ST202
Probability, Distribution Theory and Inference
This information is for the 2016/17 session.
Teacher responsible
Dr Konstantinos Kalogeropoulos COL.6.10 and Dr Matteo Barigozzi COL.7.11
Availability
This course is compulsory on the BSc in Actuarial Science 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 and BSc in Mathematics with Economics. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.
Prerequisites
Students must have completed Elementary Statistical Theory (ST102) and Mathematical Methods (MA100).
Students who have not taken these courses should contact Dr Kalogeropoulos or Dr Matteo Barigozzi.
Course content
The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics.
Michaelmas term (Dr Matteo Barigozzi): Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. 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 (Dr K Kalogeropoulos): Functions of random variables. 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.
Teaching
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 NiewiadomskaBugaj, 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).
Assessment
Exam (100%, duration: 3 hours) in the main exam period.
Student performance results
(2013/14  2015/16 combined)
Classification  % of students 

First  40.9 
2:1  19.4 
2:2  14.5 
Third  17.4 
Fail  7.8 
Key facts
Department: Statistics
Total students 2015/16: 179
Average class size 2015/16: 59
Capped 2015/16: No
Lecture capture used 2015/16: Yes (MT & LT)
Value: One Unit
PDAM skills
 Problem solving
 Application of information skills
 Application of numeracy skills
 Specialist skills
Course survey results
(2013/14  2015/16 combined)
1 = "best" score, 5 = "worst" scoreThe scores below are average responses.
Response rate: 70%
Question 
Average  

Reading list (Q2.1) 
2.3  
Materials (Q2.3) 
2.1  
Course satisfied (Q2.4) 
1.9  
Lectures (Q2.5) 
2.3  
Integration (Q2.6) 
1.9  
Contact (Q2.7) 
2.2  
Feedback (Q2.8) 
2.2  
Recommend (Q2.9) 
