Course: 2022/2023

Statistics

(15535)

Once successfully having studied this subject, the students should be able to:
- Analize problems involving random phenomena
- Define populations for a statistical study
- Build Hypothesis about a distribution
- Estimate and test hypothesis about the paramters of the chosen model
- Evaluate how well does the model fit to reality
- Understand the limitations of the methods that have been studied and the conditions under which they lead to wrong conclusions

Skills and learning outcomes

Description of contents: programme

BLOCK 0: DESCRIPTIVE STATISTICS
0. Descriptive Statistics
BLOCK I: PROBABILITY
1. Introduction to Probability
1.1 Introduction
1.2 Random phenomena
1.3 Definition of probability and properties
1.4 Conditional probability
1.5 Bayes Theorem
2. Random variables
2.1 Definition of random variable
2.2 Discrete random variables
2.3 Continuous random variables
2.4 Characteristic features of a random variable
2.5 Transformations of random variables
2.6 Random vectors
3. Distribution models
3.1 Binomial distribution
3.2 Poisson distribution
3.3 Geometric distribution
3.4 Uniform distribution (continuous)
3.5 Exponential distribution
3.6 Normal distribution (with CLT)
BLOCK II: ESTIMATION AND INFERENCE
4. Parameter estimation
4.1 Introduction and basic concepts
4.2 Sampling distributions
4.3 Maximum Likelihood Estimation
4.4 Properties of Maximum Likelihood Estimators
4.5 Inference based on MLEs
5. Statistical Inference
5.1 Introduction
5.2 Confidence Intervals
5.3 Hypothesis testing
5.4 Particualr tests on a single sample
5.5 Comparison of two populations
5.6 Statistical quality control
BLOCK III: APPLICATIONS
6. Statistical quality control
6.1 Introduction to statistical process control
6.2 Variables charts, the Xbar chart
6.3 Attributes charts, p and np charts
7. Linear regression
7.1 Introduction
7.2 Simple linear regression
7.3 Multiple linear regression
7.4 Comparison of three or more population means (ANOVA)

Learning activities and methodology

- Lectures: introducing the theoretical concepts and developments with examples, 2.2 ECTS
- Problem solving sessions: 2.2 ECTS
- Computer (practical) sessions: 0.6 ECTS --- 4 SESSIONS
- Evaluation sessions (continuous evaluation and final exam): 1 ECTS

Assessment System

- % end-of-term-examination 0
- % of continuous assessment (assigments, laboratory, practicals...) 100

Basic Bibliography

- Douglas C. Montgomery and George C. Runger. Applied Statistics and Probability for Engineers (3rd ed). Johan Wiley & Sons. 2003
- Navidi, W.. Statistics for Engineers and Scientists. McGraw-Hill. 2006

Additional Bibliography

- John D. Enderle, David D. Farden, Daniel J. Krause. Basic Probability Theory for Biomedical Engineers. Morgan & Claypool. 2006
- John D. Enderle, David D. Farden, Daniel J. Krause. Advanced Probability Theory for Biomedical Engineers. Morgan & Claypool. 2006
- Kristina M. Ropella. Introduction to Statistics for Biomedical Engineers. Morgan & Claypool Publishers. 2007

Detailed subject contents or complementary information about assessment system of B.T.

The course syllabus may change due academic events or other reasons.