Probabilities and Statistics

Presentation

Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies.

Part of this Programme

Industrial Engineering and Management.

Level of Qualification|Semesters|ECTS

| Semestral | 5

Year | Type of course unit | Language

2 |Mandatory |Português

Code

ULHT41-620

Recommended complementary curricular units

Calculus I, Calculus II

Prerequisites and co-requisites

n/a

Professional Internship

Não

Syllabus

Descriptive statistics: measures of central, of non-central tendency and of dispersion. Graphs. Linear correlation and regression. Random experiment. Events. Sample space. Algebra of events. Probability concepts (Laplace and Kolmogorov). Conditioned probability. Independence. Discrete and continuous random variables. Probability and distribution functions. Expected value, variance and standard deviation. Discrete distributions: Uniform, Bernoulli, Binomial, and Poisson distributions. Continuous distributions: Uniform. Normal, Chi-square, and t-student distributions. Statistical inference. Sample distributions. Central limit theorem. Estimation by intervals. Confidence interval for mean, known and unknown variance, large and small sample. Confidence interval for the variance, standard deviation, and proportion. Hypothesis Testing for the mean and proportion.

Objectives

Be able to calculate and interpret the most important statistical measures and identify their properties; to calculate probabilities using Laplace's definition and Kolmogorov's axiomatization; to calculate conditioned probability and apply the principles of multiplication, total probability and Bayes' theorem. Be able to use the concept of random variable and to operate with probability functions and distributions. Know the most important discrete and continuous distributions and some of their properties. Calculate confidence intervals and apply hypothesis tests and interpret the results obtained.

Teaching methodologies and assessment

The approach to the various topics is done by appealing to the active participation of the students. Students are encouraged to follow various resolution strategies when solving the exercises. Assessment of the course, expressed on a scale of 0 to 20, will be done using two tests of frequency (45% + 50%) and individual assignments to be developed outside the classroom (5%). From the weighted arithmetic average of these moments of evaluation results the final grade of the student. If the final grade is equal to or higher than 9.5 values ¿¿the student will be approved in the discipline, otherwise the student will be admitted to a recovery test. If the grade in this recovery test is equal to or greater than 9.5 values ¿¿the student will be approved in the discipline. Students may also take a final exam with the same approval criteria, which can also be used to improve a previously obtained grade. Evaluation criteria explained on day 1.

References

Murteira, B., Antunes, M. - Probabilidades e Estatística, Vol. I, Escolar Editora,2012.

Murteira, B., Antunes, M. - Probabilidades e Estatística, Vol. II, Escolar Editora,2013.

Pedrosa, A.C., Gama, S.M. - Introdução computacional à Probabilidade e Estatística, 3ª ed., Porto Editora, 2018.

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