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 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.
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.
Fourier transformMathematical transform that expresses a function of time as a function of frequencyThe Fourier transform applied to the waveform of a C majorpianochord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G).
Moment generating functionConcept in probability theory and statisticsIn probability theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification of the random variable's probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple result…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.
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.
Central limit theoremIn probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample mean converges to a standard normal distribution. This holds even if the original variables themselves are not normally distributed. There are several versions of the CLT, each applying in the context of different conditions.
Univariate distributionIn statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables).
Joint probability distributionGiven random variablesX,Y,…{\displaystyle X,Y,\ldots }, that are defined on the same probability space, the multivariate or joint probability distribution for X,Y,…{\displaystyle X,Y,\ldots } is a probability distribution that gives the probability that each of X,Y,…{\displaystyle X,Y,\ldots } falls in any particular range or discrete set of values specified for that variable.
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.Value (mathematics)In mathematics, a mathematical value is a broad term that refers to any definite entity that can be manipulated with operators according to the well-defined rules of its mathematical system. Certain values can correspond to the real world, although most values in mathematics generally exist purely as abstract objects with no connection to the real world. Numerical valuesNumbers (specifically the reals) are values that represent quantities.*As an Amazon Associate I earn from qualifying purchases.