Matematica | PROBABILITY AND STATISTICS

Matematica PROBABILITY AND STATISTICS

 0512300032 DIPARTIMENTO DI MATEMATICA MATHEMATICS 2015/2016

 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
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.
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.