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Unsolved mathematical problem
The mean value problem is an open problem in the mathematical field of complex analysis first posed by Stephen Smale in 1981. The problem asks: For a
Mean_value_problem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that
Mean_value_theorem
Numeric quantity representing the center of a collection of numbers
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several
Mean
Linear regression model with a single explanatory variable
observation, the mean response at a given value of x, say xd, is an estimate of the mean of the y values in the population at the x value of xd, that is
Simple_linear_regression
18 mathematical problems stated in 1998
additional problems, "that don't seem important enough to merit a place on our main list, but it would still be nice to solve them:" Mean value problem Is the
Smale's_problems
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Philosophical problem articulated by David Hume
deem the naturalistic fallacy a fallacy. The is–ought problem is closely related to the fact–value distinction in epistemology. Though the terms are often
Is–ought_problem
conjecture on the Mahler measure of non-cyclotomic polynomials The mean value problem: given a complex polynomial f {\displaystyle f} of degree d ≥ 2 {\displaystyle
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical problem involving optimal stopping theory
interviewed previously. Skip is used to mean "reject immediately after the interview". Since the objective in the problem is to select the single best applicant
Secretary_problem
Problem in statistical estimation
{n}{k-1}}}&{\text{if }}n\geq m\end{cases}}} For k ≥ 3, N has the finite mean value: ( m − 1 ) ( k − 1 ) ( k − 2 ) − 1 {\displaystyle (m-1)(k-1)(k-2)^{-1}}
German_tank_problem
Measure of forecasting quality
statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts. It is the mean absolute error of the forecast values, divided by
Mean_absolute_scaled_error
Measure of prediction accuracy of a forecast
possible (see section below). Mean absolute percentage error is commonly used as a loss function for regression problems and in model evaluation, because
Mean absolute percentage error
Mean_absolute_percentage_error
Number taken as representative of a list of numbers
"average" sometimes refers to "the three Ms": mean, median, and mode. The median, defined as the value in the center after sorting the group, is usually
Average
Computer software bug occurring in 2038
type's maximum value is exceeded, the integer will overflow to its minimum value, which systems will interpret as in the past. The problem resembles the
Year_2038_problem
Approximation of physical behavior
product of the mean value of the spin and the fluctuation value. Finally, the last term involves a product of two fluctuation values. The mean field approximation
Mean-field_theory
American mathematician (born 1930)
S2CID 206590734.* 5-manifold Axiom A Geometric mechanics Homotopy principle Mean value problem Smale, Steve (1985). "On the Efficiency of Algorithms in Analysis"
Stephen_Smale
Cosmological fine-tuning problem
initial density came to be so closely fine-tuned to this 'special' value. The problem was first mentioned by Robert Dicke in 1969. The most commonly accepted
Flatness_problem
Philosophical concept
lives and his beliefs about the values [valuations] and purposes that should direct his conduct is the deepest problem of modern life." Moreover, a "culture
Instrumental and intrinsic value
Instrumental_and_intrinsic_value
In mathematics, Vinogradov's mean value theorem is an estimate for the number of equal sums of powers. It is an important inequality in analytic number
Vinogradov's mean-value theorem
Vinogradov's_mean-value_theorem
Function of the observed sample results
method of combining p-values Generalized p-value Harmonic mean p-value Holm–Bonferroni method Multiple comparisons problem p-rep p-value fallacy Italicisation
P-value
Statistics computed from a sample of data
sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger population
Sample_mean_and_covariance
Functions in mathematics
harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider the sequence on ( − ∞ , 0 ) × R {\displaystyle
Harmonic_function
Probability of shared birthdays
has a maximum value of 0.3864 occurring when n = 28. The basic problem considers all trials to be of one "type". The birthday problem has been generalized
Birthday_problem
Type of average of a collection of numbers
the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or
Arithmetic_mean
Average value of a random variable
theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average. The expected value of a random variable
Expected_value
Thought experiment in ethics
The trolley problem is a thought experiment in moral philosophy and moral psychology with many variations, involving hypothetical ethical dilemmas about
Trolley_problem
Problem asking the probability that the sun will rise tomorrow
The sunrise problem can be expressed as follows: "What is the probability that the sun will rise tomorrow?" The sunrise problem illustrates the difficulty
Sunrise_problem
Paradox involving a game with repeated coin flipping
amount of money a casino would need to continue the game indefinitely. The problem was invented by Nicolas Bernoulli, who stated it in a letter to Pierre
St._Petersburg_paradox
contraharmonic mean (or antiharmonic mean) is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the Lehmer mean, L p {\displaystyle
Contraharmonic_mean
Class of ordinary differential equations
a non-trivial solution to the problem. Such values λ {\displaystyle \lambda } are called the eigenvalues of the problem. For each eigenvalue λ {\displaystyle
Sturm–Liouville_theory
Puzzle in logic and mathematics
of commentaries on the problem, much of which observes that a distribution of finite values can have an infinite expected value. There have been many solutions
Two_envelopes_problem
Statistical method for multiple testing
The harmonic mean p-value (HMP) is a statistical technique for addressing the multiple comparisons problem that controls the strong-sense family-wise
Harmonic_mean_p-value
Inverse of the average of the inverses of a set of numbers
Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones while having at least one value unchanged. [citation
Harmonic_mean
queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths
Mean_value_analysis
Distinction between what is and what ought to be
former using the latter. The fact–value distinction is closely related to, and derived from, the is–ought problem in moral philosophy, characterized
Fact–value_distinction
Concept in probability theory and gambling
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 concept
Gambler's_ruin
Approximation method in statistics
residuals—the differences between observed values and the values predicted by the model. Least squares problems fall into two categories: linear or ordinary
Least_squares
Resource problem in machine learning
posterior for the mean value of each alternative. Probability matching strategies also admit solutions to so-called contextual bandit problems. Pricing strategies
Multi-armed_bandit
Statistical phenomenon
In statistics, regression toward the mean (also called regression to the mean, reversion to the mean, and reversion to mediocrity) is the phenomenon where
Regression_toward_the_mean
Problem in computer science
In computability theory, the halting problem is the decision problem of determining, from a description of an arbitrary computer program and an input
Halting_problem
Yes-or-no question that cannot ever be solved by a computer
decision problem "is the input even?" is formalized as the set of even numbers. A decision problem whose input consists of strings or more complex values is
Undecidable_problem
Axiomatization of probability and physics
accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gases
Hilbert's_sixth_problem
Question in geometric probability
In probability theory, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: Suppose we have
Buffon's_needle_problem
Single measure of some attribute of a sample
mean) of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value
Statistic
corresponding value? The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent
Robbins'_problem
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
Monty_Hall_problem
Personal value, basis for ethical action
value intrinsic and extrinsic properties. An ethic good with instrumental value may be termed an ethic mean, and an ethic good with intrinsic value may
Value_(ethics)
Open problem on 3x+1 and x/2 functions
Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers
Collatz_conjecture
Statistical value representing the center or average of a distribution
tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution
Central_tendency
Process of replacing missing data with substituted values
Regression imputation has the opposite problem of mean imputation. A regression model is estimated to predict observed values of a variable based on other variables
Imputation_(statistics)
Middle quantile of a data set or probability distribution
it may be thought of as the "middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average")
Median
N-th root of the product of n numbers
numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of n {\displaystyle n} numbers
Geometric_mean
Measure of variation in statistics
meaning that its expected value in repeated sampling deviates from the true value, but it is still consistent. Its mean squared error, on the other
Standard_deviation
Statistical accuracy measure
The symmetric mean absolute percentage error (SMAPE or sMAPE) is an accuracy measure based on percentage (or relative) errors. It is usually defined[citation
Symmetric mean absolute percentage error
Symmetric_mean_absolute_percentage_error
Probability distribution
{\displaystyle z} has a mean of 0 and a variance and standard deviation of 1. The density φ ( z ) {\textstyle \varphi (z)} has its peak value 1 2 π {\textstyle
Normal_distribution
Probability distribution
mean (HX) of a distribution with random variable X is the arithmetic mean of 1/X, or, equivalently, its expected value. Therefore, the harmonic mean (HX)
Beta_distribution
Difference of two numbers divided by the logarithm of their quotient
This calculation is applicable in engineering problems involving heat and mass transfer. The logarithmic mean is defined by L ( x , y ) = { x , if x = y
Logarithmic_mean
Unsolved problem in computer science
whether problems that can be verified in polynomial time can also be solved in polynomial time. If P ≠ NP, which is widely believed, it would mean that there
P_versus_NP_problem
Problem of constructing equal-area shapes
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given
Squaring_the_circle
Study of strategic decision making
of players through the mean representative agent and at the same time describe complex state dynamics. This class of problems was considered in the economics
Mean-field_game_theory
System including an indeterminate value
the problem of future contingents to represent the truth value of statements about the undetermined future. Bruno de Finetti used a third value to represent
Three-valued_logic
Issues related to economic activities
fundamental problems in a mixed private enterprise system..." At competitive equilibrium, the value society places on a good is equivalent to the value of the
Economic_problem
In mathematics, a quantitative measure of the shape of a set of points
value of X n {\displaystyle X^{n}} and is called a raw moment or crude moment or population moment or uncorrected moment. The moments about its mean μ
Moment_(mathematics)
Range to estimate an unknown parameter
range of values which is likely to contain (in repeated sampling) the true value of an unknown statistical parameter, such as a population mean. Rather
Confidence_interval
Field of machine learning
stochastic search problems. The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard
Reinforcement_learning
Study of collection and analysis of data
central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean. A statistical
Statistics
Economic measure placing a monetary value on reducing the risk of death
calculate VSL is summing the total present discounted value of lifetime earnings. There are a couple of problems using this method. One potential source of variability
Value_of_a_statistical_life
Statistical algorithm
the weights change, is large, convergence in mean would be misleading. This problem may occur, if the value of step-size μ {\displaystyle \mu } is not chosen
Least_mean_squares_filter
Numerical method for solving physical or engineering problems
solution that has a finite number of points. FEM formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates
Finite_element_method
Rule for calculating an estimate of a given quantity based on observed data
range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. Estimation
Estimator
Problem in physics and celestial mechanics
some known function of time and for all of whose values the series converges uniformly. In case the problem could not be solved, any other important contribution
N-body_problem
Theory in classical and Marxian economics
overcoming would mean the abolition, not the full realization, of labor as the central organizing principle of society. While the labor theory of value is most
Labor_theory_of_value
Issue in artificial intelligence and categorical algebra
artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic to express facts about
Frame_problem
Probabilistic problem-solving algorithm
used to solve any problem having a probabilistic interpretation. By the law of large numbers, integrals described by the expected value of some random variable
Monte_Carlo_method
simple shapes such as a square or a triangle, solving for the exact value of their mean line segment lengths can be difficult because their closed-form expressions
Mean_line_segment_length
to this problem? Could axions be the main component of dark matter? Anomalous magnetic dipole moment: Why is the experimentally measured value of the muon's
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
23 mathematical problems stated in 1900
appreciation which, in my opinion, is its due—I mean the calculus of variations." The other 20 problems have all received significant attention, and late
Hilbert's_problems
Statistical measure of a test's accuracy
positive predictive value, and recall is also known as sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision
F-score
Mathematical problem
The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, is a puzzle in decision theory in which an ideally rational epistemic agent is
Sleeping_Beauty_problem
p-values can be combined using Fisher's method, techniques are still being developed to handle the case of dependent p-values. Behrens–Fisher problem:
List of unsolved problems in statistics
List_of_unsolved_problems_in_statistics
Important algorithms in numerical statistics
closer K {\displaystyle K} is to the mean value the more accurate the result will be, but just choosing a value inside the samples range will guarantee
Algorithms for calculating variance
Algorithms_for_calculating_variance
Concept in game theory
Airport problem Banzhaf power index Shapley–Shubik power index Shapley, Lloyd S. (August 21, 1951). "Notes on the n-Person Game -- II: The Value of an n-Person
Shapley_value
Indicator for how well data points fit a line or curve
cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular
Coefficient_of_determination
Problem in probability theory
first explicit reasoning about what today is known as an expected value. The problem concerns a game of chance with two players who have equal chances
Problem_of_points
Ratio in statistics
population mean from a sampling distribution of sample means if the population standard deviation is unknown. It is also used along with p-value when running
T-statistic
Concept in economics
Theories of Surplus Value (which was subsequently published as Capital, Volume IV), and features in his Capital, Volume I (1867). The problem of explaining
Surplus_value
Measured values that are relatively normal for a particular medical test
either side of the population mean (also called the expected value). However, in the real world, neither the population mean nor the population standard
Reference_range
Function's sensitivity to argument change
as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the
Condition_number
Method for estimating the unknown parameters in a linear regression model
values of the response variable equal its sample mean (if not, it is said to have no explanatory power). The null hypothesis of no explanatory value of
Ordinary_least_squares
Mathematical relationships
the mean inequality chain, state the relationship between the harmonic mean (HM), geometric mean (GM), arithmetic mean (AM), and quadratic mean (QM;
QM–AM–GM–HM_inequalities
Methods of calculating definite integrals
their geometric mean. The similar geometrical construction solves a problem of a quadrature for a parallelogram and a triangle. Problems of quadrature for
Numerical_integration
Statistical interpretation with many tests
comparisons problem also applies to confidence intervals. A single confidence interval with a 95% coverage probability level will contain the true value of the
Multiple_comparisons_problem
Philosophical question
The problem of evil, also known as the problem of suffering, is the philosophical question of how to reconcile the existence of evil and suffering with
Problem_of_evil
Type of multi-objective optimization
minimize the mean completion time, and subject to this, minimize the variance of the completion time. A lexicographic maximization problem is often written
Lexicographic_optimization
Statistical method of dividing data into equal-sized intervals for analysis
standard deviation from the mean. The above formula can be used to bound the value μ + zσ in terms of quantiles. When z ≥ 0, the value that is z standard deviations
Quantile
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
standard deviation σ {\displaystyle \sigma } to the mean μ {\displaystyle \mu } (or its absolute value, | μ | {\displaystyle |\mu |} ), and often expressed
Coefficient_of_variation
Smallest value a measuring instrument can measure
observations and taking the arithmetic mean of the result, the mean value would be very close to the true value of the measured quantity. William Woolsey
Least_count
Probability problem
In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there
Hamburger_moment_problem
Financial phenomenon
envelopes problem, the phenomenon is sometimes labeled a paradox because an agent can seem to trade for something of equal monetary value and yet, paradoxically
Siegel's_paradox
1990 film by Dennis Dugan
3/10. The site's critical consensus reads: "Mean-spirited and hopelessly short on comic invention, Problem Child is a particularly unpleasant comedy, one
Problem_Child_(film)
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
Boy/Male
Arabic
Value
Female
English
Scottish form of French Jeanne, JEAN means "God is gracious." Compare with masculine Jean.
Boy/Male
Muslim
Value, Price
Male
Hebrew
Short form of Hebrew Immanuw'el (English Immanuel), MAN means "God is with us."
Surname or Lastname
Irish
Irish : shortened form of McMeans.English : habitational names from East and West Meon in Hampshire, which take their names from the Meon river. The word is Celtic but of uncertain meaning, possibly ‘swift one’.nickname from Middle English mene ‘inferior in rank’, ‘of low degree’ (from Old English gemǣne), or from Middle English mene ‘moderate in behaviour’ (from Old French mëen, mean).
Boy/Male
Australian, Finnish
Rule
Boy/Male
Indian
Value, Price
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English vale (Old French val, from Latin vallis). The surname is now also common in Ireland, where it has been Gaelicized as de Bhál.Galician and Aragonese : topographic name from val ‘valley’, or habitational name from any of the places named with this word.
Surname or Lastname
English
English : topographic name from Middle English dene ‘valley’ (Old English denu), or a habitational name from any of several places in various parts of England named Dean, Deane, or Deen from this word. In Scotland this is a habitational name from Den in Aberdeenshire or Dean in Ayrshire.English : occupational name for the servant of a dean or nickname for someone thought to resemble a dean. A dean was an ecclesiastical official who was the head of a chapter of canons in a cathedral. The Middle English word deen is a borrowing of Old French d(e)ien, from Latin decanus (originally a leader of ten men, from decem ‘ten’), and thus is a cognate of Deacon.Irish : variant of Deane.Italian : occupational name cognate with 2, from Venetian dean ‘dean’, a dialect form of degan, from degano (Italian decano).
Girl/Female
Muslim/Islamic
Value Worth
Boy/Male
Hindu, Indian
Value
Girl/Female
Arabic
Value; Price
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Female
English
Pet form of Welsh Mared, MEGAN means "pearl."Â
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
American, British, English
Of High Value
Male
English
Anglicized form of Irish Gaelic Cian, KEAN means "ancient, distant."
Male
English
Anglicized form of Irish Gaelic Seán, SEAN means "God is gracious."
Male
English
 English occupational surname transferred to forename use, from the Latin word decanus, DEAN means "dean; ecclesiastical supervisor."
Male
French
A derivative of Anglo-Norman French Jehan, JEAN means "God is gracious." Compare with feminine Jean.
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
Boy/Male
Muslim
Administration
Boy/Male
Hindu
Name of a sage
Boy/Male
Hindu, Indian
Meh means Moon Raj means Kingdom
Girl/Female
German
Army of elves.
Boy/Male
Muslim
Rest
Female
French
Feminine form of French Sébastien, SÉBASTIENNE means "from Sebaste," a town in Asia Minor.Â
Girl/Female
Indian
Glowing Princess
Boy/Male
Arabic, Muslim
Friend of the Prophet (Muhammad)
Boy/Male
Indian, Sanskrit
Lord of the Earth
Boy/Male
Arabic, Muslim
Fruit Name
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
MEAN VALUE-PROBLEM
imp. & p. p.
of Value
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
v. t.
To be worth; to be equal to in value.
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.
v. i.
Wanting fullness, richness, sufficiency, or productiveness; deficient in quality or contents; slender; scant; barren; bare; mean; -- used literally and figuratively; as, the lean harvest; a lean purse; a lean discourse; lean wages.
superl.
Penurious; stingy; close-fisted; illiberal; as, mean hospitality.
n.
Of comparatively small value; common; mean.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
imp. & p. p.
of Mean
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
superl.
Of poor quality; as, mean fare.
superl.
Wanting dignity of mind; low-minded; base; destitute of honor; spiritless; as, a mean motive.
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
superl.
Of little value or account; worthy of little or no regard; contemptible; despicable.
n.
A quantity having an intermediate value between several others, from which it is derived, and of which it expresses the resultant value; usually, unless otherwise specified, it is the simple average, formed by adding the quantities together and dividing by their number, which is called an arithmetical mean. A geometrical mean is the square root of the product of the quantities.
n.
Value.
a.
Average; having an intermediate value between two extremes, or between the several successive values of a variable quantity during one cycle of variation; as, mean distance; mean motion; mean solar day.
n.
One who values; an appraiser.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.