## Probabilitat

### Teaching unit

### Description

basic concepts of probability: experiments, random variables, sample space, events, operations with events, concept of probability, determined probability, marginal probability, theorem of the total probability, Bayes's theorem and independence of events. Notable distributions.

### Objectives

Identify the elements of random situations and the basic probabilistic elements in real problems.

To apply the basic results of dependence or independence for the calculation of probabilities in real problems.

To identify probability distributions in real problems and to resolve their probabilistic calculations.

### Subjects

#### Lecture topics

- Basic Concepts of probability
- Probability of compound events. Properties. Dependence and independence of events.
- Conditional probability. Total probability theorem and Bayes theorem
- Random variables. Probability distribucions. Expectation and variance.
- Categorical distributions: Bernoulli, Binomial, and Poisson.
- Normal distribution and the central limit theorem
- Distributions related to the Normal: Chi-square, Student t, and F of Snedecor.

#### Laboratory topics

- The random identification in real problems
- Probability applied to real problems.
- Categorical distributions in real problems.
- Continuous distributions in real problems