Stochastics II: Probability Theory and Mathematical Statistics


Contents:
The course 'Stochstics II' continues the course 'Stochastics I' by completing several basic concepts, theorems and methods of probability theory and introduces into the mathematical treatment of statistical problems.

Typical keywords are:
- Independence of random variables
- Dealing with probability distributions and densities
- Convolution of probability distributions
- Characteristic and generating functions
- Special probability distributions, e.g., gamma, c2, p-dimensional normal distribution
- Conditional distribution for distributions with a density
- Convergence in distribution and weak convergence of measures
- Limit theorems: Laws of large numbers, central limit theorems
- Statistical problems: estimation and testing
- Point estimation and confidence intervals
- Hypotheses testing
- Common statistical procedures, e.g., Gauss test, t-test, c2-tests
- Linear models of statistics, regression models
- Elementary decision theory: optimality criteria and optimum procedures
- Basic optimality theorems: Neyman-Pearson lemma, Cramer-Rao bounds

Literature:

  1. BAUER, H.: Wahrscheinlichkeitstheorie. de Gruyter, Berlin, 1991, 520 S.
  2. BILLINGSLEY, P.: Probability and measure. Wiley, New York, 1995, 622 S.
  3. PRUSCHA, H.: Angewandte Methoden der mathematischen Statistik. Teubner, Stuttgart, 1989.
  4. ROHATGI, V.K.: An introduction to probability theory and mathematical statistics. Wiley, New York, 1976.
  5. SERFLING, R.J.: Approximation theorems of mathematical statistics. Wiley, New York, 1980, 371 S.
  6. SHIRYAYEV, A.N.: Probability. Springer, Berlin, 1984, 577 S.
  7. VOGEL, W.: Wahrscheinlichkeitstheorie. Vandenhoeck & Ruprecht, Göttingen, 1970.
  8. WINKLER, W.: Vorlesungen der mathematischen Statistik. Teubner, Stuttgart,1983.
  9. WITTING, H.: Mathematische Statistik I. Teubner, Stuttgart, 1985, 538 S.

Requirements: Basic knowledge in probability theory (Typically: 'Stochastik I')

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