## Probability theory

### Teaching unit

### Description

Deterministic and stochastic experiments. Sample space , events , operations with events . axiomatic definition of probability , probability space . Approaches to the concept of probability. conditional probability . Independence of events . Theorems compound probability , total probability and Bayes. Calculation of probabilities.

### Objectives

Know and apply the concepts and basic principles of probability theory , solving problems of probability calculation , applying the concepts and principles above and in particular the conditional probability and theorems of Bayes, the composite probability and total probability. Interpret results.

### Subjects

#### Lecture topics

- Motivation.
- Stochastic experiments. Events. Algebra of events.
- Axiomatic definition of probability. Probability space.
- Approaches to the concept of probability.
- Independence of events and conditional probability.
- Theorems composed wholly and Bayes probability.
- Concluding remarks and applications.
- Solved exercises.

#### Laboratory topics

- Probability calculation I.