Matematica | PROBABILITY

cod. 0512300043

PROBABILITY

	0512300043
	DIPARTIMENTO DI MATEMATICA
	EQF6
	MATHEMATICS
	2021/2022

PERCORSO SHARED STUDY PATHWAY

	OBBLIGATORIO
	YEAR OF COURSE 3
	YEAR OF DIDACTIC SYSTEM 2018
	AUTUMN SEMESTER

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/06	7	56	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

	Objectives
	THIS COURSE IS FINALIZED TO ILLUSTRATE THE FUNDAMENTAL TOPICS OF PROBABILITY. KNOWLEDGE AND UNDERSTANDING THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY. 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.

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

KNOWLEDGE AND UNDERSTANDING
THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF PROBABILITY. 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.

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

	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.

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.