Introduction to Mathematical Statistics

• 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 the programme R.
• 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 the programme R and interpret output from it
• Interpret power considerations and perform sample size calculations in different settings using the programme R
• Debate and critize emprically based information.

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.

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

Lectures. Group study and projects.

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.