Probability, Distribution Theory and Inference

This information is for the 2019/20 session.

Teacher responsible

Dr Miltiadis Mavrakakis-Vassilakis


This course is compulsory on the BSc in Actuarial Science, BSc in Financial Mathematics and Statistics and BSc in Statistics with Finance. This course is available on the BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics, and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.


Students must have completed Elementary Statistical Theory (ST102) and Mathematical Methods (MA100).

Students who have not taken these courses should contact Dr Mavrakakis.

Course content

The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics.

Michaelmas term: Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. Functions of random variables. Monte Carlo Simulation using R. Joint distributions and joint moments. Marginal and conditional densities. Independence, covariance and correlation. Sums of random variables and compounding. Multinomial and bivariate normal distributions. Law of large numbers and central limit theorem.

Lent term: Sampling distributions. Criteria of estimation: consistency, unbiasedness, efficiency, minimum variance. Sufficiency. Maximum likelihood estimation. Confidence intervals. Tests of simple hypotheses. Likelihood ratio tests. Wald tests, score tests. Introduction to linear regressions and least squares estimator.


20 hours of lectures, 9 hours of seminars and 10 hours of help sessions in the MT. 20 hours of lectures, 10 hours of seminars and 10 hours of help sessions in the LT. 4 hours of lectures in the ST.

Week 6 in both terms will be used for class tests.

Formative coursework

Students will be expected to produce 4 pieces of coursework in the MT and LT.

Indicative reading

G C Casella & R L Berger, Statistical Inference (primary reading); R Bartoszynski & M Niewiadomska-Bugaj, Probability and Statistical Inference (stresses comprehension of concepts rather than mathematics, supplementary reading only); J Jacod & P Protter, Probability Essentials (for further reading, a more advanced text on probability, using measure-theoretic concepts and tools, still very accessible).


Exam (100%, duration: 3 hours) in the summer exam period.

Key facts

Department: Statistics

Total students 2018/19: 180

Average class size 2018/19: 60

Capped 2018/19: No

Value: One Unit

Guidelines for interpreting course guide information

Personal development skills

  • Problem solving
  • Application of information skills
  • Application of numeracy skills
  • Specialist skills