MIE236H1

Probability

Introduction to probability (the role of probability and data in engineering; concepts of population vs. sample). Sample space and events. Definitions of probability. Conditional probability and Bayes' rule. Concept of random variables. Discrete, continuous, and joint distributions. Statistical independence. Expectation, variance, covariance, and correlation. Important discrete and continuous distributions that explain engineering-related phenomena. Brief introduction to the homogeneous Poisson process and related distributions. How to derive distributions. Transformation of random variables. Fundamental sampling distributions, Chi-square, t, and F distributions. Central limit theorem, laws of large numbers. One sample estimation (methods of maximum likelihood, bootstrapping, and jackknife) and hypothesis testing.