Description

Theory
1

Theory/Practice
2

Instructors

Rui Rocha

Contents

CP1-Probability (3h)
Revisions of the calculus of probabilities.
Conditional probability. Multiplication rule. Independent events.

CP2-Probability distributions (17h)
Discrete random variable.
Probability function and distribution function.
Mean and variance. Properties.
Binomial distribution.
Poisson's distribution.
Continuous random variable.
Probability density function and distribution function.
Mean and variance. Properties.
Uniform distribution.
Exponential distribution.
Normal distribution. Aditivity.
Central limit theorem.

CP3-Sampling (3h)
Population and sample. Random sample.
Distribution of the sample mean.
Distribution of the sample proportion.

CP4-Parameter estimation (7h)
Interval estimation. Confidence level of an estimate.
Confidence interval for the mean.
Confidence interval for the proportion.

CP5-Hypotheses tests (15h)
Error of type I and error of type II.
Tests for means.
Tests for proportions.
Chi-square test.

Learning Outcomes

In this course, students are introduced to concepts and techniques in statistics that will help them to make a rigorous analysis and interpretation of the dada, to make estimates of known uncertainty and to make decisions.
Students must learn how to compute probabilities and be clearly aware of its importance. They will learn the theoretical and practical meaning of independent events. They will get to know how to work with random variables and how to interpret the mean value and the variance in real applications. The distributions will be introduced in a way that students can compute probabilities and identify the conditions for their applicability. Students will learn to make estimates and quantify the sample size for a given accuracy. They will be able to make decisions based on the analysis of samples and to establish criteria based on the significance level and the sample size.