Statistics and probability

Introduction Monte Carlo Simulation is a powerful computational technique used to model and analyze systems that involve uncertainty or randomness. By relying on repeated random sampling, it estimates complex mathematical …

Introduction The Uniform Continuous Distribution is one of the simplest and most fundamental probability distributions in statistics and probability theory. Unlike other distributions that may concentrate probability mass around certain values, …

Exercise The number of customers served by a bank’s central counter is 2 customers per minute. What is the probability that the counter will: 1. Serve 5 customers in a …

Exercise The human resources department of a company with 5,000 employees wants to estimate the average gross monthly salary of their employees. A sample of 400 employees was randomly selected, …

Introduction The Poisson Point Process (PPP) is a fundamental concept in probability theory and stochastic processes, widely used in fields like telecommunications, physics, and ecology. It provides a mathematical framework …

Introduction The Poisson distribution is a fundamental discrete probability distribution used to model the number of events that occur within a fixed interval of time or space. This distribution is …

Exercise Suppose a large batch of light bulbs contains 10% defective bulbs. If we randomly select 3 bulbs, what is the probability of the following: 1. Exactly one bulb is …

Introduction The Hypergeometric distribution is a discrete probability distribution that arises in scenarios where sampling is done without replacement. This distribution is particularly relevant when dealing with small populations or …

Exercise A department store sells an average of 3 items per hour. Answer the following questions: 1. What is the probability of exactly 3 sales in the next hour? 2. …

Comprehensive Article on the Geometric and Negative Binomial Distributions Introduction In probability theory, the Geometric and Negative Binomial distributions are two closely related discrete distributions. Both are used to model …