Calculus and Linear Algebra

The main goal of the course is to provide the students with a set of competences for the understanding and application of statistical concepts and techniques in computer sciences. These competences can be classified as basic, general and specific. Basic competences: -Proficiency to gather and interpret relevant data (usually within their field of study) to inform judgments that include reflection on relevant social, scientific or ethical topics. (CB3) General competences: -Proficiency to apply knowledge of mathematics, statistics, computer science, and engineering as it applies to the fields of computer hardware and software. (PO a) -Proficiency to interpret data and results of experiments. (PO b) -Proficiency to independently acquire and apply required information related to statistical techniques with the aim of designing, monitoring, and managing computer systems. (PO i) -Proficiency to communicate effectively by oral, written, and graphical means, the results of statistical analysis. (PO g) -Proficiency to solve mathematical problems arising in engineering. Proficiency to apply knowledge of linear algebra; differential and integral calculus; numerical methods; numerical algorithms; statistics and optimization. (CGB1) Specific competences: -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.

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 Sampling distribution of a statistic 6.3 The sample mean distribution 6.4 Estimation and estimators 6.5 Method of moments 6.6 Diagnosis of the model 6.7 Transformations that improve normality Chapter VII: Large-Sample Inference 7.1 Confidence intervals for the mean with large samples 7.2 Determining the sample size 7.3 Other confidence intervals 7.4 Introduction to the Hypothesis Testing 7.5 Hypothesis test for the mean with large samples 7.6 Interpreting the test using the p-value 7.7 Relation between the hypothesis test and the confidence intervals Chapter VIII: Comparison of Populations 8.1 Introduction 8.2 Comparing two populations means: Independent samples 8.3 Comparing two populations means: Paired data 8.4 Comparing two population proportions 8.5 Comparing two populations variances (normal populations) Chapter IX: Introduction to Multiple Regression 9.1 Statistical model for Simple Regression. 9.2 Statistical model for Multiple Regression. 9.3 Estimation of the Multiple Regression parameters. 9.4 Inference for Multiple Regression. 9.5 Test for the Multiple Regression model. 9.6 Regression with binary variables.

The learning methodology consists on the following elements: -Lecture class will be taught synchronously and interactively online through Blackboard collaborate: 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. Classes devoted to solving exercises in small groups. -Lab class. 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. Session 29 will be taught in synchronous and interactive online through Blackboard collaborate.