Advanced statistics: distribution theory

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.


  • 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.

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

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