Probability density functionIn probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given point in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a "relative probability" that the value of the random variable would be equal to that point. Probability density is the probability per unit length, in other words.
Probability mass functionIn probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function.
Random variableVariable representing a random phenomenonA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.Cumulative distribution functionProbability that random variable X is less than or equal to xCumulative distribution function for the exponential distributionCumulative distribution function for the normal distributionIn probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variableX{\displaystyle X}, or just distribution function of X{\displaystyle X}, evaluated at x{\displaystyle x}, is the probability that X{\displaystyle X} will take a value less than or equal to x{\displaystyle x}.
Probability theoryProbability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.Event (probability theory)In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event consisting of only a single outcome is called an elementary event or an atomic event; that is, it is a singleton set.Probability measureIn mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable additivity. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire space.Probability axiomsThe standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. Like all axiomatic systems, they outline the basic assumptions underlying the application of probability to fields such as pure mathematics and the physical sciences, while avoiding logical paradoxes.Probability distributionMathematical function for the probability a given outcome occurs in an experimentIn probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more precisely, to events, which are sets of possible outcomes of a probabilistic experiment. Informally, a probability distribution tells us how likely different results are.
StatisticsStudy of collection and analysis of dataThe normal distribution, a very common probability density, is used extensively in inferential statistics.Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.Statistics (from German: Statistik, orig.
Experiment (probability theory)In probability theory, an experiment or trial (see below) is the mathematical model of any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial.
Coin flippingCoin flipping, coin tossing, or heads or tails involves launching a coin in the air and then checking which side is showing once it has landed, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes. Used in such a fashion, the coin serves as a binary lot.*As an Amazon Associate I earn from qualifying purchases.