The course has two main goals. To acquire a working knowledge of basic
a) discrete and continuous probability: probability spaces, random variables, probability distributions, and some basic limit theorems,
b) descriptive and inferential statistics: sampling, data description, sample statistics, estimators, confidence intervals, and hypothesis testing.
a) discrete and continuous probability: probability spaces, random variables, probability distributions, and some basic limit theorems,
b) descriptive and inferential statistics: sampling, data description, sample statistics, estimators, confidence intervals, and hypothesis testing.
Curriculum
Canali
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Programma
Lectures will cover the material presented in the following chapter of the book by Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc)Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Testi Adottati
Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc.Modalità Frequenza
Optional.Modalità Valutazione
The exams will be written. The typical exam text contains 5-6 questions, a couple of which are theoretical and the others are more applied. Each question is worth a certain number of points and the total sum of the points generally slightly exceeds the threshold of 30 pts.Canali
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Programma
Lectures will cover the material presented in the following chapter of the book by Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc)Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Testi Adottati
Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc.Modalità Frequenza
Optional.Modalità Valutazione
The exams will be written. The typical exam text contains 5-6 questions, a couple of which are theoretical and the others are more applied. Each question is worth a certain number of points and the total sum of the points generally slightly exceeds the threshold of 30 pts.Canali
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Programma
Lectures will cover the material presented in the following chapter of the book by Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc)Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Testi Adottati
Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc.Modalità Frequenza
Optional.Modalità Valutazione
The exams will be written. The typical exam text contains 5-6 questions, a couple of which are theoretical and the others are more applied. Each question is worth a certain number of points and the total sum of the points generally slightly exceeds the threshold of 30 pts.Canali
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Programma
Chapter and section numbers are taken from the basic textbook S. Ross "INTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS"Cap. 1: 1.1, 1.2, 1.3
Cap. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.4, 2.5, 2.6
Cap. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Cap. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.9
Cap. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.7, 5.8.1., 5.8.2.
Cap. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Cap. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7
Cap. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6,
Cap. 9: 9.1, 9.2, 9.3, 9.6
Cap. 11: 11.1, 11.2, 11.4 (for this part you may also look at chapters 6.4, 6.5 of the book (in Italian) "Moduli di matematica e statistica con uso di R" di S. Invernizzi, M. Rinaldi e F. Comoglio).
Testi Adottati
- Sheldon Ross NTRODUCTION TO PROBABILITY AND STATISTICS FOR ENGINEERS AND SCIENTISTS- "Moduli di matematica e statistica" di S. Invernizzi, M. Rinaldi e F. Comoglio, ed. Zanichelli.
additional reference: Luca Leuzzi, Enzo Marinari, Giorgio Parisi
CALCOLO DELLE PROBABILITÀ: un trattatello per principianti volenterosi
Modalità Erogazione
Standard lecture including several examples and exercisesModalità Frequenza
OptionalModalità Valutazione
Evaluations are via written exam. The typical exam contains 5-6 questions with a couple of questions of a more theoretical character. Each question carries a certain number of points whose total is slightly above 30 pts.
scheda docente
materiale didattico
Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Programma
Lectures will cover the material presented in the following chapter of the book by Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc)Ch. 1: 1.1, 1.2, 1.3
Ch. 2: 2.2, 2.2.1, 2.2.2, 2.3, 2.3.1, 2.3.2, 2.3.3, 2.4, 2.5, 2.6
Ch. 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.5.1, 3.6, 3.7, 3.8
Ch. 4: 4.1, 4.2, 4.3, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5, 4.5.1, 4.6, 4.7, 4.8, 4.9
Ch. 5: 5.1, 5.2, 5.4, 5.5, 5.6, 5.6.1, 5.8.1, 5.8.2.
Ch. 6: 6.1, 6.2, 6.3, 6.3.1, 6.3.2, 6.4, 6.5, 6.5.1, 6.5.2
Ch. 7: 7.1, 7.2, 7.3, 7.3.1, 7.3.2, 7.4, 7.5, 7.7, 7.8
Ch. 8: 8.1, 8.2, 8.3, 8.3.1, 8.3.2, 8.4.1, 8.6
Ch. 9: 9.1, 9.2, 9.3, 9.6,
Ch. 11: 11.1, 11.2, 11.4.
Testi Adottati
Sheldon Ross, “Introduction to Probability and Statistics for Engineers and Scientists", Elsevier Science Publishing Co Inc.Modalità Frequenza
Optional.Modalità Valutazione
The exams will be written. The typical exam text contains 5-6 questions, a couple of which are theoretical and the others are more applied. Each question is worth a certain number of points and the total sum of the points generally slightly exceeds the threshold of 30 pts.