# Applied Statistics (Spring 2023)

#### Official course description:

##### Course info

##### Programme

##### Staff

##### Course semester

##### Exam

##### Abstract

The course introduces the students to probability theory and applied statistics. It will focus on understanding the theoretical foundations of statistics and on applying the theory using mathematical analysis and simulations in R.##### Description

The course intends to give the student tools to identify and solve statistical problems in practice, occurring in data-analysis.

The subjects covered in the course include: probability spaces, random variables, conditional and joint probability, independence, expectation, variance, correlation and covariance, simulation of random variables, law of large numbers, central limit theorem, explorative data analysis, statistical models, bootstrapping, maximum likelihood estimation, confidence intervals, hypothesis testing.##### Formal prerequisites

The course is mandatory for second semester BSc in Data Science students and requires basics in programming and mathematics.##### Intended learning outcomes

After the course, the student should be able to:

- Apply fundamental definitions and theorems from probability theory and statistics
- Perform basic computations on random variables and simulate random variables using R
- Perform basic statistical modelling and inference (estimation and hypothesis testing) using mathematical analysis and in R
- Analyse sampling distribution of estimators using both mathematical tools and simulation (bootstrapping) with R
- Present a statistical analysis in a clear way that allows the reader to understand the conclusions and the assumptions they are based on
- Do basic programming and data manipulation in R
- Identify statistical problems in a given data analysis

##### Learning activities

The lectures will introduce the theory and give examples of apply the theory. The weekly exercises will train the students on applying the theory and using R. The problems that the students solve in the weekly exercises will prepare the students for the written exam.

##### Mandatory activities

The mandatory activities are weekly exercises that the student solve prior to the exercise session and will present the solution to the exercise class if randomly picked by the TA. In order to be qualified for the exam, the student must have solved and volunteered to present his/her solution to 50% of the mandatory problems on average. The completion rate is computed from the lists where the student check, prior to the exercise session, those problem he/she has solved and will be ready to present to the class. On the basis of the presented solution, the TA will give feedback and discuss the solution with the class and complement the solution if necessary. The mandatory weekly exercises facilitate continuous learning throughout the course. The second attempt will be provided for the students, who do not pass the mandatories in the first attempt, before the ordinary exam of the course.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

##### Course literature

Dekking, F.M, Kraaikamp, C., Lopuhaä, H.P., Meester, L.E. (2010),*A Modern Introduction to Probability and Statistics - Understanding Why and How*, Springer.

Verzani, J. (2014),

*Using R for Introductory Statistics*, Second Edition, CRC Press.

##### Student Activity Budget

Estimated distribution of learning activities for the typical student- Preparation for lectures and exercises: 15%
- Lectures: 25%
- Exercises: 25%
- Assignments: 15%
- Exam with preparation: 10%
- Other: 10%

##### Ordinary exam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A22: Written exam on premises with restrictions.

**Exam duration:**

4 hours

**Internet access:**

Restricted access - LearnIT only

**Aids allowed for the exam:**

Written and printed books and notes

E-books and/or other electronic devices

- E-books and notes on the computer are allowed

- Students should bring a computer with the R programming language installed (with packages as specified by the teachers)

##### reexam

**Exam type:**

A: Written exam on premises, External (7-point scale)

**Exam variation:**

A22: Written exam on premises with restrictions.

**Exam duration:**

4 hours

**Internet access:**

Restricted access - LearnIT only

**Aids allowed for the exam:**

Written and printed books and notes

E-books and/or other electronic devices

- E-books and notes on the computer are allowed

- Students should bring a computer with the R programming language installed (with packages as specified by the teachers)