The course is intended to provide students with: (a) a familiarity with probability theory and how it is used in practice, (b) the ability to estimate random model parameters from real-life data, (c) the tools to probabilistically model networking systems and estimate system reliability, and (d) an awareness of how risk assessment is used to quantify uncertainty and, in the end, produce optimal designs. However, students must enter the course with some prior knowledge in order for these goals to be achieved, as outlined in the following.

1. An introductory course in probability and statistics is a prerequisite for INWK 6211. See, for example ENGM2032 Applied Probability and Statistics. The first half of INWK 6211 consists of a review of basic probability and statistics concepts. If a student has not learned these topics previously in a full term university course, it will be very difficult to (re)learn them in the first half of this class (1.5 weeks). Some concepts of probability and statistics are quite subtle, and students should ensure that they are familiar with the material prior to entering this course. To assist in self-assessment, a list of sample problems have been compiled (see below). Students should be able to solve these and similar problems prior to the beginning of class. There will be a entrance assessment test on these topics given on the first morning of the course. The test will contribute 10% to the final mark. The purpose of the test is to let students know where they stand and where their weaknesses are. It is expected that students will use the results of this test to motivate any additional studying required during the course to ensure that they attain a passing mark.

2. A certain level of basic mathematical knowledge is required. Most notably, students are expected to be familiar with set theory, matrix manipulations, and how to solve linear systems of equations. These topics will not be covered during the course but will be used. Students should ensure that they have proficiency in these areas prior to the beginning of the course. To assist in self-assessment, a list of sample problems have been assembled (see below). Complete solutions are given for these problems as these will not be discussed during the class. If a student wishes to read-up on these topics, any basic textbook covering introductory probability will have a section on set theory. Matrix manipulations and linear systems of equations are covered in introductory linear algebra textbooks. One recommendation is Elementary Linear Algebra - Applications Version, seventh edition, by Howard Anton and Chris Rorres, Wiley, 1994. Textbooks can be found in local University libraries.

In summary, students are expected to arrive at this course already familiar with the following areas (upon which the entrance assessment test will be based - see basic probability problems below and the course notes, Chapters 1 and 2);

• sample spaces, events, Venn diagrams, counting principles,
• probabilities of unions and intersections of events, conditional probabilities,
• total probability theorem, Bayes' theorem, event trees,
• random variables and probability distributions, PDF's and CDF's, discrete vs. continuous random variables,
• main characteristics of random variables; mean, variance, covariance, correlation coefficient,
• mean and variance of sums of random variables,
• common probability distributions (Bernoulli, Binomial, Geometric, Poisson, Uniform, Exponential, Gamma, Weibull, Normal, and Lognormal)
• sampling distributions (Student-T, Chi-square, F)
• point estimates and confidence intervals
• hypothesis testing

The following sample problems illustrate the level of competence expected of students prior to entering this course;

• Basic probability and statistics problems
  • Answers
  • Complete Solutions
• Basic set theory and linear algebra problems
  • Solutions

Gordon A. Fenton
Jun 30, 2005