In this chapter, we delve into the key concepts of probability theory
and the most common statistical distributions. We begin by introducing Bayes’
Theorem and its application in statistical inference. Next, we address the binomial distribution function and its usefulness in analyzing binary events and calculating probabilities. Then, we examine conditional probability and its importance
in decision-making under uncertainty. Subsequently, we immerse ourselves in the
main probabilistic functions, including the normal distribution function and its role
in modeling natural phenomena. Furthermore, we study the Poisson distribution
function, which is applied to situations where the probability of rare events occurring needs to be calculated. Finally, we analyze the general concept of probability
and its interpretation in the context of statistical theory. Additionally, we present
the Total Probability’s Theorem, which allows for the calculation of the probability
of an event based on conditional event information. In summary, this chapter provides a solid foundation for the fundamentals of probability and statistics, exploring
key topics such as Bayes’ Theorem, the binomial distribution function, conditional
probability, main probabilistic functions, the normal distribution function, the Poisson distribution function, probability, and the Total Probability’s Theorem.
Keywords: Bayes’ theorem, binomial distribution function, conditional probability, main probabilistic functions, normal distribution function, poisson distribution function, probability, total probability’s theorem.
