Basic concepts like probabilities, conditional probabilities and independent events. Discrete and continuous random variables, especially one dimensional random variables. Measures of location, scale and dependency of random variables and data sets. Common distributions and models: normal, binomial and Poisson distribution. Central limit theorem and Law of large numbers.
Descriptive statistics. Graphical visualisation of data sets.
Point estimates and general methods of estimation as the method of maximum likelihood and least squares. General confidence intervals but specifically confidence intervals for mean and variance of normally distributed observations. Confidence intervals for proportions, difference in means and proportions.
Testing statistical hypothesis. Chi2-test of distribution, test of homogeneity and contigency. Linear regression.
To pass the course, the student should be able to do the following:
- construct elementary statistical models for experiments
- state standard models and explain the applicability of the models in given examples
- calculate descriptive quantities like expectation, variance, and percentiles for distributions and data sets and graphically present data sets
- with standard methods calculate estimates of unknown quantities and quantify the uncertainty in these estimates
- describe how measuring accuracy affect conclusions and quantify risks and error probabilities when testing statistical hypothesis
- perform simple computer simulations
- critically analyse statistical information and investigations
- give examples on public statistical production
To receive the highest grade, the student should in addition be able to do the following:
- Combine all the concepts and methods mentioned above in order to solve more complex problems.