## Statistics

 Faculteit Science and Engineering Jaar 2018/19 Vakcode WISTAT-07 Vaknaam Statistics Niveau(s) bachelor Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Statistics
Leerdoelen The aim of the course is that
• the students learn about statistical estimation procedures, such as maximum likelihood estimation, and understand their properties;
• the student are able to apply these procedures to a variety of settings.

The student is able to:
1. apply estimation procedures;
2. show proof for Cramer-Rao lower bound
3. derive properties, 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 Neyman-Pearson lemma;
7. apply estimation and testing principles to linear regression.
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. Then we apply both estimation and testing to a practical setting: linear regression analysis.

This course picks up where the 1st year course Probability 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 known, including conditional mean and variance. The Central Limit Theorem and ideas about convergence in probability are crucial to evaluate the quality of a statistical procedure.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(The final grade (FG) is determined as follows: FG = 0.7 x WE + 0.1 x max{WE,HW1} + 0.1 x max{WE,HW2} + 0.1 x max{WE,HW3}, with WE grade of Written Exam and HWi grade of i-th homework assignment.)
Vaksoort bachelor
Coördinator dr. M.A. Grzegorczyk
Docent(en) dr. M.A. Grzegorczyk
Verplichte literatuur
Titel Auteur ISBN Prijs
Statistical Inference (2nd edition, 2002) Casella & Berger 0534243126
Entreevoorwaarden The course unit assumes prior knowledge acquired from Calculus 1 and Probability Theory.
Opmerkingen the course prepares for Statistical modelling
Opgenomen in
Opleiding Jaar Periode Type
BSc Applied Mathematics 2 semester I a verplicht
BSc Chemical Engineering  (Minor Chemical Engineering) 3 semester I a keuze
BSc Courses for Exchange Students: Mathematics & Applied Mathematics - semester I a
BSc Mathematics and Physics (double degree) 3 semester I a verplicht
BSc Mathematics: General Mathematics  ( Major track General Mathematics) 2 semester I a verplicht
BSc Mathematics: Probability and Statistics 2 semester I a verplicht