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Programme of Course "Calcolo delle Probabilità e Statistica Matematica"



Type of course unit:

Bachelor Degree in Computer Science curriculum General: Compulsory

Level of course unit:

Undergraduate Degrees


1st semester

Number of credits:

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


Davide Gabrielli (gabriellatunivaqdotit)
Umberto Triacca (umbertodottriaccaatunivaqdotit)

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


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