Antonio DI CRESCENZO | PROBABILITY AND MATHEMATICAL STATISTICS

cod. 0512100009

PROBABILITY AND MATHEMATICAL STATISTICS

	0512100009
	DIPARTIMENTO DI INFORMATICA
	EQF6
	COMPUTER SCIENCE
	2016/2017

CURRICULUM METODOLOGICO

	OBBLIGATORIO
	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2015
	PRIMO SEMESTRE

TEACHING UNITS

SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
MAT/06	4	32	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS
MAT/06	2	16	EXERCISES	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	ANTONIO DI CRESCENZO T Curriculum
	BARBARA MARTINUCCI Curriculum

	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.

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 DISCRETE MATHEMATICS, LOGIC, COMBINATORICS, 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.

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 EXERCISES, RELATED TO PROBLEMS OF INTEREST IN COMPUTER SCIENCE.

	Verification of learning
	ORAL EXAMINATION TO TEST THE KNOWLEDGE OF THE DISCIPLINE.

	Texts
	- ROSS S. (2010) A FIRST COURSE IN PROBABILITY. 8TH EDITION. PEARSON. - FREUND J.E., WALPOLE R.E. (1992) MATHEMATICAL STATISTICS. FIFTH EDITION. PRENTICE HALL.

	More Information
	SOME UTILITIES AND EDUCATIONAL AIDS ARE AVAILABLE AT HTTP://ELEARNING.INFORMATICA.UNISA.IT/EL-PLATFORM/ THE ATTENDANCE AND REGULAR STUDY IN TERM TIME ARE RECOMMENDED.

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Antonio DI CRESCENZO | PROBABILITY AND MATHEMATICAL STATISTICS