ECE 430 Random Signal Analysis, Spring 1998

1/20	Course outline.  Section 2.1: Review of set notation.
	Section 2.2: Probability models, examples.

1/22	Continued with Section 2.2.  More examples.  Axioms of probability.

1/27	Implications of the axioms of probability: finite disjoint unions,
	probability of a complement, monotonicity, inclusion-exclusion,
	limit properties, the union bound.  Section 2.5: Independence.
	Assigned HW: Ch 2: 4, 15, 17, 24 DUE Thur. 2/5.

1/29	Independence of three events.  Independence of many events.
	Assigned HW: Handout of problems on independence DUE Thur. 2/5.

2/3	Section 2.4: Conditional probability.
	Assigned HW: Ch 2: 56, 57, 59 DUE Thur. 2/12.

2/5	Chapter 3: Random variables and their distributions.  Discrete
	reandom variables.  Bernoulli RVs.

2/10	More probability mass functions: Binomial, geometric_0 and
	geometric_1, Poisson.  Continuous random variables and
	probability density functions.
	Assigned HW: Ch 3: 1, 31, 33, 34(a)(c), 37(a), 40 DUE Thur. 2/19.

2/12	Continuous RVs and densities, mixed RVs.
	Assigned HW: Handout of problems on probability densities
	DUE Thur. 2/19.

2/17	Cumulative distribution functions (cdfs).
	Assigned HW: Ch 3: 19, 20(c), 21(c), 45, 46, 6, 8, 16, 17 DUE Thur. 2/26.
	Note for Problems 45 and 46: If X is an N(m,sigma²) random variable,
	then m is the mean and sigma is the standard deviation, and
	sigma² is the variance.

2/19	Section 3.5: Distributions of functions of random variables.

2/24	More on distributions of functions of random variables.
	Assigned HW: Handout #3, Problems 1, 2, 3, 4, 7(b), 8(d), 9(a)
	DUE Thur. 3/5.

2/26	More examples of distributions of functions of random variables.
	

3/3	Section 3.6: Expectation
	Assigned HW: Ch 3: 71, 75, 76, 78 DUE Thur. 3/19.

3/5	Section 3.9: Transform methods: Probability generating function,
	moment generating function, characteristic function.
	Started Section 3.7: Markov and Chebyshev inequalities.
	Handed out review questions from several old exams.

3/10	No class - Spring Recess
3/12	No class - Spring Recess

3/17	Review for midterm. What's on the midterm?

3/19	Midterm, in class

3/24	Went over midterm.  Discussed Markov, Chebyshev, and Chernoff
	bounds.  Started multivariate random variables.

3/26	Joint distributions, cdfs, marginal distributions, marginal cdfs.
	Jointly continuous RVS, marginal densities.
	Assigned HW: Ch 4: 3, 10, 11, 13, 17(assume N and X indep.), 25
	DUE Thur. 4/2.

3/27	FRIDAY: Last day to drop courses for undergrads

3/31	Covered bivariate Gaussian density.  Expectation E[g(X,Y)],
	bivariate characteristic functions, independent random variables.

4/2	Section 4.4: Conditional probability and conditional expectation.
	Assigned HW: Ch 4: 37(a) 38(a)(b)(c), 48, 50, 60, 37(b),
	82[Hint: First show that E[Y^4] = 3\simga^4].  DUE Thur. 4/9.

4/7	Worked examples of computing probabilities and expectations using
	the Law of Total Probability and the Substitution property.
	Started talking about the multivariate Gaussian density.

4/9	Continued multivariate Gaussian.  Used ch. fcn. to show that R is
	the covariance matrix.  Showed that if X is normal, then so is AX+b.
	Transformations of random vectors, the Jacobian formula.
	Assigned HW: Ch 4: 31, 33, 34, 76, 77, 78(a), 87 DUE Thur. 4/16.

4/14	Worked example using the Jacobian formula.  Started introduction
	to stochastic processes and wide-sense stationarity.
	Correlation functions.

4/16	Discussed Problem 4.76, which is improperly stated in the text.
	Covered the relation between the correlation function of a WSS
	input to an LTI system and the correlation function of the system
	output.  Also covered cross-correlation and the power spectral
	density.
	Assigned HW: Ch 6: 53, 56(a), 63(a) DUE Thur. 4/23.
	NOTE: If X_t is (strictly) stationary, then E[(X_t)^n] does
	not depend on t.

4/21	Derived the Wiener-Khinchin Theorem.  Defined cross PSD.
	Derived S_Y(w) = |H(w)|^2 S_X(w), etc.  Started derivation
	of matched filter.
	Assigned HW: Ch 7: 1(b), 2, 3, 7, 19, 21 DUE Thur. 4/30.

4/23	Derived Cauchy-Schwarz with conditions for equality and then finished
	matched filter.  Began discussion of Wiener filter.  Derived
	orthogonality principle.

4/28    Completed derivation of the Wiener filter.

4/30	Chapter 5: Statistics.  Estimating the mean of a random variable.
	The Weak Law of Large Numbers (WLLN).  Estimating the probability
	of an event.  The Strong Law of Large Numbers (SLLN).  Estimating
	the CDF.  Kernel density estimation.  Started discussion of the
	Central Limit Theorem (CLT).
	Assigned HW: Ch 5: 15, 16, 17, 22.  DUE Thur. 5/7.

5/5	Finshed material on the central limit theorem.  Estimating
	the variance.

5/7	Review for final exam.

5/10	SUNDAY, Final Exam, 2:45 pm in 2540 Engr. Hall.