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.
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. Choice of significance level and power. Chi2-test of distribution, test of homogeneity and contingency. Simple and multiple linear regression.
To pass the course, the student should be able to do the following:
- construct elementary statistical models for experiments
- describe standard models and explain the applicability of the models in given examples
- define and calculate descriptive quantities like expectation, variance, and percentiles for distributions and data sets.
- with standard methods calculate estimates of unknown quantities and quantify the uncertainty in these estimates
- value and compare methods of estimation
- analyse how measuring accuracy affect conclusions and quantify risks and error probabilities in statistical analysis
- design test and select sample sizes so that desired precision of estimates and significance level and power of tests are achieved
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.
