Description

Theory
2

Laboratory
3

Instructors

Luís Afonso

Contents

CP 1 - Probability Reviews: (1 week)
Rules for calculating probabilities, Law of Total Probability, and Bayes' Theorem.
 

CP 2 - Probability Distributions: (4 weeks)
Concept of a random variable. Types of variables.
Probability function and distribution function. Mean and variance. Properties.
Discrete distributions (Binomial and Poisson) and continuous distributions (Uniform, Exponential, Normal).
Additivity. Central Limit Theorem.
 

CP 3 - Sampling (1 week)
Population and sample.
Random sample.
Distribution of the sample mean and the difference of means.
Sample proportion.
 

CP 4 - Parameter Estimation: (1 week)
Interval estimation. Confidence level of an estimate.
Confidence intervals for means, differences of means, proportions, and differences of proportions.
 

CP 5 - Hypothesis Testing: (2 weeks)
Statistical hypotheses.
Type I and II errors.
Tests for population mean, differences of means, proportions, and differences of proportions.
Chapter 5 - Linear Regression (2 weeks)

Learning Outcomes

Upon successful completion of this course, the student should be able to calculate elementary probabilities, use random variables and calculate the mean and variance, use distributions and identify the conditions of their applicability, estimate parameters and determine the sample size based on the desired accuracy, and make decisions based on samples through hypothesis testing. The student should also be able to use Python as a tool to support the resolution of statistical problems.