# Matematica | PROBABILITY AND STATISTICS

## Matematica PROBABILITY AND STATISTICS

 0512300032 DIPARTIMENTO DI MATEMATICA EQF6 MATHEMATICS 2016/2017

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2010 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/06 6 48 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 ANTONIO DI CRESCENZO T BARBARA MARTINUCCI
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.

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.
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.