This course covers the fundamentals of probability and statistics, with a focus on applications from engineering and the sciences. The course begins with an introduction to graphical data representation and descriptive statistics. Topics in probability include discrete and continuous random variables, probability rules, probability distributions, the law of large numbers, the central limit theorem, and expected value. Topics in statistics include sampling distributions, estimation of population parameters, confidence intervals, and significance testing. The course does not focus exclusively on concepts from the frequentist paradigm, but also introduces Bayesian statistics (Bayes' theorem, Bayesian hypothesis testing). The goal of this course is that the students acquire a solid statistical literacy that enables them to interpret statistical information and graphs and learn how to choose the appropriate statistical methodologies and tools to analyze data scientifically. To achieve this goal, the course includes many real-world examples from engineering and the sciences.
After successful completion of this course, the students will
(1) understand how to interpret various graphical representations of statistical information;
(2) understand the key elements of probability and statistics;
(3) be able to analyze data scientifically with the appropriate statistical methodologies and tools;
(4) be able to adequately communicate analytical results in an interdisciplinary environment.
Bayes theorem; Bayesian hypothesis test; Beta function; binomial probability distribution; box-and-whiskers plot; central limit theorem; conditional probability; confidence interval; events; expected value; Gamma function; histogram; hypothesis testing; joint probability; law of large numbers; marginal probability; mean; normal probability distribution; p-value; quartile; random variable; sample space; sampling distribution; significance testing; standard deviation; variance.
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Classes usually begin with a real-world example to motivate a statistical concept. This concept is then formally described, and mathematical proofs are given where appropriate. Then, we will solve the real-world problem together.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction; organizing and graphing data; bar charts and histograms | None. |
Class 2 | Measures of dispersion and position; box-and-whiskers plot | Revise contents of previous class; complete assignment |
Class 3 | Introduction to probability theory; marginal probability, joint probability, conditional probability | Revise contents of previous class; complete assignment |
Class 4 | Probability rules; introduction to Bayes' theorem and Bayesian statistics | Revise contents of previous class; complete assignment |
Class 5 | Bayes' theorem: Applications | Revise contents of previous class; complete assignment |
Class 6 | Covariance, correlation, regression | Revise contents of previous class; complete assignment |
Class 7 | Probability distribution of discrete random variables; expected value | Revise contents of previous class; complete assignment |
Class 8 | Binomial coefficient; Gamma function; binomial probability distribution | Revise contents of previous class; complete assignment |
Class 9 | Probability distribution of a continuous random variable; normal probability distribution | Revise contents of previous class; complete assignment |
Class 10 | Central limit theorem; sampling distribution of the sample mean and sample proportion | Revise contents of previous class; complete assignment |
Class 11 | Point estimates and confidence intervals | Revise contents of previous class; complete assignment |
Class 12 | Student's t-distribution and its applications | Revise contents of previous class; complete assignment |
Class 13 | Significance testing; hypothesis testing; p-value | Revise contents of previous class; complete assignment |
Class 14 | Beta function; Bayesian hypothesis testing [1 of 2] | Revise contents of previous class; complete assignment |
Class 15 | Bayesian hypothesis testing [2 of 2] | Revise contents of previous class |
None required. Course materials are provided during class.
Dimitri P. Bertsekas and John N. Tsitsiklis (2008) Introduction to Probability. Athena Scientific; 2nd edition; ISBN: 978-1-886529-23-6.
Students' course grades will be based on the final exam.
Knowledge of elementary algebra and calculus is required.