# Matematica | PROBABILITY

## Matematica PROBABILITY

 0512300043 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2020/2021

 OBBLIGATORIO YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2018 PRIMO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/06 7 56 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 ANTONIO DI CRESCENZO T
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.
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.
Teaching Methods
LECTURES AND CLASSROOM EXERCISES.
Verification of learning
ORAL EXAMINATION TO TEST THE KNOWLEDGE OF THE DISCIPLINE.
Texts
- ROSS S.M. (2010) A FIRST COURSE IN PROBABILITY. PEARSON PRENTICE HALL.