Probability, Distribution Theory and Inference

This information is for the 2020/21 session.

Teacher responsible

Dr Miltiadis Mavrakakis-Vassilakis


This course is compulsory on the BSc in Actuarial Science and BSc in Financial Mathematics and Statistics. 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.


This course will be delivered through a combination of classes and lectures totalling a minimum of 60 hours across Michaelmas Term and Lent Term. This year, some or all of this teaching may be delivered through a combination of virtual classes and flipped-lectures delivered as short online videos. This course includes reading weeks in Week 6 of Michaelmas Term and Lent Term.

Formative coursework

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

These are exam-style class tests.

Indicative reading

M C Mavrakakis & J Penzer, Probability and Statistical Inference: From Basic Principles to Advanced Models (primary reading)

G C Casella & R L Berger, Statistical Inference (very useful as a reference)


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

Student performance results

(2017/18 - 2019/20 combined)

Classification % of students
First 50
2:1 20
2:2 14.5
Third 5.6
Fail 9.9

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Statistics

Total students 2019/20: 226

Average class size 2019/20: 76

Capped 2019/20: 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