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Concept in probability theory
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It
Law_of_total_probability
Proposition in probability theory
The proposition in probability theory known as the law of total expectation, the law of iterated expectations (LIE), Adam's law, the tower rule, and the
Law_of_total_expectation
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Theorem in probability theory
The law of total variance is a fundamental result in probability theory that expresses the variance of a random variable Y in terms of its conditional
Law_of_total_variance
Concept in probability theory
In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical
Total variation distance of probability measures
Total_variation_distance_of_probability_measures
Number measuring the chance an event occurs
Probability concerns events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger
Probability
Overview of and topical guide to probability
axioms of probability Boole's inequality Probability interpretations Bayesian probability Frequency probability Conditional probability The law of total probability
Outline_of_probability
Probability of an event occurring, given that another event has already occurred
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption
Conditional_probability
Averages of repeated trials converge to the expected value
In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent
Law_of_large_numbers
Formula in probability theory
In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are
Law_of_total_covariance
Probability distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes
Binomial_distribution
Foundations of probability theory
Cox's theorem derives the laws of probability based on a "logical" definition of probability as the likelihood or credibility of arbitrary logical propositions
Probability_axioms
Mathematical concept
In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct
Probability_space
Possible result of an experiment or trial
In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is a unique random
Outcome_(probability)
Cumulative distribution function Law of total cumulance Law of total expectation Law of total probability Law of total variance Almost surely Cox's theorem
List_of_probability_topics
Observed value of a random variable
In probability and statistics, a realization or observation (also called observed value) of a random variable or random element is the value that is actually
Realization_(probability)
Rule of logical inference
p must also be false. Modus tollens represents an instance of the law of total probability combined with Bayes' theorem expressed as: Pr ( P ) = Pr (
Modus_tollens
Conditional probability used in Bayesian statistics
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood
Posterior_probability
Mathematical rule for inverting probabilities
In probability theory, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting
Bayes'_theorem
probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of
Law_of_total_cumulance
Random process independent of past history
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability
Markov_chain
Measure of total value one, generalizing probability distributions
In 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
Probability_measure
Diagram to represent a probability space in probability theory
In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such
Tree diagram (probability theory)
Tree_diagram_(probability_theory)
Types of numerical variables in mathematics
problems. In statistical theory, the probability distributions of continuous variables can be expressed in terms of probability density functions. In continuous-time
Continuous or discrete variable
Continuous_or_discrete_variable
Theory and paradigm of statistics
{\displaystyle B} . The probability of the evidence P ( B ) {\displaystyle P(B)} can be calculated using the law of total probability. If { A 1 , A 2 , …
Bayesian_statistics
Procedure that can be infinitely repeated, with a well-defined set of outcomes
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
Experiment (probability theory)
Experiment_(probability_theory)
Mathematical function for the probability a given outcome occurs in an experiment
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more
Probability_distribution
Probability theory term
{1}{2^{10}}}{\binom {10}{x}}={\frac {1}{8}},} which is an instance of the law of total probability E ( P ( A | X ) ) = P ( A ) . {\displaystyle \mathbb {E} (\mathbb
Conditioning_(probability)
Process forming a path from many random steps
equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging
Random_walk
Probability distribution modeling a coin toss which need not be fair
probability distribution of a random variable which takes the value 1 with probability p {\displaystyle p} and the value 0 with probability q = 1 − p {\displaystyle
Bernoulli_distribution
Randomly determined process
Stochasticity is the property of being well-described by a random probability distribution. Stochasticity and randomness are technically distinct concepts:
Stochastic
Event that contains only one outcome
because the probability of each elementary event is zero, the probabilities assigned to elementary events do not determine a continuous probability distribution
Elementary_event
Determining the probability of future events based on past events
distribution. The probability estimates given by it do not always obey the law of total of probability. Applying the law of total probability to various scenarios
Inductive_probability
statistician Law of total covariance Law of total cumulance Law of total expectation Law of total probability Law of total variance Law of truly large
List_of_statistics_articles
When the occurrence of one event does not affect the likelihood of another
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically
Independence (probability theory)
Independence_(probability_theory)
Type of probability distribution
} , that are defined on the same probability space, the joint probability distribution or multivariate probability distribution for X , Y , … {\displaystyle
Joint probability distribution
Joint_probability_distribution
Discrete probability distribution
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a
Poisson_distribution
Rule of logical inference
represents a generalization of both modus ponens and the Law of total probability. Philosophers and linguists have identified a variety of cases where modus ponens
Modus_ponens
Diagram that shows all possible logical relations between a collection of sets
elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram
Venn_diagram
In statistics and probability theory, set of outcomes to which a probability is assigned
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
Event_(probability_theory)
American quantum physicist
probability distributions in a framework where the Born rule appears as a modification of the classical law of total probability. He is a Fellow of the
Christopher_A._Fuchs
Observation that in many real-life datasets, the leading digit is likely to be small
known instance of this observation and includes a distribution on the second digit as well. Newcomb proposed a law that the probability of a single number
Benford's_law
System in which no randomness is involved in determining its future states
initial state. Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given
Deterministic_system
Average value of a random variable
In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it
Expected_value
Concept in probability theory and gambling
of money, P ( R n ) {\displaystyle P(R_{n})} . Then, using the Law of Total Probability, we have P ( R n ) = P ( R n ∣ W ) P ( W ) + P ( R n ∣ W ¯ ) P
Gambler's_ruin
Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic
History_of_probability
Hypothesis in epistemological philosophy
event. It seems reasonable, as a starting position, to adopt the law of total probability and extend it to updating in much the same way as was Bayes' theorem
Radical_probabilism
Aspect of probability and statistics
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the
Marginal_distribution
Interpretation of quantum mechanics
of nature which made quantum theory so successful. The urgleichung does not replace the law of total probability. Rather, the urgleichung and the law
QBism
Probability puzzle
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and
Monty_Hall_problem
Application of quantum theory mathematics to cognitive phenomena
Contextuality implies existence of incompatible mental variables, violation of the classical law of total probability, and constructive or destructive
Quantum_cognition
Any experiment with two possible random outcomes
In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success"
Bernoulli_trial
Kazemitabar and Jal. Kazemitabar, "The Bijection Property in the Law of Total Probability and Its Application in Communication Theory," in IEEE Communications
Carleman's_condition
Opposite of a probability event
[not heads]. In a random experiment, the probabilities of all possible events (the sample space) must total to 1— that is, some outcome must occur on
Complementary_event
takes value 1 with probability p and value 0 with probability q = 1 − p. The Rademacher distribution, which takes value 1 with probability 1/2 and value −1
List of probability distributions
List_of_probability_distributions
Inequality applying to probability spaces
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at
Boole's_inequality
Topics referred to by the same term
Adam's Law may refer to either: Adam's Law, a court show presided over by Adam Levy, the son of Judy Sheindlin Law of total expectation, a result in probability
Adam's_law
Expected value of a random variable given that certain conditions are known to occur
conditional expectation Law of total cumulance (generalizes the other three) Law of total expectation Law of total probability Law of total variance Kolmogorov
Conditional_expectation
Set of all possible outcomes or results of a statistical trial or experiment
In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is
Sample_space
Probability theory concept
probability theory, conditional independence describes situations in which an observation is irrelevant or redundant when evaluating the certainty of
Conditional_independence
Random process of binary (boolean) random variables
In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is
Bernoulli_process
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random
Stochastic_process
Apparent lack of pattern or predictability in events
of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy. The fields of mathematics, probability,
Randomness
Two propositions or events that cannot both be true
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example
Mutual_exclusivity
Variable representing a random phenomenon
such as in the roll of a die; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically
Random_variable
Philosophical concept
if A's occurrence increases the probability of B. This is sometimes interpreted to reflect the imperfect knowledge of a deterministic system but other
Indeterminism
Statistical law
(in terms of probability model of single sample) thing is likely to happen. An early formulation of the law appears in the 1953 collection of Littlewood's
Littlewood's_law
Random process in probability theory
t\operatorname {E} (D^{2}).\end{aligned}}} Lastly, using the law of total probability, the moment generating function can be given as follows: Pr ( Y
Compound_Poisson_process
Subjective attitude that something is true
that these subjective probabilities follow the same rules as objective probabilities. For example, the law of total probability might be applied to predict
Belief
Stochastic process with discrete movements
one-dimensional Brownian motion hits, say, value 1) or at totally inaccessible stopping times (e.g., the jumps of a Poisson process). The jumps may have finite activity
Jump_process
System for rating game players
the difference of the players' ratings, and we use a scaling factor s = 400 {\displaystyle s=400} , and, by law of total probability Pr { B wins }
Elo_rating_system
Concept in physics and chemistry
{inc} }|}}} Law of total probability requires that T + R = 1 {\displaystyle T+R=1} , which in one dimension reduces to the fact that the sum of the transmitted
Transmission_coefficient
Counterintuitive result in probability
999th digits of pi, or a version of the King James Bible) increases as the total string increases. This probability approaches 1 as the total string approaches
Infinite_monkey_theorem
Logic error due to ignoring the base rate
theorem, which can be computed from the preceding values using the law of total probability: p ( D ) = p ( D ∣ d r u n k ) p ( d r u n k ) + p ( D ∣ s o b
Base_rate_fallacy
Probability applied to gambling
The mathematics of gambling is a collection of probability applications encountered in games of chance and can be included in game theory. From a mathematical
Gambling_mathematics
principle / (F:B) Independence / (F:BR) Indicator function / (1F:B) Law of total probability / (F:B) Le Cam's theorem / (F:B) (1:D) Leftover hash lemma / (F:B)
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Topics referred to by the same term
one of two rules in mathematics: Law of total expectation, in probability and stochastic theory a rule governing the degree of a field extension of a field
Tower_rule
Set of events whose union covers the entire sample space
In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling
Collectively exhaustive events
Collectively_exhaustive_events
Formula in probability theory
variable, the law of total probability tells us that the expected probability of success in the next experiment is just the expected value of p. Since p
Rule_of_succession
American logician
event. It seems reasonable, as a starting position, to adopt the law of total probability and extend it to updating in much the same way as was Bayes' theorem
Richard_Jeffrey
Functional relationship between two quantities
factor to ensure that the total area is 1, as required by a probability distribution. More often one uses an asymptotic power law – one that is only true
Power_law
Statistical principle about ratio of effects to causes
phenomena. The occurrence probability of rare extreme (or catastrophic) events showing power-law distribution may be of several orders of magnitude greater than
Pareto_principle
Random variable with multiple component dimensions
In probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown
Multivariate_random_variable
Formal fallacy in statistical interpretation
{\frac {P[{\text{Suicide}}]}{P({\text{Protestant}})}}} However, the law of total probability gives P [ Suicide ] = P [ Suicide ∣ Protestant ] P ( Protestant
Ecological_fallacy
Statistics concept
available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete
Bayesian_programming
Indian academic examination
combinatorics, probability (including topics like conditional probability, law of total probability, Bayes' theorem), geometry, coordinate system (points and
Joint Entrance Examination – Advanced
Joint_Entrance_Examination_–_Advanced
will be received. This type of probability is called ″pair-wise error probability″ because the probability exists with a pair of signal vectors in a signal
Pairwise_error_probability
Power series derived from a discrete probability distribution
probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the
Probability generating function
Probability_generating_function
Type of cognitive bias
The neglect of probability, a type of cognitive bias, is the tendency to disregard probability when making a decision under uncertainty and is one simple
Neglect_of_probability
Complex number whose squared absolute value is a probability
quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square modulus of this quantity at a point
Probability_amplitude
Probability distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued
Normal_distribution
Distribution of an uncertain quantity
A prior probability distribution (often simply called the prior probability, prior distribution, or prior) of an uncertain quantity is its assumed probability
Prior_probability
Game theory concept
having incomplete information, and the probability space of the game still follows the law of total probability. Bayesian games are also useful because
Bayesian_game
Probability distribution
after the Italian polymath Vilfredo Pareto, is a probability distribution in the form of a power law that is used to describe social, quality control
Pareto_distribution
however: Y can only be observed if Z = 1 {\displaystyle Z=1} . By the law of total probability, P ( Y = 1 ) = P ( Y = 1 ∣ Z = 1 ) P ( Z = 1 ) + P ( Y = 1 ∣ Z
Set_identification
Written work by John Maynard Keynes
A Treatise on Probability, published by John Maynard Keynes in 1921, provides a much more general logic of uncertainty than the more familiar and straightforward
A_Treatise_on_Probability
Observational basis of thermodynamics
The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize
Laws_of_thermodynamics
Contract bridge guideline
Law of total tricks (abbreviated here as LoTT) is a guideline used to help determine how high to bid in a competitive auction. It is not really a law
Law_of_total_tricks
Theory of cognition
The universal law of generalization is a theory of cognition stating that the probability of a response to one stimulus being generalized to another is
Universal law of generalization
Universal_law_of_generalization
Graphical model
the law of total probability along with the independencies encoded in a dependency network can be used to decompose the inference task into a set of inference
Dependency network (graphical model)
Dependency_network_(graphical_model)
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