MATHEMATICS FOR STATISTICS

Single discipline educational activity

Course Sheet

Academic Year of enrolment:

2017/2018

Type of Course:

Basic

Optional/Mandatory:

Optional

Degree:

Bachelor's Degree Programme in SECURITY AND INTERNATIONAL COOPERATION

Disciplinary Sector:

MATHEMATICAL ANALYSIS

Language:

Italian

Credits:

Programme Year:

Hours of classroom activity:

Prerequisites:

General Mathematics Knowledge, as provided by a reasonably good High School diploma. Fundamentals of vector and matrix algebra. Familiarity with systems of linear equations. Elements of differential and integral calculus.

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MATHEMATICS FOR STATISTICS

NATURAL SCIENCES

AF code:

A001305

Assessment Methods

Verification of learning:

The evaluation is determined by one or more written tests, aimed at verifying the acquisition of knowledge and skills as reported by the European descriptor system (Dublin Descriptors) for three-year college degrees. In particular, with regard to the Knowledge and Understanding, to become familiar with some basic probability and statistics techniques; with regard to the Applied Knowledge and Understanding, to develop and support reasoning on statistical and mathematical issues relevant to the scope of study; with regard to Judgment Making, to be able to perform simple statistical analysis; with regard to Communication Skills, to know how to communicate the ideas behind the solution/s to a sampling and data analysis problem; with regard to Learning Skills, to have developed the mathematical skills needed to undertake with a high degree of autonomy further studies. At the student’s or teacher's request, evaluation may be supplemented by an oral test.

Teaching period

First semester

Objectives

To develop mathematical skills in the collection, representation and analysis of data. To introduce the statistical analysis with which to extract information from raw data and the application of mathematical models capable of inducing the characteristics of a population from the observation of a part of it (sample), usually selected through random sampling techniques.

Contents

Descriptive statistics:
The statistical survey. Classification of variables. Frequency distribution of a descriptive variable. Graphic representations. Cumulative function.
Density for class distributions. Data numerical description. Central tendency measures: mode, mean and median. Variability measures: variation range and interquartile coefficient, variance and mean square deviation, variation coefficient
Asymmetry measures. Relationships between variables. Linear Relationships: Regression Model.
Probability:
Random Experiment. Sample space. Sets of events. Properties of sets of events. Conditional Events. Axiomatic definition of probability according to Kolmogorov. Elementary laws of probability. Operative definitions of probability: combinatorial, frequentist and subjective. Conditional probability. Independent Events. Total probability theorem. The Bayes Theorem. Random variables and distribution functions: discrete and continuous. Cumulative function. Expectation value. Central tendency and dispersion around the mean. Mode, mean and median of a random variable. Variance and standard deviation. Chebychev's inequality and the meaning of standard deviation. Independence between random variables. Discrete random variables: Uniform, Bernoulli, Binomial, Poisson. Probability density function. Continuous random variables: Normal, t-Student, Chi-Square, Fisher. Central limit theorem.
Inferential Statistics:
The inferential problem. The probabilistic sampling. Sample statistics and parameter estimators. Correctness, efficiency, consistency of an estimator. Sample mean and sample variance. Point Estimate. Confidence interval. Decisions under uncertainty: hypothesis tests. Significance level and critical values. Type I and Type II errors.
Estimation of the regression curve of a bivariate population: The least squares method and the method of maximum likelihood. Linear regression. Statistical significance of the regression line. Intercept and gradient confidence intervals.

Recommended Bibliography

Notes and exercises prepared by teacher.
Web pages related to the course topics, (such as: https://www.statlect.com/)

Methods of Provision

Conventional

Teaching Methods

Lessons will be held twice a week and organized in two sessions of 45 minutes each. With particular reference to issues related to the management of potential long distance students, there will be set up adequate teaching support and online communication tools.

Contacts/More Information

Contacts:
Department of SCIENCE FOR NATURE AND ENVIRONMENTAL RESOURCES
VIA PIANDANNA 4 SASSARI
Tel. 079 229486; Cell. 347 116 1591; Fax 079 229482;
e-mail: pensa@uniss.it
Supervision hours: Please contact the teacher by @mail.
Available to offer individual assistance in a foreign language to incoming students (English): YES
Materials prepared by the teacher will be made available to students in the online Moodle platform and in a dedicated DropBox file. Available to accept examination of incoming students also in foreign language (English): YES

In order to acquire greater skills in the topics considered as basics and improve understanding of the arguments
presented in the course, the use of the following website is recommended: https://www.khanacademy.org/

MATHEMATICS FOR STATISTICS

Course year: 1

Course year: 3

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MATHEMATICS FOR STATISTICS