Matematica | PROBABILITY AND STATISTICS

cod. 0512300032

PROBABILITY AND STATISTICS

	0512300032
	DIPARTIMENTO DI MATEMATICA

	MATHEMATICS
	2015/2016

CURRICULUM MATEMATICA AD INDIRIZZO APPLICATIVO

	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
	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. MAKING JUDGEMENTS CRITICAL THINKING SKILLS. ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO ANALYZE AND INTERPRET PROBLEMS. COMMUNICATION SKILLS ABILITY TO DISCUSS TOPICS INVOLVING PROBABILITY AND STATISTICS. LEARNING SKILLS ABILITY TO ACQUIRE AND MANAGE NEW INFORMATION RELATED TO MODELS IN THE PRESENCE OF RANDOMNESS.

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.

MAKING JUDGEMENTS
CRITICAL THINKING SKILLS. ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO ANALYZE AND INTERPRET PROBLEMS.

COMMUNICATION SKILLS
ABILITY TO DISCUSS TOPICS INVOLVING PROBABILITY AND STATISTICS.

LEARNING SKILLS
ABILITY TO ACQUIRE AND MANAGE NEW INFORMATION RELATED TO MODELS IN THE PRESENCE OF RANDOMNESS.

	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 AND CONTINUOUS 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. 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 AND CONTINUOUS 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. POISSON PROCESSES AND RELATED PROPERTIES. RANDOM WALKS. BROWNIAN NOTION. DESCRIPTIVE STATISTICS.

	Teaching Methods
	LECTURES AND CLASSROOM EXERCISES.

	Verification of learning
	ORAL EXAMINATION.

	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.