ECE302 Spring 1999---Probability and Applications: Lectures

Lecture	Date	Topics and Textbook Section(s)
1	Jan. 4	Introduction to course; 1.1-1.2.
2	Jan 6	Sample spaces, events, notions of probability; 1.3, 2.1, 2.2
3	Jan. 8	Class cancelled due to the "Ottawa trip"
4	Jan. 11	Set theory, axiomatic definition of probability-corollaries; 2.1,2.2
5	Jan. 13	Probability space as a triple(Sample Space, Event Space, Pro bability Measure); 2.1,2.2
6	Jan. 15	Class cancelled due to the "Snow Storm"
7	Jan. 18	Counting methods; Sampling with and without replacement or ordering; Binomial coefficient; 2.3
8	Jan. 20	Conditional and total probability;Independence of events; Examples; 2.4, 2.5
9	Jan. 22	Bayes rule; Sequencial Experiments; Bernoulli Trials; Examples; 2.5, 2.6
10	Jan. 25	Sequencial Experiments;Markov Chains; Examples; 2.6
11	Jan 27	The concept of a real random variable; the Cumulative Distribution Function (cdf); 3.1, 3.2
12	Jan 29	Properties of the Cumulative Distribution Function; The Probability Density Function (pdf); Examples; 3.2, 3.3
13	Feb 1	Conditional CDF and pdf; Discrete random variables: Bernoulli, Binomial; Geometric; 3.4
14	Feb 3	Class cancelled due to "Visionary Seminar".
15	Feb 5	Discrete random variables: Poisson r.v.; Relation between Binomial and Poisson rvs.; 3.4
16	Feb. 8	Continuous rvs: Uniform r.v. Exponential r.v; Relation between Geometric and Exponential r.vs; Gaussian r.v.; 3.4
17	Feb. 10	Functions of a random variable; Examples; 3.5
18	Feb. 12	Functions of a random variable - Fundamental Theorem; Examples; 3.5
19	Feb. 22	Review class
20	Feb. 24	Expected value of a r.v.; The mean and variance; 3.6
21	Feb. 26	Moments of a r.v; Examples on signal detection and estimation; 3.6
22	March 1	Markov and Chebyshev inequalities; Examples on parameter estimation -Unbiased and consistent estimators; 3.7
23	March 3	Characteristic function of a r.v.; Moment theorem;examples; 3.9
24	March 5	Pairs of r.vs; Joint distribution and density functions; 4.2
25	March 8	More examples on pairs of r.vs; independence of r.vs; 4.1, 4.2, 4.3
26	NMarch 10	Jointly Gaussian r.v.s; Conditional distributions and densities; Examples 4.4
27	March 12	Conditional expectation; Examples; Mean-Square-Estimation; 4.4, 4.9
28	March 15	One fuction of two random variables; Examples; 4.6
29	March 17	Two fuctions of two random variables; Fundamental Theorem; Auxiliary variable method; 4.6
30	March 19	Expected values of functions of r.vs; Joint moments; Correlation, orthogonality,independence or r.vs 4.7
31	March 22	Schwarz Inequality; Covariance and correlation matrices; Examples 4.7
32	March 24	Affine/linear transformations of Gaussian vectors (two r.v.s); Linear prediction; 4.8, 4.9
33	March 26	Multiple random variables (more than two); Definitions and properties; 4.5, 4.6
34	March 29	Multiple random variables (more than two); The fundamental theorem; Applications to linear filtering; 4.5, 4.6
35	March 31	Multiple random variables (more than two); Correlation and Covariance matrices; Applications to linear prediction; 4.5, 4.6, 4.9
	April 2	No lecture (Good Friday)
36	April 5	Sums and sequences of random variables; Sample mean and variance; 5.1, 5.2
37	April 7	Law of large numbers; The central limit theorem 5.2, 5.3
38	April 9	Review class; Material required in final exam.