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Average value of a random variable
expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. Provided that it is finite, the expected
Expected_value
Topics referred to by the same term
Look up expected in Wiktionary, the free dictionary. Expected may refer to: Expectation (epistemic) Expected value Expected shortfall Expected utility
Expected
Performance metric in football and hockey
player would be expected to score given the chances created, independent of whether those chances were actually converted. xG values are produced by statistical
Expected_goals
Decision theory term
The expected value of perfect information analysis tries to measure the expected cost of that uncertainty, which “can be interpreted as the expected value
Expected value of perfect information
Expected_value_of_perfect_information
In decision theory, the expected value of sample information (EVSI) is the expected increase in utility that a decision-maker could obtain from gaining
Expected value of sample information
Expected_value_of_sample_information
Topics referred to by the same term
Expected value is a term used in probability theory and statistics. It may also refer to: Expectation value (quantum mechanics), the probabilistic expected
Expected value (disambiguation)
Expected_value_(disambiguation)
Risk measure estimating the average loss in the worst tail of the distribution
"expected shortfall at q% level" is the expected return on the portfolio in the worst q % {\displaystyle q\%} of cases. ES is an alternative to value at
Expected_shortfall
Concept in economics
social behaviour. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e., the weighted
Expected_utility_hypothesis
Amount in information economics
known expected value of perfect information (EVPI) and expected value of sample information (EVSI). Note that VoI is not necessarily equal to "value of decision
Value_of_information
Concept in decision theory
In decision theory and quantitative policy analysis, the expected value of including uncertainty (EVIU) is a measure that quantifies the potential benefit
Expected value of including uncertainty
Expected_value_of_including_uncertainty
Theory that attempts to blend economics and ergodic theory
instance, expected-utility theory was proposed in 1738 by Daniel Bernoulli as a way of modeling behavior which is inconsistent with expected-value maximization
Ergodicity_economics
Expected gain on a financial investment
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure
Expected_return
Prospect-weighted valuation method for assessing uncertain project outcomes
Expected commercial value (ECV), also known as estimated commercial value, is a prospect-weighted value for a "project" with unclear conclusions; it is
Expected_commercial_value
Expected present value of life-contingent cash flows
The actuarial present value (APV) is the expected value of the present value of future payments whose timing or amount depends on uncertain events such
Actuarial_present_value
Probability distribution
a successful result, then the expected value of X is: E[X]=np. This follows from the linearity of the expected value along with the fact that X is the
Binomial_distribution
Valuation in finance
whether a planned activity is expected to create value. NPV works by converting future cash flows into their “present value,” recognising that money available
Net_present_value
Expected value of a quantum measurement
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as
Expectation value (quantum mechanics)
Expectation_value_(quantum_mechanics)
Averages of repeated trials converge to the expected value
small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced" by the others . Throughout
Law_of_large_numbers
Measure of spatial autocorrelation
conclusions you make about a phenomenon, especially when using distances. The expected value of Moran's I under the null hypothesis of no spatial autocorrelation
Moran's_I
Expected value of a random variable given that certain conditions are known to occur
conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional
Conditional_expectation
Probability distribution
first equation and X {\displaystyle X} does not satisfy the second. The expected value and variance of a geometrically distributed random variable X {\displaystyle
Geometric_distribution
Casino game of chance
The expected value of a $1 bet (except for the special case of top line bets), for American and European roulette, can be calculated as expected value=1n(36−n)=36n−1
Roulette
Paradox involving a game with repeated coin flipping
sum grows without bound so the expected win is an infinite amount of money. Considering nothing but the expected value of the net change in one's monetary
St._Petersburg_paradox
Proposition in probability theory
e., the expected value of the conditional expected value of X {\displaystyle X} given Y {\displaystyle Y} is the same as the expected value of X {\displaystyle
Law_of_total_expectation
Comparison of two distributions
quantile of the expected value of the order statistic of a standard normal distribution. More generally, Shapiro–Wilk test uses the expected values of the order
Q–Q_plot
Form of the utility function
one over the domain of non-negative values for c. The reason for its irrelevance is that maximizing the expected value of utility u ( c ) = ( 1 − e − a c
Exponential_utility
Statistical hypothesis testing measure
the q-value in the Storey procedure provides a means to estimate the positive false discovery rate (pFDR). Just as the p-value gives the expected false
Q-value_(statistics)
Gambling strategy where the amount is raised until a person wins or becomes insolvent
8744%. The expected amount won is (1 × 0.978744) = 0.978744. The expected amount lost is (63 × 0.021256)= 1.339118. Thus, the total expected value for each
Martingale_(betting_system)
Theorem in probability and statistics
unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability
Law of the unconscious statistician
Law_of_the_unconscious_statistician
Probability that random variable X is less than or equal to x
_{x\to +\infty }x(1-F_{X}(x))=0.} In addition, the (finite) expected value of the real-valued random variable X {\displaystyle X} can be defined on the
Cumulative distribution function
Cumulative_distribution_function
Economics theory
individuals seek to maximise their expected utility rather than the expected monetary value of assets. In defining expected utility in this sense, the pair
Risk_aversion
Probability distribution on a hyper-sphere of arbitrary dimension
the expected value is: A p ( κ ) μ {\displaystyle A_{p}(\kappa ){\boldsymbol {\mu }}} . For κ = 0 {\displaystyle \kappa =0} , the expected value is at
Von_Mises–Fisher_distribution
Concept in probability theory and gambling
gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system. The
Gambler's_ruin
industries, but has value in the protection of personal and/or corporate data—in every industry. Time to value depends on how the expected benefit of a project
Time_to_value
Difference between a variable's observed value and a reference value
difference between an observed value and the true value of a quantity of interest (where true value denotes the Expected Value, such as the population mean)
Deviation_(statistics)
Bound on optimal stopping in random sequences
expected value of a decision-making process that handles a sequence of random inputs from known probability distributions, relative to the expected value
Prophet_inequality
Financial measurement
derivative of the total expected value with respect to time. Cost of Delay combines an understanding of value with how that value leaks away over time.
Cost_of_delay
Puzzle in logic and mathematics
switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap
Two_envelopes_problem
Decision rule used for minimizing the possible loss for a worst-case scenario
making is being non-probabilistic: in contrast to decisions using expected value or expected utility, it makes no assumptions about the probabilities of various
Minimax
Concept in decision theory
( x i ) . {\displaystyle P(x_{i}).} The subjective expected utility is the resulting expected value of the utility: E [ u ( X ) ] = ∑ i u ( x i ) P ( x
Subjective_expected_utility
Technique in quantum computation
Hadamard test is a method used to create a random variable whose expected value is the expected real part R e ⟨ ψ | U | ψ ⟩ {\displaystyle \mathrm {Re} \langle
Hadamard_test
Model in probability theory
stochastic process in which the expected value of the next observation, given all prior observations, is equal to the most recent value. In other words, the conditional
Martingale (probability theory)
Martingale_(probability_theory)
Bet sizing formula for long-term growth
maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate. John
Kelly_criterion
Mathematical relation assigning a probability event to a cost
on the expected value of the loss function; however, this quantity is defined differently under the two paradigms. We first define the expected loss in
Loss_function
Concept in psychology
with higher or equal expected value. Conversely, rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking
Risk_aversion_(psychology)
Calculation of financial risk
Expected loss is the sum of the values of all possible losses, each multiplied by the probability of that loss occurring. In bank lending (homes, autos
Expected_loss
Poker term
of winning a hand with a future card in order to estimate the call's expected value. The purpose of this is to statistically guide a player's decision between
Pot_odds
Theorem in probability theory
under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. The concept can be understood
Optional_stopping_theorem
Random variable with multiple component dimensions
{\mathcal {R}}} denotes support of Y {\displaystyle \mathbf {Y} } . The expected value or mean of a random vector X {\displaystyle \mathbf {X} } is a fixed
Multivariate_random_variable
Value calculated on simplified assumptions
model. Expected value Look-through earnings Net realizable value Option (finance) § Basic decomposition Valuation of options § Intrinsic value Option
Intrinsic_value_(finance)
that the maximum discrepancy of an object is as small as possible. Expected-value discrepancy (also called Lebesgue-measure or continuous discrepancy):
Geometric_discrepancy
Type of location test in statistical analysis
two values in the pair, and εij is a random noise term that is independent across all data points. The constant values μ1, μ2 are the expected values of
Paired_difference_test
Numerical method for the valuation of financial options
value at the node. The steps are as follows: Under the risk neutrality assumption, today's fair price of a derivative is equal to the expected value of
Binomial options pricing model
Binomial_options_pricing_model
Mathematical function
probability density function of a normally distributed random variable with expected value μ = b and variance σ2 = c2. In this case, the Gaussian is of the form
Gaussian_function
Any individual whose preferences satisfy four axioms has a utility function
the form of maximizing the expected value of some cardinal utility function. The theorem forms the foundation of expected utility theory. In 1947, John
Von Neumann–Morgenstern utility theorem
Von_Neumann–Morgenstern_utility_theorem
Concept in mathematical finance
in probability theory: the expected value of a convex function is greater than or equal to the function of the expected value: E [ f ( X ) ] ≥ f ( E [ X
Convexity_(finance)
Measure of variation in statistics
This specific one is biased, meaning that its expected value in repeated sampling deviates from the true value, but it is still consistent. Its mean squared
Standard_deviation
Logarithm of probabilities, useful for calculations
intuitive interpretation in terms of information theory: the negative expected value of the log probabilities is the information entropy of an event. Similarly
Log_probability
Principle used in linear cryptanalysis
linear cryptanalysis. The lemma states that the bias (deviation of the expected value from 1/2) of a linear Boolean function (XOR-clause) of independent binary
Piling-up_lemma
Nonconstructive method for mathematical proofs
calculating the expected value of some random variable. If it can be shown that the random variable can take on a value less than the expected value, this proves
Probabilistic_method
Information theory
information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third. For random variables X
Conditional mutual information
Conditional_mutual_information
Statistical technique for smoothing categorical data
observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution
Additive_smoothing
Technique used in management and information systems
Estimates the expected value E(task) and the standard deviation SD(task) of this estimate for each task time Calculates the expected value for the total
Three-point_estimation
Probability and computer science concept
concentration inequality which bounds the deviation between the sampled value and the expected value of certain functions when they are evaluated on independent random
McDiarmid's_inequality
Real function with secant line between points above the graph itself
a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random
Convex_function
Statistical measure of how far values spread from their average
far a set of numbers are spread out from their average value. It is defined as the expected value of the squared deviation from the mean of a random variable
Variance
Monte Carlo algorithm
integral (such as the expected value of one of the variables). Typically, some of the variables correspond to observations whose values are known, and hence
Gibbs_sampling
Rule for calculating an estimate of a given quantity based on observed data
error of θ ^ {\displaystyle {\widehat {\theta }}} is defined as the expected value (probability-weighted average, over all samples) of the squared errors;
Estimator
Probability distribution modeling a coin toss which need not be fair
{\displaystyle p} based on a random sample is the sample mean. The expected value of a Bernoulli random variable X {\displaystyle X} is E [ X ] = p
Bernoulli_distribution
Average uncertainty in variable's states
"bans", or "hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable. The concept of information entropy
Entropy_(information_theory)
Variance of a random variable given value of other variables
Recall that variance is the expected squared deviation between a random variable (say, Y) and its expected value. The expected value can be thought of as a
Conditional_variance
Investment strategy
expected payout of the short option. Realized when the price of the underlying at expiration is in between the strikes of the options. Expected value
Credit_spread_(options)
Shares into which ownership of the corporation is divided
future value of the company; and that share prices of equities are priced efficiently, which is to say that they represent accurately the expected value of
Stock
Possibility of something bad happening
the value at risk. Risk is often measured as the expected value of the loss. This combines the probabilities and consequences into a single value. See
Risk
Concepts in probability and statistics
tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μX and μY and standard deviations
Covariance_and_correlation
Better to receive money now than later
their money now only if they expect a favorable net return on their investment in the future, such that the increased value to be available later is sufficiently
Time_value_of_money
Topics referred to by the same term
valuable, value, value types, valued, or values in Wiktionary, the free dictionary. Wikiquote has quotations related to Value. Value or values may refer
Value
choose q so as to maximize the expected utility of profit: Maximize Eu(pq – c(q) – g), where E is the expected value operator, u is the firm's utility
Two-moment_decision_model
Aspect of decision and prospect theories
aversion, which describes the rational behavior of valuing an uncertain outcome at less than its expected value. When defined in terms of the pseudo-utility
Loss_aversion
Gain from observing another random variable
theory and machine learning, information gain refers to the conditional expected value of the Kullback–Leibler divergence of the univariate probability distribution
Information gain (decision tree)
Information_gain_(decision_tree)
Measure of the error of an estimator
difference between the estimated values and the true value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact
Mean_squared_error
Statistical method
observed value and its expected value in a 2 × 2 contingency table. This reduces the chi-squared value obtained and thus increases its p-value. The effect
Yates's correction for continuity
Yates's_correction_for_continuity
Economics concept
this is typically modelled by assuming that the expected value of a variable is equal to the expected value predicted by the model. For example, suppose
Rational_expectations
Project management technique
for the whole project or program. Similarly, a value breakdown structure will provide the expected value-added of each activity and/or component of the
Value_breakdown_structure
Largest integer that divides given integers
greatest common divisor d is d−k/ζ(k). Using this information, the expected value of the greatest common divisor function can be seen (informally) to
Greatest_common_divisor
Discrete probability distribution
that, in the categorical distribution specifically, the expected value of seeing a particular value i is directly specified by the associated parameter pi
Categorical_distribution
In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance
Expected_mean_squares
Test of statistical significance
p)=\Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}} . As we have observed a value greater than the expected value, we could consider the probability of observing 51 6s or
Binomial_test
Class of statistical models
predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values (predictors)
Generalized_linear_model
Probability distribution
its expected value: ln G X = E [ ln X ] {\displaystyle \ln G_{X}=\operatorname {E} [\ln X]} For a beta distribution, the expected value integral
Beta_distribution
Variation of the minimax algorithm
this variant has "chance" ("move by nature") nodes, which take the expected value of a random event occurring. In game theory terms, an expectiminimax
Expectiminimax
Form of gambling
fixed-odds arbitrage actions and Dutch books. When a bet has a positive expected value, it is said to be getting "the best of it." In contrast, "laying odds"
Fixed-odds_betting
Concept in statistics and wave theory
{(x-x_{0})^{2}}{2\sigma ^{2}}}\right]} where σ is the standard deviation and x0 is the expected value, then the relationship between FWHM and the standard deviation is F
Full_width_at_half_maximum
Probabilistic inequality applying on sum of bounded random variables
that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by
Hoeffding's_inequality
Software testing technique
difficulty of determining the expected outcomes of selected test cases or to determine whether the actual outputs agree with the expected outcomes. Metamorphic
Metamorphic_testing
Measure of the shape of a function
function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment
Moment_(mathematics)
Card game
voluntarily by a player who either believes the bet has a positive expected value or who is trying to bluff other players for various strategic reasons
Poker
Measure of relative information in probability theory
because limθ→0+θlogθ=0. Intuitively, notice that by definition of expected value and of conditional probability, H(Y|X) can be written as H(Y|X)=𝔼[f(X
Conditional_entropy
Compound probability distribution
then P(X=k)=∫0∞qλ(k)π(λ)dλ. The variance is always bigger than the expected value. This property is called overdispersion. This is in contrast to the
Mixed_Poisson_distribution
Approximation in mathematics
x+1/2)} where Y is a normally distributed random variable with the same expected value and the same variance as X, i.e., E(Y) = np and var(Y) = np(1 − p).
Continuity_correction
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