## Public University of Navarre

 Course code: 252201 Subject title: STATISTICS Credits: 6 Type of subject: Basic Year: 1 Period: 2º S Department: Lecturers: UGARTE MARTINEZ, M. DOLORES (Resp)   [Mentoring ]

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M11 Mathematics

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### Contents

Descriptive statistics, probability, statistical inference.

• General Probability and Random Variables (Chap. 3)
• Univariate probability distribution (Chap. 4)
• Sampling and sampling distribution (Chap. 6)
• Point estimation and confidence intervals (Chap. 7-8)
• Hypothesis testing (Chap. 9)
• Introduction to modeling in statistics: anova (Chapter 11)

Descriptive statistics and statistical software -R- will be dealt with through the whole course.

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### Descriptors

Descriptive statistics, probability, statistical inference, statistical models.

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### General proficiencies

• CG3: Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations.
• CG4: Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in industrial engineering.

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### Specific proficiencies

• CFB1: Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, geometry, differential geometry, calculus, differential equations, numerical methods, algorithms, statistics and optimization.
• CFB3: Basic kowledge on computing, operative systems, data bases and software with engineering applications.

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### Learning outcomes

R1. To perform descriptive statistical analysis to databases.

R2. To apply appropriate statistical treatments according to the nature of the statistical variables in databases.

R3. To use a statistical package for statistical analysis of databases and simulation results of random phenomena.

R4. To recognize the main probability distributions, both discrete and continuous, together with methods general of probability.

R5. To use statistical tools to adequately estimate the unknown model parameters raised in engineering by methods of point estimation and intervals.

R6. To learn statistical techniques for facilitating the process of decision making in uncertain environment.

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### Methodology

 Methodology - Activity Attendance Self-study A-1 Lectures 45 A-2 Practical classes 15 A-3 Self-study 75 A-4 Exams, tests, and tutorial 15 Total 75 75

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### Evaluation

 Learning outcomes Evaluation activities Weight Recovery character R1, R3, R4, R5, R6 Final Exam (a minimun of 5 over 10 is necessary to overcome this part) 60% Yes, second exam R1, R2 Evaluation proofs 30% No R6 Monitoring proofs and active participation in class 10% No

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### Agenda

1.-Exploring Data
Displaying Qualitative and Quantitative Data
Bivariate and Multivariate data

2.- General Probability and Random Variables
Counting Techniques (a review)
Axiomatic Probability
Discrete and Continuous Random Variables

3.- Univariate probability distribution
Discrete and Continuous Univariate Probability Distributions

6.- Sampling and Sampling Distributions
Sampling
Parameters
Estimators
Sampling Distribution of the Sample Mean, Sample Variance and Sample Proportion
Sampling Distributions Associated with the Normal Distribution

7.- Point Estimation and Confidence Intervals
Properties of Point Estimators
Confidence Intervals

8.-Hypothesis Testing
Type I and Type II Errors
Power Function
Uniformly Most Powerful Test
p-Value or Critical Level
Tests of Significance

9. Introduction to modeling in statistics

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### Bibliography

Access the bibliography that your professor has requested from the Library.

TEXTBOOK:
Ugarte, M. D., Militino, A. F., Arnholt, A. T. (2016). Probability and Statistics with R. Second Edition.  CRC Press/Chapman and Hall.

OTHER BOOKS:
Devore, J. (2005) Applied statistics for engineers and scientists. Thomson

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English.

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Aulario.

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