29611 - Statistics
110 - Escuela de Ingeniería y Arquitectura
430 - Bachelor's Degree in Electrical Engineering
5.2. Learning tasks
The course is divided into four hours of class a week for 15 weeks. Two hours are for exposure of theoretical concepts and examples, in the complet group, and the other two hours to develop skills in planning, resolution and interpretation of realistic problems, in the lab class.
A problem is proposed a each student for to resolve. In addition throughout the course application proposed in a real case of the techniques presented . This activity will take place continuously during the course, making periodic reviews .
Module 1: Exploratory Data Analysis.
1. Exploratory analysis of a variable. descriptive measures and graphical tools
2.- Fitting distributions. Calculation of percentiles and probability plots
3. Exploratory analysis of several variables. Linear regression
Module 2: Probability and Random Variables
1. Introduction to the probability. Definition of probability. Bayes theorem. Independence
2. Random variables: Definition of random variable: discrete and continuous. Probability function. Density function. Distribution function. Characteristics of a random variable: mean, variance, skewness and direction. Chebychev inequality
3. Discrete variables: Binomial, Hypergeometric, Geometric, Negative Binomial and Poisson
4. Continuos variables: Uniform, Normal, Exponential, Gamma, Weibull
5. Poisson Process
6. Multivariate probability models
Module 3: Sampling, estimation and hypothesis test.
1. Simple random sample. Statisticians. Distributions Pearson chi-square, Student's t and Snedecor F-Fisher. central limit theorem. Fisher theorem. Calculation of sample sizes
2. Point and interval estimation. Confidence interval estimation. Confidence intervals for means, variances and proportions.
3. Hypothesis test: null and alternative hypotheses. critical region. Type I and II errors. Significance level of contrast and power. Relationship between confidence intervals and hypothesis testing. Hypothesis of means, variances and proportions. Contrasts associated with quality control: graphics Xbar, S. contingency tables. Contrast independence. Contrast goodness of fit. Analysis of variance of a factor
Module 4: Introduction to Optimization. Optimization problems: decision variables, objective function and constraints. Linear programming problems: graphic resolution
5.4. Course planning and calendar
Master class: 30 h .
Resolution of case studies in computer lab : 30 h .
Making report on a real case with group work : 15 h .
Personal study of theoretical aspects : 30 h.
Troubleshooting: 34 h.
Evaluation Activities : 6 h.