Topic 2 (Algebra). Vectorial spaces and linear applications |
Vector space and subspace. Generator systems.
Linear independence. Basis and dimension.
Systems of coordinates. Change of basis.
Linear applications. Associated matrix. Kernel and rank of a linear application. |
Topic 4 (Algebra). Vectorial spaces with scalar product. Quadratic forms |
Vector spaces with scalar product.
Orthogonality. Orthonormal basis. Gram-Schmidt orthogonalization procedure. Orthogonal diagonalization of symmetric matrices. Real quadratic forms. Classification. Sylvester criterion. |
Topic 2 (Statistics). Probability |
Concept and properties. Conditioned probability and independence of events. Bayes Theorem. |
Topic 3 (Statistics). Discrete and continuous random variables |
Concept. Types.
Probability distribution function of a random variable.
Discrete and continuous random variables.
Characteristics of a random variable.
Remarkable distributions: Binomial, geometric, Poisson, hypergeometric, uniform, exponential, normal.
Central limit theorem |
Topic 4 (Statistics). Statistical inference |
General concepts.
Sampling distributions.
Estimation.
Confidence interval estimate.
Hypothesis testing. |