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If the conditional distribution of given is a continuous distribution, then its probability density function is known as the conditional density function. [1] The properties of a conditional distribution, such as the moments , are often referred to by corresponding names such as the conditional mean and conditional variance .
In item analysis, an item–total correlation is usually calculated for each item of a scale or test to diagnose the degree to which assessment items indicate the underlying trait. Assuming that most of the items of an assessment do indicate the underlying trait, each item should have a reasonably strong positive correlation with the total ...
The partial conditional probability (, …,) is about the probability of event given that each of the condition events has occurred to a degree (degree of belief, degree of experience) that might be different from 100%.
Note that the conditional expected value is a random variable in its own right, whose value depends on the value of . Notice that the conditional expected value of given the event = is a function of (this is where adherence to the conventional and rigidly case-sensitive notation of probability theory becomes important!).
The conditional distribution of a variable given another variable is the joint distribution of both variables divided by the marginal distribution of the other variable. [3] That is, For discrete random variables , p Y | X ( y | x ) = P ( Y = y ∣ X = x ) = P ( X = x , Y = y ) P X ( x ) {\displaystyle p_{Y|X}(y|x)=P(Y=y\mid X=x)={\frac {P(X=x ...
In statistics, a k-th percentile, also known as percentile score or centile, is a score (e.g., a data point) below which a given percentage k of arranged scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition); i.e. a score in the k-th percentile would be above approximately k% of all scores in its set.
In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem.It was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n many k th powers of positive integers is itself a k th power, then n is greater than or equal to k:
In other words, a quintic function is defined by a polynomial of degree five. Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a quartic function.