Lectures: 2 sessions / week, 1.5 hours / session
1.151 is a first-year graduate subject, very similar in content to 1.010, which is a sophomore-level undergraduate subject. Both aim at introducing students to quantitative uncertainty analysis and risk assessment for engineering applications. The subjects cover similar material, but the 1.151, the graduate version, includes additional topics (such as system reliability) and is faster-paced and more in-depth. The undergraduate course includes weekly recitations mainly to solve problems, review material presented in class, and engage students in bi-weekly 30-minute mini-quizzes. Along with these small quizzes, there is a final exam.
Both subjects try to strike a balance between mathematical rigor and applications. No previous familiarity with probability or statistics is assumed. However, students should be conversant with basic linear algebra (vectors and matrices) and calculus (derivatives, and integrals).
Emphasis is on probability theory and its applications, with a smaller module at the end covering basic topics in statistics (parameter estimation, hypothesis testing and regression analysis). The probability part includes events and their probability, the Total Probability and Bayes' Theorems, discrete and continuous random variables and vectors, the Bernoulli trial sequence and Poisson process models, conditional distributions, functions of random variables and vectors, statistical moments, second-moment uncertainty propagation and second-moment conditional analysis, and various probability models such as the exponential, gamma, normal, lognormal, uniform, beta and extreme-type distributions. In addition, the graduate subject has a module on system reliability, which covers both second-moment and full-distribution techniques. Throughout the subjects, emphasis is on application to engineering and everyday life problems.
The recommended text for this class is: