Elements of the theory of probability: discrete and continuous random variables, probability distributions and densities. Multivariate random variables.
Lecture notes and exercises available on the teachers' web page.
P. Baldi – Calcolo delle Probabilita' e Statistica.
S.M.Ross – Calcolo delle probabilita' e Statistica.
Learning Objectives
Knowledge acquired:
Basic knowledge for the statistical treatment of data.
Competence acquired:
Fundamentals of probability.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Courses required: none
Courses recommended: none
Teaching Methods
CFU: 3
Lectures (hours): 24
Type of Assessment
Oral exam. The exam generally consists in theoretical questions on Probability .
Course program
PROBABILITY
Frequentist, subjective, axiomatic definition off probability. Conditional probability, Bayes Theorem. Independence. Random variables. Distribution functions and probability density function. Expected value of a R.V., variance. Functions of random variables.
Most common discrete and continuous probability distributions.
Normal distribution; normalization of a random variable. Joint distributions, marginal density function. Chebychev inequality. Law of large numbers and the central limit theorem.