Antonio DI CRESCENZO | PROBABILITY AND STATISTICS
Antonio DI CRESCENZO PROBABILITY AND STATISTICS
cod. 0522200033
PROBABILITY AND STATISTICS
| 0522200033 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF7 | |
| MATHEMATICS | |
| 2016/2017 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/06 | 6 | 48 | LESSONS |
| 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. |
| More Information | |
|---|---|
| THE ATTENDANCE IN TERM TIME IS RECOMMENDED. |
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