CC Mathematics 2. - 3PMKMAT2

Goal(s)

This course has three main objectives

• 1. model experiments/problems with the aid of probability theory
  2. apply statistical inference to adjust a model to given data
  3. test a hypothesis to evaluate the conformity of a model (family) to given data

Content(s)

• 1. Probabilities
  • probability axioms of Kolmogorov
  • real random variables (numbers and vectors): definitions, properties
  • mathematical expectation, moments, and characteristic functions
  • variable change and the transfer theorem
  • concentration inequalities (Chebychev, Kolmogorov) and the laws of big numbers (weak, strong and central limit theorem)
  1. Statistics
  • vocabulary and terminology
    • descriptive statistics
    • empirical moments
    • Fisher's theorem (Fisher's theorem, Helmert's law, Gosset's theorem)
  • parametric estimation
    • method of moments (K. Pearson)
    • maximum likelihood estimator (R.A. Fisher) and properties
    • the eternal balance between bias and variance: inequality of Cramér-Rao
  • hypothesis testing
    • test of adequacy (Khi2 of K. Pearson) and introduction to the number of degrees of freedom
    • comparison tests (Kolmogorov and Smirnov)

• mathematical analysis
• TU 3PUKMATH
• probabilities : axioms, combinatorial, discrete