Statistics
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBMA00905 
Vaknaam  Statistics 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Statistics  
Leerdoelen  At the end of the course, the student is able to: 1. estimate unknown parameters from data; 2. show proof for CramerRao lower bound; 3. determine statistical properties of estimators, such as bias, consistency, sufficiency, efficiency, of estimation procedures; 4. derive and apply maximum likelihood estimation; 5. apply hypothesis testing and derive its properties; 6. show the proof of the NeymanPearson lemma; 7. apply estimation and testing principles to simple linear regression models; 8. compute confidence intervals for parameters. 

Omschrijving  Up till now in your academic career, you might have calculated a probability of some event, given some known state of the world (i.e. the probability distribution). However, in practice we are often more interested to learn about the state of the world, given some event (i.e. the data). Statistics, therefore, is probability theory turned upside down. In this course we will learn about estimation procedures, in particular maximum likelihood, and some of their theoretical properties. We also learn about hypothesis testing and confidence intervals. For illustration purposes, we eventually apply estimation and testing in a practical setting: linear regression analysis. This course picks up where the 1st year course Probability Theory has finished: It is assumed known that students know the basic probability theory, including mean, variance and standard distributions such as the binomial, normal, Poisson etc. Also the basis of conditional probability is assumed to be known, including the conditional mean and the conditional variance. The Law of the Large Numbers, the Central Limit Theorem and ideas about convergence in probability are crucial to evaluate the quality of statistical inference methods. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(Let E be the final exam and H1, H2 and H3 be the homework grades IF (E>5.4) Final grade = 0.1 x max(H1, E) + 0.1 x max(H2, E) + 0.1 x max(H3, E) + 0.7 x E Else (E<5.5) Final grade = E Homework grades do not count for the resit exam. Then: Final grade = Resit exam grade. The final grade needs to be at least 5.5 to pass the course.) 

Vaksoort  bachelor  
Coördinator  prof. dr. M.A. Grzegorczyk  
Docent(en)  prof. dr. M.A. Grzegorczyk  
Verplichte literatuur 


Entreevoorwaarden  The course unit assumes prior knowledge acquired from Calculus 1 and Probability Theory.  
Opmerkingen  It is recommended that the students buy one of the two textbooks, but this is NOT mandatory. The provided lecture material will cover all topics in a selfexplanatory way.  
Opgenomen in 
