10.022 Modelling Uncertainty
Uncertainty appears everywhere in life, arising naturally in science, engineering, design, and humanities. Probability and statistics are two powerful and complementary ways to explain, forecast, and visualise uncertainty. Probability uses knowledge of a system’s behaviour to predict its future outcomes, while statistics analyses data from past outcomes to model a system’s behaviour. Probability and statistics are applied in virtually all industries that govern modern society; they are particularly important in disciplines including (but not limited to) finance, big data, artificial intelligence and machine learning. In this course, we will introduce the fundamentals of probability and statistics through real life problems and software. Students will complete projects related to applications such as climate adaptation, pharmaceutical testing, vaccine distribution, and product safety assurance.
Learning objectives
At the end of the term, students will be able to:
- Understand the basics of probability, such as laws of probability, independence, conditional probability, common distributions, random variables and common operations on them
- Develop and evaluate simple probabilistic models for a variety of situations
- Apply the central limit theorem
- Examine data, and use tools to visualize data and uncover relationships
- Compute point estimates and construct confidence intervals from a data sample
- Perform hypothesis tests
- Build regression models and estimate their parameters
Measurable outcomes
- Apply enumeration to solve simple problems in discrete probability
- Understand the notion of independence; apply Bayes theorem and the law of total probability to solve problems involving conditional probability
- Compute the probability mass (or density) function, cumulative distribution function, mean, and variance of a random variable
- Understand common distributions (such as binomial, geometric, normal) and recognize when to use them
- Set up 1‐ or 2‐dimensional integrals, then evaluate them to solve problems involving continuous random variables
- Recognize situations when the central limit theorem may be applied, and carry out the computations
- Summarize and visualize data using histograms and scatter plots
- Compute the sample mean and sample variance from a data sample, and use them as point estimates for the population mean and variance; construct one‐ and two‐sided confidence intervals for the mean
- Form a null and an alternative hypothesis for a statistical problem, then carry out a hypothesis test; compute the p‐value for a hypothesis test and interpret the result
- Construct the least square regression line from a data sample
Grading scheme
Students are graded based on exam test results, class participations, homework, and team-based design projects (eg. 1D and 2D projects etc).
Prerequisites
Workload: 5-0-7
*The first number represents the number of hours per week assigned for lectures, recitations and cohort classroom study. The second number represents the number of hours per week assigned for labs, design, or field work. The third number represents the number of hours per week assigned for independent study.
Prior to AY2020, it was 10.007 Modelling the Systems World