Description

Theory
1

Theory/Practice
2

Instructors

Gabriela Gonçalves

Contents

0. PROBABILITY (Review)
Axioms of probability. Conditional probability, Baye's Rule, Additional properties.

I. RANDOM VARIABLE DISTRIBUTIONS
Random variables. Definitions. Discrete random variables. Probability
mass and distribution functions. Mean value and variance. Properties.
The Binomial distribution. The Poisson distribution.
Continuous random variables, Probability density function, and distribution function, Mean value, and variance.
Uniform, Exponential, and Normal distributions. Properties.
Central Limit Theorem.

II. SAMPLING
Population and sample.
The sampling distribution of the mean.
The sampling distribution of a sample proportion.

III. CONFIDENCE INTERVALS
Descriptive statistics concepts
Confidence Interval for a mean.
Confidence Interval for a proportion.

IV. HYPOTHESIS TESTING
Statistical Hypothesis.
Error types.
Tests for one population mean.
Tests for the proportion in one population.
Tests for the difference of two populational means and proportions.

Learning Outcomes

OB1: Calculate probabilities and apply elementary probability concepts to engineering problems.

OB2: Explain the concept of random variables and distinguish them from deterministic variables.

OB3: Identify and apply appropriate probabilistic models to analyse random phenomena.

OB4: Estimate parameters and formulate and test statistical hypotheses.

OB5: Apply statistical methods to solve engineering problems involving data analysis and uncertainty.

OB6: Use computational tools such as Python, R, and Excel to support statistical analysis and problem-solving.