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Advanced statistics: distribution theory ST2133

Half course

This half-course is intended for students who already have some grounding in statistics. It provides the basis for an advanced course in statistical inference.


Prerequisite: A course that you must have ordinarily attempted all elements of before you are permitted to register for another particular course.

  • (ST104a Statistics 1 and ST104b Statistics 2)
  • and (MT1174 Calculus or (MT105a Mathematics 1 and MT105b Mathematics 2)
  • or MT1186 Mathematical Methods).

Topics cover


  • Probability measure.
  • Conditional probability.
  • Bayes’ theorem.

Distribution Theory:

  • Distribution function.
  • Mass and density.
  • Expectation operator.
  • Moments, moment generating functions, cumulant generating functions.
  • Convergence concepts

Multivariate Distributions:

  • Joint distributions.
  • Conditional distributions, conditional moments.
  • Functions of random variables.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Recall a large number of distributions and be a competent user of their mass/density and distribution functions and moment generating functions
  • Explain relationships between variables, conditioning, independence and correlation
  • Relate the theory and method taught in the unit to solve practical problems.


Unseen written examination (2 hrs). 

Essential reading

  • Grimmett, G. and D. Stirzaker. Probability and Random Processes. OUP.
  • Casella, G. and R.L. Berger. Statistical Inference. Duxbury.

Course information sheets

Download the course information sheets from the LSE website.