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31 relations: Abel's theorem, Absolute convergence, Bernoulli distribution, Binomial distribution, Characteristic function (probability theory), Complex number, Compound Poisson process, Cumulant, Degenerate distribution, Derivative, Expected value, Factorial moment, Fair coin, Formal power series, Generating function, Geometric distribution, Independence (probability theory), Integer, Integer lattice, Law of total expectation, Moment-generating function, Negative binomial distribution, One-sided limit, Poisson distribution, Power series, Probability mass function, Probability theory, Radius of convergence, Random variable, Variance, Z-transform.
Abel's theorem
In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients.
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Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
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Bernoulli distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q.
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Binomial distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.
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Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Compound Poisson process
A compound Poisson process is a continuous-time (random) stochastic process with jumps.
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Cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.
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Degenerate distribution
In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Factorial moment
In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable.
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Fair coin
In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin.
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Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Geometric distribution
In probability theory and statistics, the geometric distribution is either of two discrete probability distributions.
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Independence (probability theory)
In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Integer lattice
In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose lattice points are ''n''-tuples of integers.
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Law of total expectation
The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, and the smoothing theorem, among other names, states that if X is a random variable whose expected value \operatorname(X) is defined, and Y is any random variable on the same probability space, then i.e., the expected value of the conditional expected value of X given Y is the same as the expected value of X. One special case states that if _i is a finite or countable partition of the sample space, then.
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Moment-generating function
In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.
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Negative binomial distribution
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.
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One-sided limit
In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.
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Poisson distribution
In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.
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Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
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Probability mass function
In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Radius of convergence
In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
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Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.
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References
[1] https://en.wikipedia.org/wiki/Probability-generating_function
