TecnoCampus Foundation
eCampus
University Business
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General information

Subject type: Basic

Coordinator: Joan Triadó Aymerich

Trimester: Third term

Credits: 6

Teaching staff: 

Cristina Steegmann Pascual

Teaching languages

  • Catalan

Skills

Basic skills

  • B5_That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy

     

Specific skills

  • E1_Training for the resolution of mathematical problems that may arise in engineering. Train to apply knowledge about: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithm; statistics and optimization

Transversal competences

  • T2_That students have the ability to work as members of an interdisciplinary team either as one more member, or performing management tasks, in order to contribute to developing projects with pragmatism and a sense of responsibility, making commitments taking into account available resources

     

Description

The subject as a discipline of science responsible for learning from data and analyzing phenomena with uncertainty provides the basis for: synthesizing information, analyzing random phenomena with the application of probability theory and the study of different probability distributions. Applied examples of sampling and statistical inference applied in areas close to the degree areas and an introduction to linear models will be given.

 

Contents

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SUBJECT 1. DESCRIPTIVE STATISTICS

1. Types of data and their graphic representation

1.1. Types of variables

1.2. Qualitative variables and discrete quantitative variables

1.3. Continuous quantitative variables

1.4. Continuous quantitative variables and histogram

2. Center measures and properties

2.1. fashion

2.2. Median

2.3. Average

2.4. Mean - median comparison

2.5. Center measurements and tabular data

3. Dispersion measures

3.1. The quartiles and the median

3.2. Standard deviation and variance (and mean)

3.3. Uses of the mean and standard deviation or the median and the five summary numbers

3.4. Variance and tabulated data

SUBJECT 2. PROBABILITY

1. Introduction to probability

1.1. Introduction

1.2. Random event or happening

1.3. Successful operations

2. Combinatorics and counting techniques

2.1. Variations

2.2. Variations with repetition

2.3. permutations

2.4. Combinations

3. Probability

3.1. Introduction and relative frequency

3.2. Probability theory

3.3. Properties that derive from the definition of probability

3.4. Laplace's rule

3.5. Probabilities in non-uniform sample spaces and relative frequency

3.6. Conditional probability

3.7. Independence of events

4. Bayes' theorem

4.1. Partitions

4.2. Theorem of total probabilities

4.3. Probability trees and conditional probability

4.4. Contingency tables

4.5. Bayes theorem

SUBJECT 3. DISCRETE RANDOM VARIABLES

1. Introduction to discrete random variables

1.1. Introduction to random variables

1.2. Discrete random variables

2. Expectation and variance

2.1. Definitions

2.2. Properties of hope

2.3. Properties of variance

2.4. Chebyshev's inequality

3. Discrete distributions

3.1. Bernoulli distribution

3.2. Binomial distribution

3.3. Geometric distribution

3.4. Poisson distribution

SUBJECT 4. CONTINUOUS RANDOM VARIABLES

1. Continuous variables

1.1. Density function

1.2. Relationship between distribution and density functions. Calculation of probabilities.

1.3. independence

1.4. Hope and variance

2. Continuous laws. normal law

2.1. Uniform distribution

2.2. Exponential distribution

2.3. Normal distribution

SUBJECT 5. CENTRAL LIMIT THEOREM

1. The distribution of the sample mean

1.1. Distribution of the sample mean for normal variables

2. The central limit theorem

2.1. Approximation of the binomial to the normal

2.2. The central limit theorem

SUBJECT 6. STATISTICAL INFERENCE. CONFIDENCE INTERVALS

1. Introduction to confidence intervals

1.1. The concept of confidence interval

1.2. Confidence interval for the arithmetic mean when the population is normal and we know the standard deviation

1.3. Confidence interval for the mean when the population is normal and we do not know the standard deviation

1.4. Comparison between the cases studied

2. Confidence interval for the proportion

2.1. Procedure to construct a confidence interval for the ratio

2.2. The effect of sample size

Evaluation system

The final grade is the weighted sum of the grades for the learning activities:

Q = 0.60 (PT + PP) + 0.20 PLab + 0.20 Proj

PT: Theoretical part of the subject

PP: Practical part of the subject (syllabus exercises)

PLab: Deliverable laboratory practices, in groups

Proj: Deliverable project, individual

 

The theory part of the subject (PT) + the practice part (PP) must be completed and a minimum of 5 points must be taken in order to be able to choose to count the other scores.

 

Observations relating to Recovery:

The theory part of the subject (PT) + practical part (PP) is indeed recoverable. The rest of the parts are not recoverable. For students who attend the make-up exam, their grade will be the one obtained in this test and their final grade (Q) will be calculated using the formulas detailed above and in no case will it be higher than 6.

 

REFERENCES

Basic

Sanchís, C .; Salillas, J .; Riera, T .; Fontanet, G. (1987): Making statistics. Madrid (Spain), Alhambra

MENDENHALL, William and SINCICH, Terry. Statistics for Engineering and the Sciences. 5. Prentice Hall, 2006.

Complementary

 Max Kuhn and Kjell Johnson, Applied Predictive Modeling. Sringer 2013