# Course Details

#### Name:

**Calcolo delle Probabilità e Statistica Matematica / Probability And Mathematical Statistics**

### Basic information

##### Credits:

*Bachelor Degree in Computer Science:* 6 Ects (c)

##### Degree(s):

Compulsory 2^{nd} year Bachelor Degree in Computer Science curriculum General

##### Language:

Italian

### Course Objectives

An introduction to the theory of probability up to the weak law of large numbers

### Course Content

- BASIC PROBABILITY: probability space, sets and elementary operations, Venn diagragms, basic axioms, inclusion-exclusion formula, enumeration principle
and generalized enumeration principle, uniform probability spaces, permutations and combinations, conditional probability, disintegration formula, Bayes Formula, independence.
- RANDOM VARIABLES AND EXPECTED VALUE: discrete and continuous random variables, mass distribution and density, distribution function, joint and marginal distributions, expected value and its properties, variance and covariance, weak law of large numbers.
- EXAMPLES OF RANDOM VARIABLES: random variables of the following type: Bernoulli, binomial, Poisson, uniform,
Gaussian, exponential, geometric.
- INTRODUCTION TO STATISTICAL INFERENCE: the inference problem, parametric and non parametric inference
- ELEMENTS OF PARAMETRIC ESTIMATES: random samples, estimators, mean squared error. Estimators for finite samples and their properties
(bias and efficiency). Estimators for large samples (consistency and asymptotic normality). maximum likelihood method, estimates for intervals.
- ELEMENTS OF HYPOTHESIS VERIFICATION: the statistical test, general facts, first order error, significance level and the p value.
The power function of a test. Hypothesis test on the average of a Gaussian sample with given variance. Hypotesis test on the average
of Gaussian sample with unknown variance.

### Prerequisites and Learning Activities

elementary mathematics and some notions of mathematical analysis

### Teaching Methods

**Language**: Italian

frontal lectures

### Assessment Methods and Criteria

written exam with exercises and theoric questions

### Textbooks

- S M Ross,
**Probabilità e statistica**. Maggioli. * *

### Online Teaching Resources

### Recent teaching material

This list contains only the latest published resources. Resources marked with an asterisk belong to other courses (indicated between brackets)

### Course page updates

This course page is available (with possible updates) also for the following academic years:

*Course information last updated on: 16 gennaio 2018, 14:08*