Objectives and Contextualisation
The objective of this course is to introduce the basic statistical tools to analyze data arising from experiments or observations, focusing on their correct use and the interpretation of the results.
The practices with computer of this subject, that are realized with a statistical software package in the computer classroom, are an indispensable part of the course in order to achieve these goals.
Competences
Electronic Engineering for Telecommunication
Communication
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Work in a team.
Telecommunication Systems Engineering
Communication
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Work in a team.
Learning Outcomes
Analyse measurements in the area of engineering, using statistical tools to extract and understand information.
Analyse measures in the area of engineering, using statistical tools to extract and understand information.
Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
Develop scientific thinking.
Develop the capacity for analysis and synthesis.
Manage available time and resources.
Manage available time and resources. Work in an organised manner.
Prevent and solve problems.
Reason and model non-deterministic engineering systems or processes using discreet and continuous random variables and their corresponding distributions.
Reason and model non-deterministic systems and processes in engineering using discreet and continuous random variables and their corresponding distributions.
Resolve the mathematical problems that can arise in engineering.
Work autonomously.
Work cooperatively.
Content
1. Descriptive statistics:
Types of variables and data. Data frames.
Empirical experimet associated to a data frame.
Frequency tables and graphs: histograms and others.
Measures of localization. Scattering measures
Correlation coefficient and regression line.
Joint, marginal and conditional data distributions.
2. Introduction to the theory of probability:
Basic properties of probability. Combinatorics.
Conditional probability and independence. Bayes Formula.
Random variables. Density and distribution functions.
Expected value and variance. Moments of a random variable.
Discrete distributions: Bernoulli, Binomial, Poisson and others
Continuous distributions: uniform, exponential, normal and others.
Central limit theorem and laws of large numbers.
3. Random vectors and stochastic processes:
Joint, marginal and conditional distributions.
Bivariate normal distribution. Covariance and correlation coefficient.
Functions of random variables: distributions khi-square, Rayleigh, Rice.
Concept of stochastic process. Poisson processes. Markov chains.
4. Statistical Inference:
Estimation and confidence intervals of averages, variances and proportions.
Tests for the expected value and for the proportion.
Comparison tests for expected values and proportions.
Khi-square tests: goodness of fit, independence and homogeneity.
