Courses Detail Information
ECE4010J – Probabilistic Methods in Engineering
Instructors:
Credits:
4 credits
Pre-requisites:
MATH2160J/256/286
Description:
This first course in probability and statistics gives a broad introduction to the field. The focus is on conveying fundamental concepts that will prepare students for more advanced courses in statistics (Bayesian statistics, advanced regression) as well as in applied fields (data analytics, machine learning, financial mathematics). The course emphasizes rigorous mathematics (a solid background in multivariable calculus and familiarity with matrices, determinants, eigenvalues etc. is assumed), a deep understanding of the relevant concepts, and the meaning and interpretation of mathematical results in statistics in real life.
The first one-third of the course is devoted to an introduction to probability theory, while the latter two-thirds focus on statistical methods.
Course Topics:
1. Elementary probability, conditional and total probability, Bayes’s theorem
2. Discrete random variables (binomial, geometric, uniform, Pascal, hypergeometric, Poisson)
3. Continuous random variables (exponential, gamma, chi-squared, uniform, normal, Weibull, Cauchy)
4. Expectation, variance, moment-generating functions
5. Multivariate random variables (multivariate normal distribution), covariance, correlation
6. Introduction to reliability
7. Samples and data
8. Parameter estimation, distribution and independence of sample mean and sample variance
9. Interval estimation
10. Fisher test and Neyman-Pearson decision theory
11. T-test, chi-squared test, sign test, Wilcoxon signed rank and rank-sum tests
12. Inferences on proportions
13. Tests for comparison of variances, Student’s and Welch’s T tests, pooled vs. paired tests, inferences on correlation
14. Pearson’s goodness-of-fit test and applications
15. Simple linear regression
16. Multiple linear regression