In mathematics, a function f(x) between two ordered sets is unimodal if for some value m (the mode), it is monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m. In that case, the maximum value of f(x) is f(m). Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ...
Partial plot of a function f. ...
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In statistics, the mode is the value that has the largest number of observations, namely the most frequent value or values. ...
In mathematics, functions between ordered sets are monotonic (or monotone) if they preserve the given order. ...
The largest and the smallest element of a set are called extreme values, or extreme records. ...
In probability and statistics, a unimodal probability distribution is a probability distribution whose probability density function is a unimodal function, or more generally, whose cumulative distribution function is convex up to m and concave thereafter (this allows for the possibility of a nonzero probability for x=m). For a unimodal probability distribution of a continuous random variable, the VysochanskiiPetunin inequality provides a refinement of the Chebyshev inequality. Informally, probable is one of several words applied to uncertain events or knowledge, being closely related in meaning to likely, risky, hazardous, and doubtful. ...
A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ...
In mathematics and statistics, a probability distribution, more properly called a probability density, assigns to every interval of the real numbers a probability, so that the probability axioms are satisfied. ...
In mathematics, a probability density function (pdf) serves to represent a probability distribution in terms of integrals. ...
In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a realvalued random variable, X. For every real number x, the cdf is given by where the righthand side represents the probability that the random variable X takes on a value less than...
In mathematics, convex function is a realvalued function f defined on an interval (or on any convex subset C of some vector space), if for any two points x and y in its domain C and any t in [0,1], we have Convex function on an interval. ...
In calculus, a differentiable function f is convex on an interval if its derivative function f â€² is increasing on that interval: a convex function has an increasing slope. ...
In probability theory, the VysochanskiïPetunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variables mean. ...
This article is not about Chebyshevs sum inequality. ...
