"Probability theory or probability calculus is the branch of mathematics concerned with probability."
The study of random events and their likelihood, including the rules of probability and statistical inference.
Basic Probability: Introduction to the concept of probability and how it is calculated.
Sampling: Methods of sampling and its applications in probability.
Probability Distributions: Various types of probability distributions like binomial, normal, Poisson, etc.
Conditional Probability: Calculation of probability when some conditions are already given.
Bayes' Theorem: The concept of prior probability and posterior probability and its applications.
Central Limit Theorem: A theorem which states that the sampling distribution of the sample means approaches a normal distribution.
Hypothesis Testing: A process of testing a hypothesis about a population parameter with the help of sample data.
Confidence Intervals: An interval estimate of a population parameter with a level of confidence.
Regression Analysis: A process of studying the relationship between a dependent variable and one or more independent variables.
Markov Chains: A stochastic model that describes a sequence of events where the probability of each event depends only on the state attained in the previous event.
Monte Carlo Simulation: A probabilistic modeling technique that uses random sampling to obtain numerical results.
Game Theory: A study of mathematical models of conflict and cooperation between intelligent rational decision-makers.
Stochastic Processes: A collection of random variables that change over time.
Queuing Theory: A mathematical study of waiting lines or queues.
"Probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms."
"Typically these axioms formalize probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space."
"Any specified subset of the sample space is called an event."
"Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes."
"Stochastic processes provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion."
"Two major results in probability theory describing such behavior are the law of large numbers and the central limit theorem."
"It is not possible to perfectly predict random events."
"As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data."
"Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation."
"A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics."
"...expressing it through a set of axioms."
"...a measure taking values between 0 and 1."
"A set of outcomes called the sample space."
"Discrete and continuous random variables..."
"...mathematical abstractions of non-deterministic or uncertain processes or measured quantities..."
"The law of large numbers describes the behavior of random events."
"The central limit theorem describes the behavior of random events."
"Probability theory is essential to many human activities that involve quantitative analysis of data."
"Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state."