Dr Konstantinos Kalogeropoulos COL.610

This course is available on the BSc in Business Mathematics and Statistics and BSc in Mathematics, Statistics, and Business. This course is not available as an outside option. This course is available to General Course students.

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

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

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 in 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.

20 hours of lectures and 10 hours of seminars in the MT. 2 hours of lectures in the ST.

Students will be expected to produce 4 pieces of coursework which will consist of written exercises aimed at practising calculations and understanding of theory.

A formative in class exam-style assessment will be done in Week 6.

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, complimentary 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: 2 hours) in the summer exam period.