Probability Theory and Statistics

What it covers

• Probability axioms, conditional probability, Bayes' rule
• Discrete/continuous random variables (Binomial, Poisson, Uniform, Exponential, Normal, etc.), expectation, variance, joint distributions, covariance
• Law of Large Numbers, Central Limit Theorem
• Exploratory data analysis, point estimation (bias, MSE, Method of Moments, MLE)
• Confidence intervals, hypothesis testing (Type I/II errors, p-values, t-tests, multiple testing)
• Simple and multiple linear regression, R², residual analysis, bootstrap

Assessment

Midterm (lectures 1-8) + Endterm (lectures 9-16/17), weighted equally, average = final grade. Single comprehensive resit. Closed-book; non-graphing calculator allowed; one handwritten A4 formula sheet (midterm: one side; endterm/resit: both sides); distribution tables provided. Mix of MC and open questions. Up to +1 bonus point available from 4 ungraded computer assignments (R/Python), applied only if the exam average already passes.

Resources

• Essence of Probability – 3Blue1Brown, Probability Distributions – 365 Data Science, Statistics – Cody Baldwin, StatQuest

Worth knowing

• Each question/subpart is weighted equally, so careless MC mistakes cost proportionally as much as missed steps on the open questions.
• One student note in the material claims the textbook plays only a minor role and that Grasple content alone was sufficient for a top grade — treat as one data point, not a guarantee.
• Exam questions are provided in both English and Dutch.