Antonio DI CRESCENZO | PROBABILITY AND STATISTICS

cod. 0512300032

PROBABILITY AND STATISTICS

	0512300032
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2016/2017

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO Cohort 2014/2015

	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2010
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/06	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

PROFESSORS

	ANTONIO DI CRESCENZO T Curriculum
	BARBARA MARTINUCCI Curriculum

	Objectives
	THIS COURSE IS FINALIZED TO ILLUSTRATE THE FUNDAMENTAL TOPICS OF PROBABILITY AND DESCRIPTIVE STATISTICS. KNOWLEDGE AND UNDERSTANDING THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY AND 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 INVOLVING RANDOMNESS. ABILITY TO OUTLINE A RANDOM PHENOMENON, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE TOOLS OF PROBABILITY AND STATISTICS.

THIS COURSE IS FINALIZED TO ILLUSTRATE THE FUNDAMENTAL TOPICS OF PROBABILITY AND DESCRIPTIVE STATISTICS.

KNOWLEDGE AND UNDERSTANDING
THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY AND 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 INVOLVING RANDOMNESS. ABILITY TO OUTLINE A RANDOM PHENOMENON, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE TOOLS OF PROBABILITY AND STATISTICS.

	Prerequisites
	THE STUDENT MUST HAVE ACQUIRED THE ABILITY TO DEVELOP LOGICAL-MATHEMATICAL REASONING, BASED ON NOTIONS OF COURSES THE FIRST TWO YEARS OF THE DEGREE IN MATHEMATICS.

	Contents
	SAMPLE SPACE. PROBABILITY. PROBABILITY SPACE. CONDITIONAL PROBABILITY. INDEPENDENCE. RANDOM VARIABLES. DISTRIBUTION FUNCTION. MEAN, STANDARD DEVIATION, VARIANCE. DISCRETE, CONTINUOUS, AND SINGULAR RANDOM VARIABLES. RANDOM VECTORS. INDEPENDENCE. COVARIANCE AND CORRELATION. MOMENTS. MOMENT GENERATING FUNCTION. PROBABILITY GENERATING FUNCTION. CHEBYSHEV INEQUALITY. CONVERGENCE OF RANDOM VARIABLES. LAW OF LARGE NUMBERS. CENTRAL-LIMIT THEOREM. STOCHASTIC PROCESSES. MARKOV PROCESSES. POISSON PROCESSES AND RELATED PROPERTIES. RANDOM WALKS. BROWNIAN NOTION. DESCRIPTIVE STATISTICS.

Contents

SAMPLE SPACE. PROBABILITY. PROBABILITY SPACE. CONDITIONAL PROBABILITY. INDEPENDENCE. RANDOM VARIABLES. DISTRIBUTION FUNCTION. MEAN, STANDARD DEVIATION, VARIANCE. DISCRETE, CONTINUOUS, AND SINGULAR RANDOM VARIABLES. RANDOM VECTORS. INDEPENDENCE. COVARIANCE AND CORRELATION. MOMENTS. MOMENT GENERATING FUNCTION. PROBABILITY GENERATING FUNCTION. CHEBYSHEV INEQUALITY. CONVERGENCE OF RANDOM VARIABLES. LAW OF LARGE NUMBERS. CENTRAL-LIMIT THEOREM. STOCHASTIC PROCESSES. MARKOV PROCESSES. POISSON PROCESSES AND RELATED PROPERTIES. RANDOM WALKS. BROWNIAN NOTION. DESCRIPTIVE STATISTICS.

	Teaching Methods
	LECTURES AND CLASSROOM EXERCISES.

	Verification of learning
	ORAL EXAMINATION TESTING THE KNOWLEDGE OF THE DISCIPLINE.

	Texts
	- KARLIN S., TAYLOR H.M. (1975) A FIRST COURSE IN STOCHASTIC PROCESSES. II EDIZIONE. ACADEMIC PRESS. - ROSS S.M. (1996) STOCHASTIC PROCESSES. II EDIZIONE. WILEY.

	More Information
	THE ATTENDANCE IN TERM TIME IS RECOMMENDED.

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Antonio DI CRESCENZO | PROBABILITY AND STATISTICS