ECE 331 Introduction to Random Signal Analysis and Statistics, Lec. 1, Spring 2005

1/19	Wednesday.  Course overview.  pp. 1-4.
	Assigned HW #1 Ch 1: 3, 4, 5, 6, 7(a)-(f) DUE WED 1/26.

1/21	Covered Outcomes & Events on p. 5.  Covered Section 1.2 Review of
	Set Notation, but only briefly mentioned the subsection on Partions.
	Skipped subsection on Functions and subsection on Countable and
	Uncountable Sets.

1/24	Section 1.3 Probability Models -- through Example 1.15.

1/26	Examples 1.16 and 1.17.  Covered Section 1.4 Axioms and Properties
	of Probability.
	Assigned HW #2 Ch 1: 21, 22, 23, 24, 25, 26, 27 DUE WED 2/2.

1/28	Covered Section 1.5 Conditional Probability.  Started Section 1.6
	Independence; covered through Example 1.23.

1/31	Finished Section 1.6.  Started Chapter 2.  Covered through Example 2.3.

2/2	Worked Example 2.3.  Covered Section 2.2 Discrete RVs.  Started
	Section 2.3 Multiple RVs.  Covered through Example 2.8
	Assigned HW #3 Ch 1: 29, 53, 54, 55, 56, 62, 63, 65, 67 AND
	Ch 2: 1, 2, 3 DUE WED 2/9.

2/4	p. 45 Multiple independent RVs.  Examples 2.9, 2.10.  Max and Min	
	Problems: Example 2.11.  Geometric RVs: Examples 2.12 and  2.13.

2/7	Joint Probability Mass Functions: Computation of marginal pmfs using
	(2.8) and (2.9).  Also know the pmf characterization of independence in
	the gray box on p. 48.  Worked Example 2.14 and derived (2.8) and
	the characterization of independence.  We are skipping the subsection
	Computing probabilities with Matlab.  Section 2.4 Expectation: Worked
	Examples 2.20, 2.21, 2.22, and 2.24.  Skipped Examples 2.23 and 2.25.
	Stated the Law of the Unconscious Statistician (LOTUS) (2.14).
	Skipped Derivation of LOTUS.

2/9	Discussed linearity of expectation, Example 2.26.  Moments: variance,
	Example 2.27, variance formula (2.17), standard deviation, Example 2.28,
	2.29.  Defined cental moments, skewness, kurtosis, Example 2.30.
	Defined indicator functions, Example 2.31.  Mentioned Markov and
	Chebyshev inequalities.
	Assigned HW #4 Ch 2: 9, 14, 17, 19, 23, 29, 32, 34 DUE WED 2/16.
	Exam 1 Review Questions:  Ch 1: 57, 58, 60, 61, 66
				  Ch 2: 10, 11, 12, 13, 16, 18, 31, 33.

2/11	Derivation of Markov and Chebyshev inequalities.  Expectations of
	independent RVs, correlation, Cauchy-Schwarz inequality, correlation
	coefficient.

2/14	Covariance.  For uncorrelated RVs, the variance of the
	sum is the sum of the variances --- see (2.28).  Worked Example 2.36.
	Started Ch. 3, covered Section 3.1

2/16	Covered Section 3.2 The Binomial RV.  Covered Section 3.3 The Weak Law
	of Large Numbers.
	NO HW, but do Exam 1 Review questions given on 2/9/05 (see above).

2/18	Started Section 3.4 Conditional Probability.  Covered through
	Example 3.13.

2/21	Answered questions from Exam 1 Review problems.

2/23	Exam 1 -- IN CLASS
	Assigned HW #5 Ch 3: 1, 5, 8, 12, 14, 17 DUE WED 3/2.

2/25	Returned and went over Exam 1.  Worked Example 3.15 and the
	first part of Example 3.16.

2/28	Finished Example 3.16.  Worked Examples 3.17 and 3.18 illustrating
	the Law of Substitution.  Skipped Binary Channel Receiver Design.
	Introduced the Law of Total Probability for Expectation.

3/2	Worked Example 3.20.  Derived Law of Substitution for conditional
	expectation.  Worked Example 3.21.  Started Chapter 4.  Covered up
	through the uniform density.
	Assigned HW #6 Ch 3: 11, 23, 24, 27, 30, 31, 40, 41 DUE WED 3/9.

3/4	Worked Examples 4.1-4.5.  Started discussion of Gaussian/normal RVs.

3/7	Showed Gaussian density integrates to one (p. 89).  Location and
	Scale Parameters and the Gamma Densities, pp. 89-91.  Started
	Section 4.2 Expectation of a Single Random Variable.  Law of the
	Unconscious Statistician (LOTUS).  Example 4.7.

3/9	Worked Examples 4.9-4.14.  Started Section 4.3: Transform Methods.
	Assigned HW #7 Ch 4: 4, 6, 7, 8 (y=lambda x^p),
	12, 13, 14(a)(b) DUE WED 3/16.

3/11	Worked Examples 4.15-4.18.  Introduced characteristic functions.
	Mentioned result in Examples 4.19-4.21.

3/14	Started Section 4.4 Expectation of Multiple Random Variables.
	Worked Examples 4.23-4.24.  Briefly discussed Problems 13, 14(d),
	16, 17, 18, 20.  Started Chapter 5 CDFs.  Worked Examples 5.1,
	special case of Example 5.2.  Discussed normal cdf pp. 112-113.

3/16	Worked Examples 5.3-5.9.
	Assigned HW #8 Ch 4: 23, 24, 32, 37, 42(a), 52, 54 DUE WED 3/30.

3/18	Briefly discussed simulation of continuous RVs on p. 117.  Discussed
	cdfs of discrete RVs in Section 5.2.  Skipped simulation of discrete
	RVs.  Covered Section 5.3 Mixed RVs: Be sure you understand the
	discussion on obtaining the cdf of Y.

3/21	NO CLASS - Spring Break
3/23	NO CLASS - Spring Break
3/25	NO CLASS - Spring Break

3/28	Covered all of Section 5.4 Functions of RVs and Their CDFs.

3/30	Worked Problems 7, 10, 37, 38 in Ch 5.  Also discussed Problems 37
	and 43 in Ch 4.
	Assigned HW #9 Ch 5: 11, 12, 14(a), 26, 39, 40 DUE WED 4/6.

4/1	Section 5.5 Properties of CDFs.  Discussed 8 properties.  Derived
	Property (vii).  Section 5.6 Central Limit Theorem (CLT).  Some
	discussion.  Did derivation that starts 1/3 the way down on the
	right-hand side of p. 129.  Did "typical calculation" at the lower
	left of p. 126.  Discussed Figs. 5.15 and 5.16 (rhs of p. 126).
	Skipped rest of the section.  Briefly introduced Chapter 7.

4/4	Chapter 7 through left-hand side of p. 175.

4/6	Marginal Cumulative Distribution Functions, p. 175.  Skipped
	Example 7.6.  Worked Example 7.7.  Independent RVs, Example 7.8.
	Section 7.2 Jointly Continuous RVs, but skipped Examples 7.10 & 7.11;
	we'll do these with another method later in the chapter.
	Exam 2 Review Questions:
	Ch 3: 13, 29, 32, 43, 45
	Ch 4: 30, 31, 33, 53, 55, 56, 57 (solutions: see Discussion Notes of 3/28/05)
	Ch 5: 37(b), 38(b), 41, 42.

4/8	pp. 180-182: Density characterization of independence: if X and Y are
	jointly continuous, then they are independent if and only if their
	joint density factors: f_{XY}(x,y) = f_X(x) f_Y(y).  LOTUS for pairs
	of jointly continuous RVs, bivariate characteristic function.
	Section 7.3: Developed conditional probability and densities for
	jointly continuous RVs.  Law of total probability, law of substitution.
	Worked Example 7.14.

4/11	Went over exam review problems.

4/13	Exam 2 -- IN CLASS
	Assigned HW #10 Ch 7: 6, 9, 30, 32(a), 33(a)(b), 36, 38 DUE WED 4/20.
4/15	No class -- EXPO

4/18	Went over Exam 2.  Worked Example 7.15.  Skipped Examples 7.16 & 7.17.
	Quickly introduced the laws of total probability and substitution for
	conditional expectation for pairs of jointly continuous RVs.

4/20	Worked Example 7.18.  Skipped Section 7.4.  Discussed Section 7.5,
	extensions to 3 or more RVs.  Worked Examples 7.23 and 7.24.
	Started Ch. 10 Introduction to Random Processes.  Covered through
	Example 10.4.
	Assigned HW #11 Ch 7: 35, 39(c), 41, 58, 59
	Ch 10: 1, 21 DUE WED 4/27.

4/22	Covered Examples 10.5-10.7.  Mean and Correlation Functions,
	Example 10.8.  Skipped Examples 10.9 and 10.10.  Mentioned
	cross-correlation functions.  Worked Example 10.11.

4/25	Worked Example 10.12.  Discussed Strict-Sense and Wide-Sense
	Stationarity.  Worked Example 10.16.  Discussed Transforms of
	Correlation Functions.  See Figs. 10.8 and 10.9.  Showed that
	S_X(f) is real and even.

4/27	Worked Examples 10.21, 10.22.  Covered Section 10.4 WSS Processes
	through LTI Systems.  We skipped Example 10.23 in class, but you
	should go over it on your own.  Started Section 10.5 Power Spectral
	Densities for WSS Processes.  Know three ways to think about the
	power in a WSS process (10.24).  Started Example 10.24 Power in a
	Frequency Band.
	Assigned HW #12 Ch 10: 16, 22, 35, 38, 46, 48 DUE WED 4/27.

4/29	Finished Example 10.24.  Introduced white noise, discussed Example
	10.25.  Skipped Examples 10.26, 10.27, and 10.28, but you should
	go over them on your own.  Note that we covered the first part
	of Section 10.6 Characterization of Correlation Functions earlier,
	but you may want to look over Examples 10.29 and 10.30.  We are
	skipping the subsection Correlation Functions of Deterministic
	Signals.  Covered Section 10.7 The Matched Filter through Example
	10.31.  We are skipping the subsection Analysis of the Matched Filter
	Output.

5/2	Introduced the Poisson process, Section 11.1, through p. 267.
	Distributed teaching evaluations.

5/4	Distributed TA evaluations.  Worked Problems 2, 4, 11 in Ch 11.
	Worked Problem 28 in Ch 10.
	Suggested Review Problems:
	Ch 3: 3, 28, 42
	Ch 4: 29, 51, 53, 59
	Ch 5: 9, 13
	Ch 7: 31, 34, 37, 40
	Ch 10: 36, 37, 39, 40, 42
	Ch 11: 1, 3, 5, 9, 10

5/6	Worked Problems in Ch 10.  Discussed Marked Poisson processes and
	shot noise (will not be on Final).

5/13	FRIDAY, Final Exam, 2:45 pm in 2535 EH.
	You may bring to the exam two 8.5 in. x 11 in. sheets of paper
	with any formulas you want.  Since the following tables
	of pmfs, pdfs, transforms, and series will be included on the
	exam, you don't need to write these down or memorize them.