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Probability, statistics and computer science

A.Y. 2019/2020

Learning objectives

The aim of this course is to provide the students with the basic instruments of data analysis, univariate statistics and informatics needed to store, manage and statistically analyse real data. The course is divided into 2 modules

Part 1: Descriptive statistics; introduction to probability and random variables; inferential Statistics; computer lab case studies.

Part 2: Introduction to Informatics; hardware and software; elements of scientific programming.

Part 1: Descriptive statistics; introduction to probability and random variables; inferential Statistics; computer lab case studies.

Part 2: Introduction to Informatics; hardware and software; elements of scientific programming.

Expected learning outcomes

At the end of the course the student will have acquired the basic knowledge related to the descriptive statisitca, the probability, the inferential statisitca, the computer science and the scientific programming. The student will acquire skills that will allow him to independently perform simple data analysis, formalize a real problem in mathematical or probabilistic terms, and develop simple programming codes.

**Lesson period:**
Second semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### Single session

Responsible

Lesson period

Second semester

**Course syllabus**

MODULE 1: Probability and Statistics.

Descriptive statistics:

1)Sampling from populations. Types of data and variables.

2)Partitioning of data into classes and construction of frequency tables. Histograms and bar charts.

3)Centrality indexes (mean, mode, median, midrange). Dispersion indices (range, standard deviation, variance), percentiles, quartiles. Outliers, boxplots.

Probability and random variables:

4)Sample space, events, probability of events

5)Probability of union and intersection of events. Complementary events. Independent events. Conditional probability. Bayes theorem. Factorials and binomial coefficients.

6)Random variables. Expected value, variance and standard deviation of discrete r.v.

7)Discrete r.v.'s: binomial and Poisson. Continuous r.v.'s: uniform and normal.

8)Standardization and properties of normal distribution. Normal approximation of the binomial distribution.

Inferential statistics:

9)Fundamental concepts: population, sample, parameter, statistics, estimator. Behaviour of the sample mean: law of large numbers and central limit theorem. Punctual estimate.

10)Confidence intervals: general concepts. Confidence interval for a proportion.

11)Confidence interval for the mean, both with known and unknown standard deviation. T Student distribution.

12)Statistical hypothesis testing. General concepts: null and alternate hypotheses, first and second type errors, significance level, power function, p value, test statistics, critical region.

13)Hypothesis test on a proportion. Hypothesis tests on the mean (both with known and unknown variance)

14)Inference for two samples: inference for two proportions. Inference for two means, both for paired or independent samples.

15)One and two way ANOVA

Bivariate statistics:

16)Test of independence and of fit. Chi squared distribution.

Computer lab

17)Illustrative examples of applications of descriptive, inferential and predictive statistics on real data, through the use of simple statistical softwares.

MODULE 2: Informatics

The module consists of theoretical lectures and labs.

Theory:

1) The meaning of Computer Science, algorithms and programs;

2) Computer architecture and digital information;

3) Low and high level programming: compilers and interpreters;

4) Foundations of structured programming;

5) The Python language: data types, control structures, functions and files.

Lab:

1) Operating systems and file system;

2) Programming environment and tools;

3) Programming activity related to theoretical topics above presented.

Descriptive statistics:

1)Sampling from populations. Types of data and variables.

2)Partitioning of data into classes and construction of frequency tables. Histograms and bar charts.

3)Centrality indexes (mean, mode, median, midrange). Dispersion indices (range, standard deviation, variance), percentiles, quartiles. Outliers, boxplots.

Probability and random variables:

4)Sample space, events, probability of events

5)Probability of union and intersection of events. Complementary events. Independent events. Conditional probability. Bayes theorem. Factorials and binomial coefficients.

6)Random variables. Expected value, variance and standard deviation of discrete r.v.

7)Discrete r.v.'s: binomial and Poisson. Continuous r.v.'s: uniform and normal.

8)Standardization and properties of normal distribution. Normal approximation of the binomial distribution.

Inferential statistics:

9)Fundamental concepts: population, sample, parameter, statistics, estimator. Behaviour of the sample mean: law of large numbers and central limit theorem. Punctual estimate.

10)Confidence intervals: general concepts. Confidence interval for a proportion.

11)Confidence interval for the mean, both with known and unknown standard deviation. T Student distribution.

12)Statistical hypothesis testing. General concepts: null and alternate hypotheses, first and second type errors, significance level, power function, p value, test statistics, critical region.

13)Hypothesis test on a proportion. Hypothesis tests on the mean (both with known and unknown variance)

14)Inference for two samples: inference for two proportions. Inference for two means, both for paired or independent samples.

15)One and two way ANOVA

Bivariate statistics:

16)Test of independence and of fit. Chi squared distribution.

Computer lab

17)Illustrative examples of applications of descriptive, inferential and predictive statistics on real data, through the use of simple statistical softwares.

MODULE 2: Informatics

The module consists of theoretical lectures and labs.

Theory:

1) The meaning of Computer Science, algorithms and programs;

2) Computer architecture and digital information;

3) Low and high level programming: compilers and interpreters;

4) Foundations of structured programming;

5) The Python language: data types, control structures, functions and files.

Lab:

1) Operating systems and file system;

2) Programming environment and tools;

3) Programming activity related to theoretical topics above presented.

**Prerequisites for admission**

It is required the knowledge of the contents of the course Mathematics, of which is advised to take previously the exam.

**Teaching methods**

Frontal lectures and computer labs

**Teaching Resources**

MODULE 1:

-Triola M.M. e Triola M.F., Statistica per le discipline biosanitarie, Pearson, 2009.

-Lecture notes and slides of the teachers available on the web site of the course on ARIEL

MODULE 2:

Textbook: Tony Gaddis, "Introduzione a Python",

Editor: Pearson

Series: Informatica

Year edition: 2016

Website of the course: http://palano.di.unimi.it/informatica/

-Triola M.M. e Triola M.F., Statistica per le discipline biosanitarie, Pearson, 2009.

-Lecture notes and slides of the teachers available on the web site of the course on ARIEL

MODULE 2:

Textbook: Tony Gaddis, "Introduzione a Python",

Editor: Pearson

Series: Informatica

Year edition: 2016

Website of the course: http://palano.di.unimi.it/informatica/

**Assessment methods and Criteria**

MODULE 1:

The final examination consists of a written exam during which the student must solve some exercises in the format of open-ended and/or multiple choice answer questions, plus comments to computer outputs with the aim of assessing the student's ability to solve simple problems in probability and statistics.

The duration of the written exam will be proportional to the number of exercises assigned, also taking into account the nature and complexity of the exercises themselves (however, the usual duration is two hours).

MODULE 2:

The exam of the module of Informatics consists of a lab test, composed both by theoretical questions or exercises on the course programme, and in the development of a small project in Python.

The global exam is passed if both the tests of the first and second module are passed. Final marks are given using the numerical range 0-30 and is composed as the weighted mean (with credits) of the grades of the two modules. It will be available in the SIFA service through the UNIMIA portal, and on the web sites of the course.

It is mandatory to pass the exams of both modules by the end of the academic year. After this time, the tests of both modules must be taken and passed again.

The final examination consists of a written exam during which the student must solve some exercises in the format of open-ended and/or multiple choice answer questions, plus comments to computer outputs with the aim of assessing the student's ability to solve simple problems in probability and statistics.

The duration of the written exam will be proportional to the number of exercises assigned, also taking into account the nature and complexity of the exercises themselves (however, the usual duration is two hours).

MODULE 2:

The exam of the module of Informatics consists of a lab test, composed both by theoretical questions or exercises on the course programme, and in the development of a small project in Python.

The global exam is passed if both the tests of the first and second module are passed. Final marks are given using the numerical range 0-30 and is composed as the weighted mean (with credits) of the grades of the two modules. It will be available in the SIFA service through the UNIMIA portal, and on the web sites of the course.

It is mandatory to pass the exams of both modules by the end of the academic year. After this time, the tests of both modules must be taken and passed again.

Computer science

INF/01 - INFORMATICS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

Practicals: 16 hours

Lessons: 24 hours

Lessons: 24 hours

Professors:
Palano Beatrice Santa, Valota Diego

Probability, statistics

INF/01 - INFORMATICS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

Practicals: 16 hours

Lessons: 32 hours

Lessons: 32 hours

Professors:
Maurelli Mario, Micheletti Alessandra

Professor(s)

Reception:

Monday 14-16 by appointment by email; other days by appointment by email

online meeting