Bernoulli Trial and Binomial Distribution AbstractIn this class, we will study the concept of Bernoulli trials and their implications in probability theory. We begin with a detailed definition of Bernoulli trials, then address the concept of independence between events. After clarifying these ideas, we apply the binomial theorem to understand...
Poisson Process: Approximation of the Binomial Process SummaryThis class focuses on the Poisson Process as an approximation to the Binomial Process, starting with the definition of the coefficients and the Poisson distribution, which is derived from a Bernoulli event with a large number of trials and a very small individual...
Random Variables and Probability Distributions SummaryThis class provides an in-depth immersion into the concepts of random variables and probability distributions, fundamental pillars of probability theory and statistical analysis. The definition of a random variable as a number that depends on the outcome of a random experiment is introduced. The distribution...
Discrete Probability Distributions and Examples Summary In this class, we will explore discrete probability distributions in depth, starting with their definition from continuous and discrete sample spaces. We will cover the five most well-known discrete probability distributions: Binomial (or Bernoulli), Poisson, Geometric, Negative Binomial, and Hypergeometric, each with examples demonstrating...
Continuous Probability Distributions SummaryIn this section, we will delve deeply into the concept of continuous probability distributions, highlighting the characteristics and uses of the five most well-known ones: the exponential distribution, the rectangular uniform distribution, the normal (Gaussian) distribution, the Weibull distribution, and the Gamma distribution. The mathematical formulas defining...
How to Calculate the Normal Distribution Using the Table? Summary In this class, we will address the topic of the normal distribution, one of the most common continuous probability distributions. We will analyze how a random variable X with parameters μ and σ can follow a normal distribution and how...
Statistical Simulations for Business and Industry Statistical Simulation for Business and Industry: The Normal Distribution as a Strategic Tool Discover the fascinating world of statistical simulations applied to various fields of commerce, business, and industry. In this article, we will explore four simulations, each addressing a different challenge: from optimizing...
