Module 1 (3 ECTS): Basic Probability Theory. The notions probability, discrete and continuous random variable, probability function, probability density function, cumulative distribution function, expected value, variance, standard deviation, covariance and correlation, are defined. Furthermore, the most common probability distributions for technical applications are treated, with special emphasis on the normal distribution, distributions for linear combinations of normally and non-normally random variables (in the latter case applying the central limit theorem), and approximations of expected values and variances for non-linear functions of random variables.
Module 2 (3 ECTS): Basic Inference Theory with special emphasis on Technical applications. The notions point estimate, unbiasedness, efficiency, hypothesis, significance level, power, type I and II errors, rejection region, p value and confidence level, are defined. The t-, Chi2-, and F-distributions are applied for hypothesis testing and interval estimation for one and two samples. During the course the sign test, Wilcoxon's two sample test, the analysis of contingency tables, basic analysis of variance, and simple and multiple regression analysis, are covered.
Module 3 (1.5 ECTS): Computer Labaorations using Statistical Software.