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

DT0003

### Type of course unit:

Bachelor Degree in Computer Science curriculum General: Compulsory

1st semester

### Number of credits:

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

### Teachers:

Davide Gabrielli (gabriellunivaqit)
Umberto Triacca (umbertotriaccaunivaqit)

## 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