Single-Course Dansk 5 ECTS

# Introduction to Mathematical Statistics

## Overall Course Objectives

To give the participants an introduction to statistical thinking and methods and to provide them with an understanding of random variation and of the use of statistical models. A mathematical approach to statistics will be introduced.
Important statistical principles for collection and analysis of data are introduced, and methods for model choice, estimation, testing and model verification are presented. The participants learn to handle a number of elementary problems which occur frequently in engineering practice and are thus enabled to critically assess statistical (empirical) investigations and references.

See course description in Danish

Learning Objectives

• Estimate and interpret simple summary statistics, such as mean, standard deviation, variance, median and quartiles as well as correlation.
• Apply simple graphical techniques, including histograms, qq-normal plots, and box plots.
• Identify and describe probability distributions, including Poisson, binomial, exponential and the Normal distribution using statistical software.
• Understand the background for classical sample distributions:: t-, χ²-, F- distributions.
• Compare different statistical methods.
• Apply and interpret important statistical concepts, such as the formulation of models, paramteter estimation, construction of confidence intervals and hypothesis testing.
• Apply and interpret simulation based statistical methods.
• Apply and interpret simple statistical methods within one- and two sample situations and for count data. And account for the mathematical background.
• Apply and interpret simple statistical methods within simple and multiple linear regression and one- two-way analysis of variance.
• Use statistical software and interpret output from it
• Interpret power considerations and perform sample size calculations in different settings using the statistical software
• Debate and critize emprically based information.

Course Content

Simple methods for graphical and tabular assessments of collected or measured data: empirical distributions, histogram, normal probability plot, box plot. Model formulation. Model control: control of distribution function. Application of especially Poisson-, binomial-, exponential- and normal distribution. Estimation and test of parameters and construction of confidence intervals in frequently occuring situations (e.g. means, variances, proportions). Regression analysis with one independent variable and introduction to the analysis of variance and to the analysis of contingency tables, estimation theory and simulation based methods.
For all methods the focus is both on applications and on the mathematical background of the statistical methods.

Recommended prerequisites

01001/01002/01003/01004/01005, At the latest at the same time.

Teaching Method

Lectures. Group study and projects.

Faculty

Remarks

The course is a general methodological course aimed at mathematically oriented engineering students. Lectures are given in Danish but similar English lectures are available online.

See course in the course database.

## Registration

Language Dansk 3 weeks Compute DTU Lyngby Campus 02403 Bachelor Week 23 Week 26 Mon-fri 8:00-17:00
Price 9.250,00 DKK