# Programme of Course "Calcolo delle Probabilità e Statistica Matematica"

### Code:

DT0003

### Type of course unit:

*Bachelor Degree in Computer Science curriculum General:*Compulsory

### Level of course unit:

Undergraduate Degrees

### Semester:

1

^{st}semester### Number of credits:

*Bachelor Degree in Computer Science:*6 (workload 150 hours)

### Teachers:

## 1. Course Objectives

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

## 2. Course Contents and learning outcomes (Dublin Descriptors)

Topics of the course include:

- 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.

## 3. Course Prerequisites

elementary mathematics and some notions of mathematical analysis

## 4. Teaching methods and language

frontal lectures

**Language:**Italian

### Reference textbooks

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

## 5. Assessment Methods

written exam with exercises and theoric questions

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