# Computer science | PROBABILITY AND MATHEMATICAL STATISTICS

## Computer science PROBABILITY AND MATHEMATICAL STATISTICS

 0512100009 COMPUTER SCIENCE EQF6 COMPUTER SCIENCE 2022/2023

 OBBLIGATORIO YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2017 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/06 6 48 LESSONS BASIC COMPULSORY SUBJECTS

 VIRGINIA GIORNO T
Objectives
KNOWLEDGE AND UNDERSTANDING
UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY AND MATHEMATICAL STATISTICS. ABILITY TO IDENTIFY A PROBABILISTIC MODEL AND TO UNDERSTAND ITS MAIN FEATURES.

APPLYING KNOWLEDGE AND UNDERSTANDING
INDUCTIVE AND DEDUCTIVE REASONING SKILLS IN DEALING WITH PROBLEMS, MAINLY OF COMPUTER SCIENCE, INVOLVING RANDOMNESS. ABILITY TO OUTLINE A RANDOM PHENOMENON, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE TOOLS OF PROBABILITY AND MATHEMATICAL STATISTICS, WITH PARTICULAR REFERENCE TO DISCRETE PROBABILITY AND COMBINATORICS, RANDOM VARIABLES (AND THEIR MAIN CHARACTERISTICS), LIMIT THEOREMS AND THEIR APPLICATIONS TO STATISTICS.

Prerequisites
STUDENTS MUST HAVE ACQUIRED KNOWLEDGE ON ELEMENTS OF SET THEORY, FUNCTIONS, DERIVATIVES, INTEGRALS.
Contents
SAMPLE SPACE. PROBABILITY. PROBABILITY SPACE. CONDITIONAL PROBABILITY. INDEPENDENCE. RANDOM VARIABLES. DISTRIBUTION FUNCTION. MEAN, STANDARD DEVIATION, VARIANCE. DISCRETE AND CONTINUOUS RANDOM VARIABLES. BIDIMENSIONAL DISCRETE RANDOM VARIABLES. INDEPENDENCE. COVARIANCE AND CORRELATION. MOMENTS. MARKOV AND CHEBYSHEV INEQUALITYIES. LAW OF LARGE NUMBERS. CENTRAL-LIMIT THEOREM. SAMPLING. STATISTICAL INFERENCE. ESTIMATION. DISTRIBUTION OF SAMPLE MEAN. FREQUENCY TABLES. DIAGRAMS. HISTOGRAMS. SAMPLE PERCENTILES. DATA ANALYSIS.
Teaching Methods
LECTURES AND CLASSROOM (4 CFU) AND SOLUTION OF EXERCISES (2 CFU), RELATED TO PROBLEMS OF INTEREST IN COMPUTER SCIENCE.
Verification of learning
ORAL EXAMINATION TO TEST THE KNOWLEDGE OF THE DISCIPLINE.

THE ORAL TEST MAY BE REPLACED BY TWO MID-TERMS WRITTEN EXAMS.
Texts
- DI CRESCENZO A., GIORNO V., NOBILE A.G. E RICCIARDI L.M. (2009) UN PRIMO CORSO IN PROBABILITÀ. PER SCIENZE PURE E APPLICATE. LIGUORI.
- RICCIARDI L.M. E RINALDI S. (1994) ESERCIZI DI CALCOLO DELLE PROBABILITÀ. LIGUORI.

TESTI DI CONSULTAZIONE E APPROFONDIMENTO:
- ROSS S.M. (2007) CALCOLO DELLE PROBABILITÀ. II EDIZIONE. APOGEO.
- JOHNSON R.A. (2007) PROBABILITÀ E STATISTICA PER INGEGNERIA E SCIENZE. PEARSON.