Statistical Methods – Instituto Politécnico de Coimbra

Base Knowledge

Set elementary theory

Logic

DeMorgan laws

Teaching Methodologies

Theoretical part – expository/deduction

Theoretical-practical part – student participation in the resolution of the proposed exercises

Practical part – solving exercises in partnership teacher/student with the aid of appropriate software for the

contents of the UC

Learning Results

Thinking mathematically
Reasoning mathematically
Posing and solving mathematical problems
Modeling mathematically
Representing mathematical identities
Handling mathematical symbols and formalism
Communicating in, with, and about mathematics
Making use of ads and tools

objectives and competences applied to the curricular unit of Statistical Methods.

Program

1-Probabilities

Introduction. Random experience, space for results, events. Probability definition. Conditional probability. Independent events. Total probability theorem. Bayes’ theorem.

2-Random Variables and Discrete Probability Distributions

Introduction. Discrete random variables: Definition; Probability function; Distribution function; Location and dispersion parameters. Special discrete distributions: Bernoulli distribution; Binomial Distribution; Hypergeometric Distribution; Poisson distribution. Discrete bidimensional random variables: Definition; Joint probability and distribution functions; Marginal probability function; Conditioned probability function; Independence from random variables; Covariance and linear correlation coefficient.

3-Random Variables and Continuous Probability Distributions

Definition; Probability density function; Distribution function; Location and dispersion parameters. Special continuous distributions: Brief reference to Uniform and Exponential Distributions; Normal Distribution; Chi-square distribution; T-Student distribution.

4-Sampling and Sampling Distributions

Introduction. Random sample. Statistics. Distribution of the Sample Average. Sampling Variance Distribution.

5-Estimation

Fundamental notions of Point and Interval Estimation. Confidence intervals for the mean value and for the population variance.

6-Parametric Hypothesis Tests

Fundamental notions. Tests for the mean value and for the variance of a population.

Curricular Unit Teachers

Deolinda Maria Lopes Dias Rasteiro

Internship(s)

NAO

Bibliography

Main bibliography

MARQUES, C., & RASTEIRO, D. – Teacher notes and exercises list (available at Moodle inforestudante.ipc.pt/nonio).

MONTGOMERY, D., & RUNGER, G. (2018) – Applied Statistics and Probability for Engineers. Wiley.

(Biblioteca do ISEC: 3-3-192 (ISEC) – 15053, edição de 2007)

MURTEIRA, B.J.F. (1993). Probabilidade e Estatística, Volumes I e II. McGraw Hill.

(Biblioteca do ISEC: Vol I – 3-3-50 (ISEC) V.1º v. – 05528; Vol II – 3-3-51 (ISEC) V.2º v. – 07049)

PEDROSA, A.C., & GAMA, S.M.A. (2018)– Introdução Computacional à Probabilidade e Estatística. Porto Editora.

(Biblioteca do ISEC: 3-3-236 (ISEC) – 18887)

Another bibliography

GUIMARÃES, R.C., & CABRAL, J.A.S. (2010). Estatística. Portugal: Verlag Dashöfer.

(Não existe na biblioteca)