Statistics and probability

Introduction Independence of events is a fundamental concept in probability theory that describes situations where the occurrence of one event does not influence the occurrence of another. Understanding independence is crucial …

Total Probability Theorem and Bayes’ Theorem Introduction In probability theory, the Total Probability Theorem and Bayes’ Theorem are fundamental concepts used to compute probabilities based on known conditions or prior events. …

Understanding Conditional Probability Introduction Conditional probability is the probability of an event occurring given that another event has already occurred. This concept is essential in probability theory, as it helps …

Introduction Probability theory provides a framework for quantifying uncertainty and randomness in various processes. At the core of this theory are fundamental properties that govern how probabilities behave in relation …

Introduction Combination probability involves the calculation of the probability of selecting a subset of items from a larger set, where the order of selection does not matter. It is a crucial …

Introduction Probability theory is a branch of mathematics that deals with the analysis of random phenomena. It provides a framework for quantifying uncertainty and making informed predictions about events whose outcomes …

Introduction A two-dimensional discrete random variable involves a pair of random variables that can take on discrete values in a finite or countably infinite sample space. These random variables are studied …

Introduction In probability theory and statistics, numerous probability distributions help model different types of random events. Some distributions are well-suited for modeling real-world processes like reliability, uncertainty, or risk, while …

Introduction The Exponential Distribution is a continuous probability distribution that describes the time between events in a Poisson process. It is widely used in fields such as physics, engineering, finance, and …

Introduction The Normal Distribution, also known as the Gaussian distribution, is one of the most important and widely used probability distributions in statistics. It plays a central role in many …