.

9/27	The substitution law, Examples 2.21-2.22.
	Assigned HW #4 Ch 2: 14, 16, 17, 18, 26, 27, 29 DUE WED 10/4.

9/29	Section 2.4 Conditional Expectation, pp. 56-59.
	Students worked Problem 37 in class.

10/2	Worked Problems 39 and 41 of Ch. 2 in class.  Started Chapter 3.
	Announced Exam 1 will be on Wed. Oct. 11 in class.

10/4	Worked Problems 26 and 29 in class.  Finshed Example 3.1.  Worked
	Examples 3.2 and 3.3.  Started discussion of normal random variables.
	In addition to going over old HW, it may be helpful to solve
	the following problems.  Ch 1: 19, 21, 25, 26.
	Ch 2: 4, 10, 19, 30, 31, 35, 36.

10/6	Worked Problem 19 in Ch. 1, Problems 11 and 35 in Ch. 2.

10/9	Worked Problem 21 in Ch. 1, Problems 4, 10, 19, 36 in Ch. 2.

10/11	Exam 1, in class.  You may bring to the exam one 8.5x11 sheet
	of paper with any formulas you want.  The exam covers only material
	in Chapters 1 & 2.
	Assigned HW #5 Ch 3: 3, 4, 5, 6, 10(a), 11(a)(b) DUE WED 10/18.
	Solution to Problem 5(c)

10/13	Went over Exam 1.  Covered Section 3.2 on Expectation, pp. 70-76;
	however, skipped derivation of (3.2) and jumped right to
	Examples 3.5 & 3.6.  Skipped subsection on "When Expectation is
	Not Defined" and Example 3.7.  Covered Moment Generating Functions,
	including Examples 3.8, 3.9, and 3.10.

10/16	Worked first part of Example 3.10.  Characteristic Functions.
	Worked Example 3.11.  Stated result of Example 3.13.  Skipped
	derivations at beginning of Section 3.3.  Worked Examples 3.14
	AND 3.15.  In Section 3.4, Probability Bounds, derived
	Markov's inequality and Chebyshev's inequality.  Started
	Example 3.18.

10/18	Discussed uncorrelated RVs and the fact that for uncorrelated RVs,
	the variance of the sum is the sum of the variance.  Applied this
	in Example 3.18.  Worked Problems 28 and 29 in Chapter 3.
	Assigned HW #6 Ch 3: 19, 21, 30, 37(a), 41, 42, 20 DUE WED 10/25.

10/20	Chapter 4, pp. 95-101 (Skipped subsection on normal cdf and the
	error function on pp. 101-102.)  Covered Section 4.2, Mixed RVs.

10/23	Section 4.3, Functions of RVs and Their CDFs.
	Section 4.4, Properties of CDFs (pp. 111-112 only).

10/25	Worked Problem 11 and 22(a)(b)(c) in Chapter 4.  Also worked
	an old exam problem.
	Assigned HW #7 Ch 4: 5, 7, 10, 20, 31, 32 DUE WED 11/1.

10/27	Covered Chapter 5, pp. 127-138, but skipped all examples except
	Example 5.8.  Also skipped stuff on specifying joint densities.

10/30	Worked a "Find P(g(X)<=y)" problem from an old exam.
	Worked Examples 5.3, 5.6, and 5.7.

11/1	Worked Example 5.9.  Discussed Bivariate Normal in Section 5.4.
	Worked Examples 5.10, 5.11, and 5.12.  Started Section 5.5
	Multivariate Random Variables.  Worked Example 5.13.
	Assigned HW #8 Ch 5: 6, 7, 14, 15, 16(a)(b), 18(b)(c) DUE WED 11/8.

11/3	Worked Examples 5.14 and 5.15.  Started Chapter 7, worked first
	part of Example 7.1.

11/6	Finished Example 7.1.  Worked Examples 7.2-7.4.

11/8	Discussed properties of correlation functions and power spectral
	densities.  Worked Examples 7.5 and 7.6.  Started Section 7.3.,
	joint WSS, WSS processes through LTI systems.
	Suggested review problems:
	Ch 3: 1, 29, 43
	Ch 4: 11, 29(c), 30(c)
	Ch 5: 17, 26, 29, 30, 31

11/10	Derived key equation (7.5).
	Worked Problem 17 in Ch 5, Problem 29 in Ch 3.  Discussed
	characteristic functions and their application.

11/13	Solved Problems from Ch 5: 31, 30, 29.  Showed that for uncorrelated
	random variables, the variance of the sum is the sum of the
	variances.

11/15	Exam 2, in class.  You may bring to the exam one 8.5x11 sheet
        of paper with any formulas you want.  The exam covers mostly material
        in Chapters 3, 4, & 5.
	Assigned HW #9 Ch 7: 3(b)(d), 4, 5(b)(c), 6(d)(f), 12, 13 DUE WED 11/22.

11/17	Reviewed WSS processes.  Went over Section 7.4 and derived the
	matched filter.  You are not responsible for Section 7.4.

11/20	Went over Exam 2.
	Derived Wiener filter in Section 7.5.  You are not responsible
	for Section 7.5.

11/22	Worked Problem 11 in Ch. 7.  Gave hints on HW.  Talked about
	time correlation of waveforms.

11/24	NO CLASS, Thanksgiving Recess

11/27	Covered Section 8.1 through Example 8.2.

11/29	Skipped "Derivation of Poisson Probabilities."  Discussed marked
	Poisson processes and shot noise on pp. 209-210.
	Assigned HW #10 Ch 8: 1, 3, 4, 7, 8(Use prob. gen. fcn.) DUE WED 12/6.

12/1	Covered Section 10.1 through eq. (10.4).

12/4	Covered Example 10.3, Derivation of the Central Limit Theorem,
	Example 10.4.  Started Section 10.2: Confidence Intervals.

12/6	Worked Example 10.5, finishing Section 10.2.  Covered Section 10.3,
	The Sample Variance, and Section 10.4, Confidence Intervals
	When the Variance Is Unknown - Applications: Estimating the
	number of defectives in a lot, Predicting the outcome of an election.
	Briefly discussed Sampling with and without Replacement.
	Assigned HW #11 Ch 10: 1, 5, 9, 10, 11, 13 DUE WED 12/13.

12/8	Finished discussing confidence intervals.  Worked Problems 6 and
	12 in Chapter 10.

12/11

12/13	Worked Example of how to estimate the fraction of the population's
	answer to a question they would not want to answer.
	Did teaching evaluations.
	Review Problems: All old HW and old review problems.  Also:
	Ch 2: 37, 38
	Ch 3: 23, 27(Example 3.6 is helpful)
	Ch 4: 21
	Ch 5:  8, 16(c)(d), 18(a), 28
	Ch 7: 10, 14, 15, 17
	Ch 8:  9, 10.

12/15	Answered review questions.

12/20	WEDNESDAY, Final Exam, 2:45 pm in 2534 EH.