# Applied Statistics (7,5 ECTS) (Spring 2024)

#### 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 only open for BDS students admitted 2022 and before and who have not yet passed the course.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 course lectures are organised as self-study: they contain no live lectures but priorly recorded course lectures will be used instead. They introduce the theory and give examples how to 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 together with the live exercise session will prepare the students for the written exam.

##### Mandatory activities

There are twelve mandatory assignments weekly throughout the semester. All twelve assignments must be approved to qualify for the exam. Opportunities for re-submission of non-approved assignments will be given. The mandatory assignments form an integral part of the learning activities and ensures that all students get extensive feedback on written work. The mandatory weekly exercises facilitate continuous learning throughout 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)