Encyclopedia - Probability: Encyclopedia - Probability
The word probability derives from the Latin probare (to prove, or to test). Informally, probable is one of several words applied to uncer...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Probabilities Of Probabilities
One criticism levelled at the Bayesian probability interpretation has been that a single probability assignment cannot convey how well gr...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Formalization Of Probability
Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms -- that is, in terms that ca...   » Read the article

Encyclopedia - Haemophilia: Encyclopedia Ii - Haemophilia - Probability
If a female gives birth to a haemophiliac child, she is possibly a carrier for the disease. Until modern direct DNA testing, however, it ...   » Read the article

Encyclopedia - Haemophilia: Encyclopedia Ii - Haemophilia - Probability
If a female gives birth to a haemophiliac child, she is possibly a carrier for the disease. Until modern direct DNA testing, however, it ...   » Read the article

Encyclopedia - Statistics: Encyclopedia Ii - Statistics - Probability
Statistics makes extensive use of the concept of probability. The probability of an event is often defined as a number between one and ze...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Historical Remarks
The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of p...   » Read the article

Encyclopedia - Algorithmic Probability: Encyclopedia - Algorithmic Probability
Around 1960, Ray Solomonoff invented the concept of algorithmic probability. Take a universal computer and randomly generate an input pro...   » Read the article

Encyclopedia - Appeal To Probability: Encyclopedia - Appeal To Probability
The appeal to probability is a logical fallacy, often used in conjunction with other fallacies. It assumes that because something could h...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia - Bayesian Probability
Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of a statement. ...   » Read the article

Encyclopedia - Conditional Probability: Encyclopedia - Conditional Probability
This article defines some terms which characterize probability distributions of two or more variables. Conditional probability is the pro...   » Read the article

Encyclopedia - Frequency Probability: Encyclopedia - Frequency Probability
The problems and paradoxes of the classical interpretation of probability motivated the development of the relative frequency concept of ...   » Read the article

Encyclopedia - Characteristic Function Probability Theory: Encyclopedia - Characteristic Function Probability Theory
In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, wh...   » Read the article

Encyclopedia - Wigner Quasi-probability Distribution: Encyclopedia - Wigner Quasi-probability Distribution
The Wigner quasi-probability distribution was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical m...   » Read the article

Encyclopedia - Probability Axioms: Encyclopedia Ii - Probability Axioms - Lemmas In Probability
From the Kolmogorov axioms one can deduce other useful rules for calculating probabilities: This is called The Addition Law of Probabi...   » Read the article

Encyclopedia - Probability Axioms: Encyclopedia Ii - Probability Axioms - Lemmas In Probability
From the Kolmogorov axioms one can deduce other useful rules for calculating probabilities: This is called the additition law of proba...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Varieties Of Bayesian Probability
The terms subjective probability, personal probability, epistemic probability and logical probability describe some of the schools of tho...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Applications Of Bayesian Probability
Today, there are a variety of applications of Bayesian probability that have gained wide acceptance. Some schools of thought emphasise Co...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Bayesian And Frequentist Probability
The Bayesian approach is in contrast to the concept of frequency probability where probability is held to be derived from observed or pre...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - History Of Bayesian Probability
"Bayesian" probability or "Bayesian" theory is named after Thomas Bayes (1701? — 1761), who proved a special case of what is called Bay...   » Read the article

Encyclopedia - Coupling Probability: Encyclopedia Ii - Coupling Probability - Definition
Using the standard formalism of probability, let X1 and X2 be two random variables defined on probability spaces (Ω1,F1,P1) and (Ω2,F2,...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Controversy
A quite different interpretation of the term probable has been developed by frequentists. In this interpretation, what are probable are n...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Varieties Of Bayesian Probability
The terms subjective probability, personal probability, epistemic probability and logical probability describe some of the schools of tho...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Applications Of Bayesian Probability
Today, there are a variety of applications of personal probability that have gained wide acceptance. Some schools of thought emphasise Co...   » Read the article

Encyclopedia - Prior Probability: Encyclopedia Ii - Prior Probability - Prior Probability Distribution
In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p (for examp...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - History Of Bayesian Probability
"Bayesian" probability or "Bayesian" theory is named after Thomas Bayes (c. 1702 — 1761), who proved a special case of what is called B...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Bayesian And Frequentist Probability
The Bayesian approach is in contrast to the concept of frequency probability where probability is held to be derived from observed or ima...   » Read the article

Encyclopedia - Probable Cause: Encyclopedia Ii - Probable Cause - Definition
The most widely held common definition is "a reasonable belief that a crime has been committed". An alternative definition has been propo...   » Read the article

Encyclopedia - Stability Probability: Encyclopedia Ii - Stability Probability - Examples
The most familiar stable distribution is the normal distribution with PDF and characteristic function: Note that the stability prop...   » Read the article

Encyclopedia - Conditional Probability: Encyclopedia Ii - Conditional Probability - Definition
If A and B are events, and P(B) > 0, then the conditional probability of A given B is Equivalently, we have ... See also:Condi...   » Read the article

Encyclopedia - Stability Probability: Encyclopedia Ii - Stability Probability - Definition
A random variable represents the possible outcomes of a set of events or a process. If it is a real-valued random variable, for any parti...   » Read the article

Encyclopedia - Probability Theory: Encyclopedia Ii - Probability Theory - Philosophy Of Application Of Probability
Some statisticians will assign probabilities only to events that are random, i.e., random variables, that are outcomes of actual or theor...   » Read the article

Encyclopedia - Probable Cause: Encyclopedia Ii - Probable Cause - Related Cases
The Supreme Court decision Illinois v. Gates (1983) lowered the threshold of probable cause by ruling that a "substantial chance" or "fai...   » Read the article

Encyclopedia - Probability Interpretations: Encyclopedia Ii - Probability Interpretations - Epistemological Controversy
While frequentism is widely accepted as a scientific tool, the use of Bayesian probability often raises the philosophical debate as to wh...   » Read the article

Encyclopedia - Probability Axioms: Encyclopedia Ii - Probability Axioms - Kolmogorov Axioms
The following three axioms are known as the Kolmogorov axioms, after Andrey Kolmogorov who developed them. We have an underlying set Ω, ...   » Read the article

Encyclopedia - Probability Axioms: Encyclopedia Ii - Probability Axioms - Kolmogorov Axioms
The following three axioms are known as the Kolmogorov axioms, after Andrey Kolmogorov who developed them. We have an underlying set Ω, ...   » Read the article

Encyclopedia - Probability Interpretations: Encyclopedia Ii - Probability Interpretations - Practical Controversy
The difference of view has also many implications for the methods by which statistics is practiced, and for the way in which conclusions ...   » Read the article

Encyclopedia - Probability Density Function: Encyclopedia Ii - Probability Density Function - Probability Function Associated To Multiple Variables
For continuous random variables , it is also possible to define a probability density function associated to the set as a whole. This den...   » Read the article

Encyclopedia - Bayesian Probability: Encyclopedia Ii - Bayesian Probability - Bayesian Data Analysis
One criticism levelled at the Bayesian probability interpretation by frequentists is that a single probability cannot convey how much evi...   » Read the article

Encyclopedia - Conditional Probability: Encyclopedia Ii - Conditional Probability - Mutual Exclusivity
Two events A and B are mutually exclusive if and only if as long as and . Then and . In other words, the probability of A ha...   » Read the article

Encyclopedia - Conditional Probability: Encyclopedia Ii - Conditional Probability - Statistical Independence
Two random events A and B are statistically independent if and only if Thus, if A and B are independent, then their joint probability ...   » Read the article

Encyclopedia - Probability Distribution: Encyclopedia Ii - Probability Distribution - List Of Important Probability Distributions
Several probability distributions are so important in theory or applications that they have been given specific names: Probability distr...   » Read the article

Encyclopedia - Probability-generating Function: Encyclopedia Ii - Probability-generating Function - Properties
Probability-generating function - Power series. Probability-generating functions obey all the rules of power series with non-negative c...   » Read the article

Encyclopedia - Prior Probability: Encyclopedia Ii - Prior Probability - Informative Priors
An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at...   » Read the article

Encyclopedia - Prior Probability: Encyclopedia Ii - Prior Probability - Uninformative Priors
An uninformative prior expresses vague or general information about a variable. The term "uninformative prior" is a misnomer; such a prio...   » Read the article

Encyclopedia - Probability-generating Function: Encyclopedia Ii - Probability-generating Function - Definition
If X is a discrete random variable taking values on some subset of the non-negative integers, {0,1, ...}, then the probability-generating...   » Read the article

Encyclopedia - Probability Theory: Encyclopedia Ii - Probability Theory - A Somewhat More Abstract View Of Probability
Mathematicians usually take probability theory to be the study of probability spaces and random variables — an approach introduced by K...   » Read the article

Encyclopedia - Stability Probability: Encyclopedia Ii - Stability Probability - Calculating The Pdf For The Linear Combination
To determine if a family is stable, we need to be able to calculate the PDF for the Y variable. The probability that Y takes on a value f...   » Read the article

Encyclopedia - Probability Density Function: Encyclopedia Ii - Probability Density Function - Probability Function Associated To Multiple Variables
For a set of continuous random variables , it is also possible to define a probability density function associated to the set as a whole....   » Read the article

Encyclopedia - Probability Density Function: Encyclopedia Ii - Probability Density Function - Further Details
For example, the continuous uniform distribution on the interval [0,1] has probability density f(x) = 1 for 0 ≤ x ≤ 1 and zero elsewh...   » Read the article

Encyclopedia - Probability Density Function: Encyclopedia Ii - Probability Density Function - Simplified Explanation
A probability density function is any function f(x) that describes the probability density in terms of the input variable x in a manner d...   » Read the article

Encyclopedia - Lottery: Encyclopedia Ii - Lottery - Probability Of Winning
The chances of winning a lottery jackpot are principally determined by several factors: the count of possible numbers, the count of winni...   » Read the article

Encyclopedia - Probability Mass Function: Encyclopedia Ii - Probability Mass Function - Mathematical Description
Suppose that X is a discrete random variable, taking values on some countable sample space  S ⊆ R. Then the probability mass funct...   » Read the article

Encyclopedia - Probability Density Function: Encyclopedia Ii - Probability Density Function - Link Between Discrete And Continuous Distributions
The definition of a probability density function at the start of this page makes it possible to describe the variable associated with a c...   » Read the article

Encyclopedia - Poker Probability: Encyclopedia Ii - Poker Probability - Frequency Of 5 Card Poker Hands
The following enumerates the frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52, without wil...   » Read the article

Encyclopedia - Event Probability Theory: Encyclopedia Ii - Event Probability Theory - A Simple Example
If we assemble a deck of 52 playing cards and two jokers, and draw a single card from the deck, then the sample space is a 54-element set...   » Read the article

Encyclopedia - Characteristic Function Probability Theory: Encyclopedia Ii - Characteristic Function Probability Theory - The Inversion Theorem
More than that, there is a bijection between cumulative probability distribution functions and characteristic functions. In other words, ...   » Read the article

Encyclopedia - Wigner Quasi-probability Distribution: Encyclopedia Ii - Wigner Quasi-probability Distribution - Mathematical Properties
1. P(x, p) is real 2. The x and p probability distributions are given by the marginals: Typically the trace of ρ is equal to 1. 1. a...   » Read the article

Encyclopedia - Characteristic Function Probability Theory: Encyclopedia Ii - Characteristic Function Probability Theory - Uses Of Characteristic Functions
Characteristic functions are particularly useful for dealing with functions of independent random variables. For example, if X1, X2, ...,...   » Read the article

Encyclopedia - Maximum Entropy Probability Distribution: Encyclopedia Ii - Maximum Entropy Probability Distribution - Definition Of Entropy
If X is a discrete random variable with distribution given by then the entropy of X is defined as If X is a continuous random varia...   » Read the article

Encyclopedia - Maximum Entropy Probability Distribution: Encyclopedia Ii - Maximum Entropy Probability Distribution - Examples Of Maximum Entropy Distributions
Maximum entropy probability distribution - Given mean and standard deviation: the normal distribution. The most important maximum entro...   » Read the article

Encyclopedia - Median: Encyclopedia Ii - Median - Medians Of Probability Distributions
For any probability distribution on the real line with cumulative distribution function F, regardless of whether it is any kind of contin...   » Read the article

Encyclopedia - Cumulant: Encyclopedia Ii - Cumulant - Cumulants Of Probability Distributions
In probability theory and statistics, the cumulants κn of the probability distribution of a random variable X are given by In other w...   » Read the article

Encyclopedia - Negligible: Encyclopedia Ii - Negligible - Examples In Probability
The continuing success of the global travel industry depends upon the general public's perception that the personal risks involved in air...   » Read the article

Encyclopedia - Parameter: Encyclopedia Ii - Parameter - Probability Theory
In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, dist...   » Read the article

Encyclopedia - Bloom Filter: Encyclopedia Ii - Bloom Filter - Probability Of False Positives
Assume that a hash function selects each array position with equal probability. The probability that a certain bit is not set to one by a...   » Read the article

Encyclopedia - Subject Philosophy: Encyclopedia Ii - Subject Philosophy - Subjectivism In Probability
In probability, a subjectivism stands for the view that probabilities are simply degrees-of-belief by rational agents in a certain propos...   » Read the article

Encyclopedia - Correlation Function: Encyclopedia Ii - Correlation Function - Properties Of Probability Distributions
With these definitions, the study of correlation functions is equivalent to the study of probability distributions. Probability distribut...   » Read the article

Encyclopedia - Aztlán: Encyclopedia Ii - Aztlán - Probable Etymology
Aztlan is believed to mean "Place of Whiteness" or "Place of Herons" (Nahuatl aztatl herons/white-plumed birds + tlan(tli) rooted in (as ...   » Read the article

Encyclopedia - Uncertainty: Encyclopedia Ii - Uncertainty - Relation Between Uncertainty Probability And Risk
In his seminal work Risk, Uncertainty, and Profit, Frank Knight (1921) established the important distinction between risk and uncertainty...   » Read the article

Encyclopedia - Gamma Distribution: Encyclopedia Ii - Gamma Distribution - Probability Density Function
The probability density function of the gamma distribution can be expressed in terms of the gamma function: where k > 0 is the shap...   » Read the article

Encyclopedia - Checking If A Coin Is Fair: Encyclopedia Ii - Checking If A Coin Is Fair - Posterior Probability Density Function
One way of verifying this is to calculate the posterior probability density function of Bayesian probability theory. A test is performed ...   » Read the article

Encyclopedia - Degrees Of Freedom Statistics: Encyclopedia Ii - Degrees Of Freedom Statistics - Parameters In Probability Distributions
The probability distributions of residuals are often parametrized by these numbers of degrees of freedom. Thus one speaks of a chi-square...   » Read the article

Encyclopedia - Infinite Monkey Theorem: Encyclopedia Ii - Infinite Monkey Theorem - Probabilities
Ignoring punctuation, spacing, and capitalization, and assuming a uniform distribution of letters, a monkey has one chance in 26 of corre...   » Read the article

Encyclopedia - Autocatalytic Set: Encyclopedia Ii - Autocatalytic Set - Probability That A Random Set Is Autocalytic
Studies of the above model show that random RS can be autocatalytic with high probability under some assumptions. This comes from the fac...   » Read the article

Encyclopedia - Dirichlet Distribution: Encyclopedia Ii - Dirichlet Distribution - Probability Density Function
The probability density function of the Dirichlet distribution of order K is the following function of a K-dimensional vector x = (x1, .....   » Read the article

Encyclopedia - Nuclear Chain Reaction: Encyclopedia Ii - Nuclear Chain Reaction - Numerical Example For The Probability Of A Chain Reaction
Suppose a fission caused by a neutron hitting a nucleus produces 3 neutrons (i.e. 2 extra). Also suppose k > 1. The probability that a...   » Read the article

Encyclopedia - Riemann-stieltjes Integral: Encyclopedia Ii - Riemann-stieltjes Integral - Application To Probability Theory
If g is the cumulative probability distribution function of a random variable X that has a probability density function with respect to L...   » Read the article

Encyclopedia - Alignments Of Random Points: Encyclopedia Ii - Alignments Of Random Points - An Estimate Of The Probability Of Alignments Existing By Chance
Statistically, finding alignments on a landscape gets progressively easier as the area to be considered increases. One way of understandi...   » Read the article

Encyclopedia - Bayes' Theorem: Encyclopedia Ii - Bayes' Theorem - Derivation From Conditional Probabilities
To derive the theorem, we start from the definition of conditional probability. The probability of event A given event B is Likewise, ...   » Read the article

Encyclopedia - Checking If A Coin Is Fair: Encyclopedia Ii - Checking If A Coin Is Fair - Estimator Of True Probability
This estimator has an error (E) where | p − r | < E at a particular confidence level. To determine the number of times, a coin shoul...   » Read the article

Encyclopedia - Cia Cryptonym: Encyclopedia Ii - Cia Cryptonym - Partial List Of Cia Cryptonyms And Probable Definitions
CIA cryptonym - Operations and Projects. APPLE ARTICHOKE: Anti-interrogation project. Precusor to MKULTRA. AQUATONE: Lockheed U-2 Spy ...   » Read the article

Encyclopedia - Birthday Paradox: Encyclopedia Ii - Birthday Paradox - Calculating The Probability
To compute the approximate probability that in a room of n people, at least two have the same birthday, we disregard variations in the di...   » Read the article

Encyclopedia - Convergence Of Random Variables: Encyclopedia Ii - Convergence Of Random Variables - Convergence In Probability
We say that the sequence Xn converges towards X in probability if for every ε > 0. Convergence in probability is, indeed, the (poi...   » Read the article

Dictionary - Probability: Oceanography Dictionary - Probability
  Definition and meaning of probability:   probability - a quantitative description of the likely occurrence of a partic...   » Read the article

Dictionary - Probability: Parapsychology Dictionary On Probability
Probability: The likelihood that results in a test were due to chance.   See also Significance.   (See also: Probabili...   » Read the article

Dictionary - Probability: Insurance Terms Dictionary - Probability
Definition and meaning of Probability :   Probability: The likelihood or relative frequency of an event expressed in a number b...   » Read the article

Dictionary - Probability: Insurance Terms Dictionary - Probability
Definition and meaning of Probability :   Probability: The likelihood or relative frequency of an event expressed in a number b...   » Read the article

Dictionary - Simple Probability: Insurance Terms Dictionary - Simple Probability
Definition and meaning of Simple Probability :   Simple Probability: See Probability. (Source: InsWeb)   Also see the...   » Read the article

Dictionary - Simple Probability: Insurance Terms Dictionary - Simple Probability
Definition and meaning of Simple Probability :   Simple Probability: See Probability. (Source: InsWeb)   Also see the...   » Read the article

Dictionary - Theory Of Probability: Insurance Terms Dictionary - Theory Of Probability
Definition and meaning of Theory of Probability :   Theory of Probability: The mathematical principle upon which insurance is b...   » Read the article

Dictionary - Theory Of Probability: Insurance Terms Dictionary - Theory Of Probability
Definition and meaning of Theory of Probability :   Theory of Probability: The mathematical principle upon which insurance is b...   » Read the article

Dictionary - Joint Probability: Oceanography Dictionary - Joint Probability
  Definition and meaning of joint probability:   joint probability - the probability of two or more things occurring tog...   » Read the article

Dictionary - Theoretical Probability: Oceanography Dictionary - Theoretical Probability
  Definition and meaning of theoretical probability:   theoretical probability - the chances of events happening as dete...   » Read the article

Dictionary - Probable Maximum Loss, Pml: Property Insurance Glossary Dictionary - Probable Maximum Loss, Pml
Definition and meaning of Probable Maximum Loss, PML :   Probable Maximum Loss (PML): The maximum amount of loss that one would...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Probability In Mathematics
Probability axioms form the basis for mathematical probability theory. Calculation of probabilities can often be determined using combina...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Formalization Of Probability
Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms—that is, in terms that can...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Applications Of Probability Theory To Everyday Life
A major effect of probability theory on everyday life is in risk assessment and in trade on commodity markets. Governments typically appl...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Applications Of Probability Theory To Everyday Life
Two major applications of probability theory in everyday life are in risk assessment and in trade on commodity markets. Governments typic...   » Read the article

Encyclopedia - Probability: Encyclopedia Ii - Probability - Concepts
There is essentially one set of mathematical rules for manipulating probability; these rules are listed under "Formalization of probabili...   » Read the article