5006631: Statistics

Qualifications

• • Know about the roles of quantiles, variances, standard deviations and correlations to measure risks.
  • Know the axioms of a discrete probability space.
  • Know the most important distributions and their properties.
  • Know the importance of the central limit theorem.
  • Can describe univariate and bivariate data according to the level of scale using numerical measures and graphical representations.
  • Can explain the content of the axioms of a discrete probability space while modelling a random experiment.
  • Use the law of large numbers to interpret a probability as a relative frequency in the long run.
  • Can explain why and when a certain distribution is used to model economic situations.
  • Can name the basic idea of testing hypotheses referring to the possible types of errors.
  • Name the basic ideas of standard testing procedures.
  • Calculate the critical values in the decision rules of binomial tests.
  • Can explain the meaning of confidence intervals and indicate the duality between confidence intervals and testing hypotheses.
  • Use the principle of ordinary least squares to estimate the parameters of a regression model.
  • Run simple linear regressions, set up the ANOVA-table and judge the residual plot.
  • Calculate probabilities using addition rules, decision trees and combinatorics.
  • Can explain the results of Bayes' theorem.
  • Use limits theorems to approximate distributions and probabilities.
  • Use calculations rules for expectations and variances correctly and can explain their meanings in the context of risk measuring.
  • Calculate the critical values of binomial tests and the resulting probability of a type 2 error.
  • Evaluate the test statistics of standard procedures, read the corresponding critical values from statistical tables and formulate the conclusion of the testing procedure correctly in the given context.
  • Calculate confidence intervals and interpret them correctly in a given context.
  • Interpret measures as quantiles, variances, standard deviations, correlations, skewness, curtosis correctly.
  • Use the vocabulary introduced to them to describe graphical representations correctly and include the advantages and disadvantages of such representations while interpreting them.
  • Judge the certainty or uncertainty of statistical conclusions and formulate their interpretations accordingly.
  • Judge the practical relevance of a linear regression in the given context.
  • Judge the uncertainty in the conclusions from statistical testing procedures correctly
• • Know the central statistical techniques that are often used in business applications.
  • Understand the meaning of statistical notions.
  • Use the concepts introduced in a purposeful way, interpret the results in the context and formulate their conclusions correctly.
  • Use basic commands of the software package R to analyze data graphically and numerically.
  • Apply standard learning techniques in abstract contexts so that they get used to working with scientific publications on their own.
  • Analyze data to justify decisions in business applications.
  • Analyze business cases using methods of probability theory.