Matrices, determinants and systems of linear equations. |
Definition and types of matrices.
Matrices operations.
Elementary transformations, row echelon forms, rank of a matrix.
Inverse and determinant of a square matrix.
Consistency of systems of linear equations and their solutions. |
Eigenvalues and eigenvectors. |
Definition of eigenvalue and eigenvector of a square matrix.
Diagonalization of matrices by similarity transformation.
Applications of eigenvalues and eigenvectors. |
Probability. |
Concept and properties.
Conditional probability and independence of events.
Bayes Theorem. |
Discrete random variables and continuous random variables. |
Definition of random variable. Types of random variables.
Distribution function.
Discrete random variables. Continuous random variables.
Characteristics of a random variable.
Main distributions: Binomial, Geometric, Poisson, Hypergeometric, Uniform, Exponential, Normal.
Central Limit Theorem. |
Statistical inference. |
General concepts.
Sampling distributions.
Point estimation.
Confidence intervals.
Tests of hypotheses. |