The main goal of this course is that each student acquires basic skills in
a) basic techniques of integral calculus, essential for analysing quantitatively mathematical models of statistical or deterministic type
b) minimum knowledge of probability theory in order to be able to understand statistical inference techniques
c) some knowledge about techniques of statistical inference; the main concern is that the student understands the mechanisms subsequent to the various techniques in order to adapt and apply them to concrete problems in the area of Natural and Health Sciences.
d) critical thinking and the ability to interpret the results obtained by applying statistical techniques (either in work done by the student or in another's work)
I. Calculus
1. Riemann integral
a) Definition and properties
b) Fundamental theorem of calculus
2. Primitives
a) The substitution technique
b) Primitives by parts
3. Improper integrals
4. Area and volume
II. Probability
1. Preliminaries
a) notion of probability
b) discrete and continuous rv
c) density and distribution functions
d) quantiles, mean, median variance and standard deviation
2. Usual Probabilistic Models:
a) uniform, binomial, multinomial, Poisson, normal, chi-square, t-Student, exponential
b) relations between distributions
3. Sampling
a) empirical distribution, histogram, box-plot
b) law of large numbers
c) central limit theorem
III. Statistical Inference
1. Confidence intervals for the mean, variance and proportion
2. Hypothesis testing:
a) Errors of type I II, significance level
b) p-value
c) relation between hypothesis testing and confidence intervals
d) tests for the mean, variance and proportion
The classroom theoretical lectures are maninly devoted to expose the matter and explain the program content dynamically and adjusted to the audience assimilation speed, being that, whenever possible, they include historical issues and potential application examples.
The classroom theoretical/practical sessions will have a period in which students are encouraged to independently solve the proposed practical exercises, being that its resolution is always subsequently made and commented by the teacher.
The evaluation is done mainly by final exam, and in mid-November there will be a test that deals with the content of Chapter I and weighs 7/20 of the final grade.
Spivak, M. (2008). Calculus, Publish or Perish; fourth edition. ISBN: ISBN-13: 978-0914098911
Stewart , J.(2008). Calculus : early transcendentals, Thonson Brooks/Cole. ISBN: 978-0-495-38273-7
Pedrosa, W.W. & Gama, S.M.A. (2004). Introdução Computacional à Probabilidade e Estatística, Porto Editora. ISBN: 972-0-06056-5
Daniel, W.W. (1999). Biostatistics: a foundation for analysis in the health sciences, John Wiley and sons. ISBN: 0-471-16386-4
Não há bibliografia obrigatória e os alunos são encorajados a seguirem as aulas teóricas para adquirirem os fundamentos e as aulas teórico-práticas para consolidarem-nos.
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