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YZZ205 - Probability and Statistics (Autumn Term)

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Course Information

  • Venue: Class Z3, Department Floor, Annex Building, Faculty of Arts and Sciences

  • Date&Time: 13:15-17:00 on Tuesdays

  • Objectives: This course aims to provide students a rigorous foundation in probability theory and statistical inference with an emphasis on their application to problems in artificial intelligence and machine learning. Students will develop the mathematical and computational skills required to model uncertainty, analyse data, and evaluate statistical claims, thereby preparing them for subsequent coursework in machine learning, data engineering, and related disciplines.

  • Textbook:

    • Ethem Alpaydın, Fundamentals of Probability and Statistics for Machine Learning, 1st Ed., MIT Press, 2025.​

  • Auxiliary Sources:

    • Charu C. Aggarwal, Probability and Statistics for Machine Learning: A Textbook, 1st Ed., Springer, 2024.​

    • Jose Unpingco, Python for Probability, Statistics, and Machine Learning, 1st Ed., Springer, 2016.​

    • Michael Akritas, Probability & Statistics with R for Engineers and Scientists, 1st Ed., Pearson, 2016.

    • Sujit K. Sahu, Introduction to Probability, Statistics & R: Foundations for Data-Based Sciences, 1st Ed., Springer, 2024.

    • Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye, Probability & Statistics for Engineers & Scientists, 9th Ed., Pearson, 2016.

    • Richard A. Johnson, Miller & Freund's Probability and Statistics for Engineers, 9th Ed., Pearson, 2018.

    • Murray R. Spiegel, John Schiller, and R. Alu Srinavasan, Schaum's Outlines Probability and Statistics, 4th Ed., McGraw-Hill, 2013.

  • Contents: Introduction, Random Experiments and Probabilities, Probability Distributions, Sampling and Estimation, Hypothesis Testing, Multivariate Models, Regression, Classification, and Clustering.

  • Learning Outcomes: Upon successful completion of this course, students will be able to:

    • Apply the fundamental axioms of probability and combinatorial counting techniques to solve problems involving random experiments and events.

    • Identify and work with common discrete and continuous probability distributions, and compute their expectations, variances, and related moments.

    • Formulate and apply methods of statistical estimation, including maximum likelihood estimation, to infer population parameters from sample data.

    • Construct and interpret confidence intervals and conduct hypothesis tests to draw statistically sound conclusions from data.

    • Analyse multivariate data using covariance structures and dimensionality reduction techniques such as principal component analysis.

    • Formulate and solve linear regression problems, and critically evaluate model fit and assumptions.

    • Apply Bayesian decision theory and probabilistic generative models to formulate classification problems, and use mixture models to formulate clustering problems.

    • Recognise the connections between probabilistic and statistical concepts and their applications in machine learning contexts, such as model evaluation and feature selection.

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Lecture Notes​​​

1. Course Introduction and Scope

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Laboratories

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Exams

  • Week 9: Midterm Examination (2026)

  • Week 16: Final Examination (2027)

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Announcements

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