Calculus (Course 1 - Semester 1) and Linear Algebra (Course 1 - Semester 1)

The objective of this course is for the student to acquire a set of tools or skills related to Statistics both at a theoretical and applied level. -Proficiency to analyze and synthetize the main information content in a set of univariate and multivariate data. -Proficiency to compute probabilities and statistical moments at different dimensions -Proficiency to use random variables as a statistical device to model real phenomena. -Proficiency to identify the appropriate probability model for specific real situations. -Knowledge of the properties of point and interval estimation methods, with the aim of doing statistical inference. -An Proficiency to use statistical models as well as the Proficiency to perform an optimal estimation of the parameters by maximizing the likelihood and minimizing the prediction errors. -Proficiency to formulate and testing hypothesis about a population. -Proficiency to design lineal models that help to understand and predict real phenomena. -Proficiency to use statistical software.

RA1.1: Knowledge and understanding of the mathematics and other basic sciences underlying their engineering specialisation, at a level necessary to achieve the other programme outcomes. RA6.1: Ability to gather and interpret relevant data and handle complexity within their field of study, to inform judgements that include reflection on relevant social and ethical issues. CB3: Students have the ability to gather and interpret relevant data (usually within their field of study) in order to make judgements which include reflection on relevant social, scientific or ethical issues. CGB1: Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; differential and integral calcu- lus; numerical methods; numerical algorithms; statistics and optimisation.

Chapter I: Univariate Descriptive Statistics 1.1 Introduction. The purpose of Statistics. 1.2 Description of data by tables 1.3 Description of data by graphs 1.4 Characteristics measures of a variable Chapter II: Bivariate Descriptive Statistics 2.1 Introduction. 2.2 Bivariate Frequency Tables 2.3 Scatterplots 2.4 Measures of linear dependence 2.5 The regression line Chapter III: Probability 3.1 Introduction 3.2 Probability: definition and properties 3.3 Conditional and total probability 3.4 Independence of events 3.5 Bayes Theorem Chapter IV: Introduction to Random Variables 4.1 Introduction 4.2 Univariate discrete random variables 4.3 Univariate continuous random variables 4.4 Characteristics measures of a random variables Chapter V: Probability models 5.1 Introduction 5.2 Bernoulli process 5.3 Poisson process 5.4 Normal distribution 5.5 Relationship between Normal, Binomial and Poisson distributions 5.6 Simple regression model Chapter VI: Introduction to statistical inference 6.1 Statistical inference. Population and sample 6.2 Estimation and estimators 6.3 Confidence intervals for the mean with large samples 6.4 Determining the sample size 6.5 Other confidence intervals 6.6 Introduction to the Hypothesis Testing 6.7 Hypothesis test for the mean with large samples 6.8 Interpreting the test using the p-value 6.9 Diagnosis of the model 6.10 Transformations that improve normality Chapter VII: Comparison of Populations 7.1 Introduction 7.2 Comparing two populations means: Independent samples 7.3 Comparing two populations means: Paired data 7.4 Comparing two population proportions 7.5 Comparing two populations variances (normal populations) Chapter VIII: Introduction to Multiple Regression 8.1 Statistical model for Simple Regression. 8.2 Statistical model for Multiple Regression. 8.3 Estimation of the Multiple Regression parameters. 8.4 Inference for Multiple Regression. 8.5 Test for the Multiple Regression model. 8.6 Regression with binary variables.

The learning methodology consists on the following elements: -Lecture class will be taught in face-to-face mode (0.8 ECTS): Presentation of the main statistical concepts, with their justification and examples. The instructor will illustrate the methodologies with the computer and real or simulated data. Discussion of the concepts with the students. Discussion of the questions and doubts aroused during the self learning process. -Exercises class (0.8 ECTS): Classes devoted to solving exercises in small groups. -Lab class (0.2 ECTS): The students solve data analysis problems by using a statistical package. They are asked to solve exercises and conceptual problems by using the statistical software. After each class and organized in small groups, they are asked to make a case study that will be evaluated. -Tutorials (1.1 ECTS): Individualized or group assistance to students by the teaching staff with 25% attendance. -Individual or group work (2.9 ECTS). -Final exam (0,2 ECTS).