Statistics

DESCRIPTION

The main goal of the course is to provide students with a set of competences for the understanding and application of statistical concepts and techniques in engineering disciplines. Students will learn to represent data information using tables, graphs and parameters in order to facilitate comprehension and decisions; they will be able to identify situations with random behavior and calculate probability of these phenomena. Besides, they will know, identify and classify random variables from different sources of information. Students will learn to identify and solve problems in which the variable under study follows a known probability distribution. They will elaborate, build up and validate statistical models suitable for real problems. They will make use of estimation and inference for studying the behavior of a population model from a sample of the population under study. Student will study two or more variables sets identifying independence and interdependence situations, and be able to assess the importance of statistics and its proper use in specific engineering problems.

OBJECTIVES

- Represent data information using tables, graphs and parameters in order to facilitate
comprehension and decisions.
- Identify situations with random behaviour and calculate probability of these
phenomena.
- Know, identify and classify random variables from different sources of information.
- Identify and solve problems in which the variable under study follows a known
probability distribution. Elaborate,build up and validate statistical models suitable for
real problems.
- Use of estimation and inference for studying the behaviour of a population model from
a sample of the population under study.
- Study two or more variables sets identifying independence and interdependence
situations.
- Assess the importance of statistics and its proper use in specific engineering problems.

CONTENTS

Chapter 1. Descriptive Statistics Type of data. Graphical and numerical methods to describe qualitative and quantitative data. Descriptive statistics applications using a spreadsheet computer tool.

Chapter 2. Calculation of probabilities. The concept of probability. Experiments and events. Set theory. Interpretations of probability. The axioms of probability. Study of simple probabilities. Independent events. Conditional probability. Total probability theorem. Bayes' Theorem.

Chapter 3. Random Variable. Concept of one-dimensional random variable. Discrete random variables. Continuous random variables. Uniform distribution. Distribution function. One-dimensional random variable function. Transformed distribution. Moments of random variable; Measures of position, dispersion measures, Markov and Chebychev inequalities. Concept of two-dimensional random variable.

Chapter 4. Discrete probability distributions. Distribution of Bernoulli. Binomial distribution. Geometric distribution. Poisson distribution.

Chapter 5. Continuous probability distributions. General normal distribution. Central Limit Theorem.

Chapter 6. Introduction to statistical inference. Theory of samples Sample and population. Types of sampling. Concept of statistic. Sample distributions. Distribution of the sample mean. Distribution of the corrected sample variance. Statistics and distributions used in comparison of normal groups.

Chapter 7. Parameter estimation and Hypothesis contrast. Classical theory of parameter estimation. Estimation of parameters by confidence interval. Parametric Hypothesis Contrast. Classification of hypotheses. Hypothesis test methodology. Type errors. Unilateral or bilateral testing. Stages of a contrast. Contrasts related to stockings. Contrasts related to variances. Contrasts related to proportions.

Chapter 8. Linear Regression. Simple linear regression model (SLR). Modelling. Forecasts.

METHODOLOGY
Classroom activities:
- Lectures explaining the theoretical aspects
- Resolution of exercises and example problems
Out-of-class activities:
- Individual study of lectures material
- Undertaking of proposed exercises and revision

ASSESSMENT
Subject assessment will be done by knowledge tests and also through exercises that must be
handled in during the course.
- Three continuous assessment tests will be done in class time. Each of them will have a value
of 20% of the overall mark. If the student passes them, the corresponding chapters will be
considered as passed, and it is not necessary to repeat the test of that block in the final exam.
- After finishing each unit, an activity or a battery of exercises will be proposed. When the
deadline is finished, the results and indications for auto evaluation will be uploaded to ALUD
(Deusto online platform). All the activities will be valued with a 20% of the final score.
- The final test will have four parts. The fourth one will be compulsory for all students, and will
have a value of 20% of the overall mark. The other three parts will have a value of 60% of the
overall mark, and will be done by those students who have not passed them during continuous
assessment tests done during the course.

READINGS
Presentations, class notes and exercises statements at ALUD Statistic Course:
http://alud.deusto.es

BIBLIOGRAPHY

Probability and statistics for engineering and the sciences. Jay L. Devore
Introduction to probability and statistics for engineers and scientist. Ross, Sheldon M
Probability & Statistics for Engineers and Scientists. Pearson. R.E. Walpole