Deterministic and Indeterministic Processes, Probabilities and Chance SummaryIn this introductory class to Probability Theory, we will explore the connection between deterministic and indeterministic processes and their relationship with probabilities and chance. We will see how processes in nature are classified into two mutually exclusive species and how they are understood...
Understanding the Sample Space in Probability Theory SummaryIn this lesson, we explore the concept of Probability Space, a mathematical structure consisting of a Sample Space, Sigma-Algebra, and Probability Measure. We examine the Sample Space in detail, understood as the collection of all possible states of a random process. Through practical...
What is a Sigma-Algebra? Definition and Examples SummaryThis class discusses the importance of sigma-algebra in probability theory. Sigma-algebra is a structure that contains all measurable events in a sample space, enabling the definition of a probability measure. Practical examples, such as coin tosses and the lifespan of an electronic device,...
Key Properties of Probability Measure SummaryIn this class, we present the basic definitions of probability theory, including probability measure and sigma-algebra. Additionally, we explore the notion of probability as a limit of relative frequencies, using the example of rolling a six-sided die. Through the relative frequency function, it is demonstrated...
Counting Techniques: Permutation, Variation, and Combination AbstractIn the study of probabilities, counting techniques are fundamental tools for measuring the cardinality of the sample space and the event to be measured. In this context, the techniques of combination, variation, and permutation are the most used due to their ease of use...
The Stirling Formula The Stirling formula is an essential tool for simplifying calculations with factorials of large numbers, offering a quick and practical approximation. This result is especially useful in areas such as thermodynamics, probability, and asymptotic analysis, where working with extremely large numbers is common. Understanding its derivation not...
Useful Theorems for Probability Calculation SummaryThis class presents solved exercises demonstrating some useful theorems for probability calculation, including proofs and deductions. The exercises cover topics such as complementary probability, set inclusion, and event convergence. Completing these exercises will provide you with a solid foundation for further studying probability theory. LEARNING...
Practical Problems with Fundamental Probability Concepts Abstract In this class, we will review practical exercises such as the reliability of a control system, card game strategies, and probability calculations in everyday situations. The solutions to the problems are presented in video format, allowing you to strengthen your understanding and skills...
Conditional Probability and Independence Between Events SummaryIn this session, we will explore the concept of conditional probability and the interaction between events. We will acquire the skills to calculate conditional probabilities and determine the dependence or independence between events. We will apply practical examples, such as the study of the...
Bayes' Theorem and Compound Probability AbstractIn this class, two fundamental concepts in probability were discussed: conditional probability and compound probability. The difference between and was emphasized. The Compound Probability Theorem states that the probability of an event can be expressed as the sum of the conditional probabilities multiplied by the...
