PROBABILITY AND STATISTICS
PROBABILITÀ E STATISTICA MATEMATICA
Probability and Statistics
Probabilità e statistica matematica
| A.Y. | Credits |
|---|---|
| 2017/2018 | 6 |
| Lecturer | Office hours for students | |
|---|---|---|
| Vincenzo Ambrosio | Wednesday from 11.00 to 13.00. |
| Teaching in foreign languages |
|---|
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Course with optional materials in a foreign language
English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language. |
Assigned to the Degree Course
| Date | Time | Classroom / Location |
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| Date | Time | Classroom / Location |
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Learning Objectives
The aim of the course is to provide the basics of the calculus of probability, with particular interest to the probability theory, random variables and probability functions, as well as the main concepts of inferential statistics.
Program
01: Set theory.
02: Combinatorics:
02.01: Sampling, permutation and combination without replacement.
02.02: Sampling, permutation and combination with replacement.
03. Probablity calculus:
03.01 Probability space, events.
03.02 Conditional probability. Independence.
03.03 Law of total probability (and its proof).
03.04 Bayes rule (and its proof).
03.05 Examples, problems and applications.
04. Random variables:
04.01 Independent random variables.
04.02 Expected value, variance and their properties.
05. Discrete random variables:
05.01 Probability Mass function, distribution function.
05.02 Special discrete distributions: Bernoulli, binomial and Poisson distributions.
05.03 Poisson distribution as an approximation for binomial: theorem and proof.
05.04 Geometrical distributions and negative binomial distributions.
06. Continuous random variables:
06.01 Probability density function, distribution function.
06.02 Special continuous distributions: the uniform distribution, Exponential distribution, Gaussian distributions, Chi-squared, the t-distribution, the F-distribution.
07. Limit theorems:
07.01 Markov inequality (and its proof).
07.02 Law of large numbers (and its proof).
07.03 Central limit theorem.
08. Statistical Inference:
08.01 Random samples.
08.02 Consistent and unbiased estimators.
08.03 Sample mean and variance.
08.04 Normal samples.
08.05 Maximum Likelihood Estimation.
09. Hypotheses testing:
09.01 Hypotheses testing for mean and variance of a normal sample. Hypotheses testing for mean and variance of normal independent samples.
09.02 Confidence intervals: confidence intervals for mean and variance of a normal sample.
09.03 Goodness of fit test.
09.04 Test of independence.
Bridging Courses
It is recommended, but not mandatory, to have done the Calculus exam.
Learning Achievements (Dublin Descriptors)
Knowledge and understanding: the student will be acquainted with the basis of the mathematical theory of Probability and of the Inferential Statistics.
Applying knowledge and understanding: the student will be able to theoretically analyse problems where stochastic variability plays a fondamental role.
Making judgements: the student will be able to choose among several approaches the suitable solution to probabilistic problems.
Communication skills: the student will be able to communicate probabilistic informations by use of the techniques of the differential and integral calculus.
Learning skills: the student will learn the methodology to be used in the mathematical formulation of empirical phenomena.
Teaching Material
The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Teaching, Attendance, Course Books and Assessment
- Teaching
Frontal lectures.
- Attendance
The attendance at courses is not mandatory.
- Course books
P. Baldi, "Calcolo delle Probabilità e Statistica", McGraw-Hill.
R. Lupini, "Lezioni di Probabilità e Statistica", Quattroventi.
W. Navidi, "Statistics", Mc Graw-Hill.
D. Posa e S. De Iaco: ”Fondamenti di statistica inferenziale”, CLEUP.
S. Ross: ”Probabilità e statistica per l’ingegneria e le scienze”, APOGEO.
- Assessment
The exam of Probability and Statistics consists of a written exam and an oral one, both of them mandatory.
The written exam, to carry out in two hours, consists of exercises related to the topics of the course. The written exam is passed if the mark is, at least, 15/30. During the written exam it is not allowed to use textbooks, workbooks or notes. Moreover, it is not allowed to use mobile phones, under penalty of disqualification.
The oral exam consists of a discussion related to the topics of the course. The oral exam can be taken only if the written one has been passed. If so, the oral exam can be taken only in the same call in which the written exam has been passed or in the other calls of the same session.
The evaluation of the oral test considers the acquired knowledge, the understanding of the subject, and the ability to present the subject matter strictly.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
Additional Information for Non-Attending Students
- Teaching
Frontal lectures.
- Attendance
The attendance at courses is not mandatory.
- Course books
P. Baldi, "Calcolo delle Probabilità e Statistica", McGraw-Hill.
R. Lupini, "Lezioni di Probabilità e Statistica", Quattroventi.
W. Navidi, "Statistics", Mc Graw-Hill.
D. Posa e S. De Iaco: ”Fondamenti di statistica inferenziale”, CLEUP.
S. Ross: ”Probabilità e statistica per l’ingegneria e le scienze”, APOGEO.
- Assessment
The exam of Probability and Statistics consists of a written exam and an oral one, both of them mandatory.
The written exam, to carry out in two hours, consists of exercises related to the topics of the course. The written exam is passed if the mark is, at least, 15/30. During the written exam it is not allowed to use textbooks, workbooks or notes. Moreover, it is not allowed to use mobile phones, under penalty of disqualification.
The oral exam consists of a discussion related to the topics of the course. The oral exam can be taken only if the written one has been passed. If so, the oral exam can be taken only in the same call in which the written exam has been passed or in the other calls of the same session.
The evaluation of the oral test considers the acquired knowledge, the understanding of the subject, and the ability to present the subject matter strictly.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
Notes
The course offers additional e-learning facilities on the Moodle platform > elearning.uniurb.it
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