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  2. Binomial coefficient - Wikipedia

    en.wikipedia.org/wiki/Binomial_coefficient

    This number can be seen as equal to the one of the first definition, independently of any of the formulas below to compute it: if in each of the n factors of the power (1 + X) n one temporarily labels the term X with an index i (running from 1 to n), then each subset of k indices gives after expansion a contribution X k, and the coefficient of ...

  3. Cohen's kappa - Wikipedia

    en.wikipedia.org/wiki/Cohen's_kappa

    Cohen's kappa measures the agreement between two raters who each classify N items into C mutually exclusive categories. The definition of is =, where p o is the relative observed agreement among raters, and p e is the hypothetical probability of chance agreement, using the observed data to calculate the probabilities of each observer randomly selecting each category.

  4. Combination - Wikipedia

    en.wikipedia.org/wiki/Combination

    In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.

  5. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    Since the probabilities must satisfy p 1 + ⋅⋅⋅ + p k = 1, it is natural to interpret E[X] as a weighted average of the x i values, with weights given by their probabilities p i. In the special case that all possible outcomes are equiprobable (that is, p 1 = ⋅⋅⋅ = p k), the weighted average is given by the standard average. In the ...

  6. Degrees of freedom (statistics) - Wikipedia

    en.wikipedia.org/.../Degrees_of_freedom_(statistics)

    Then, at each of the n measured points, the weight of the original value on the linear combination that makes up the predicted value is just 1/k. Thus, the trace of the hat matrix is n/k. Thus the smooth costs n/k effective degrees of freedom. As another example, consider the existence of nearly duplicated observations.

  7. Binomial distribution - Wikipedia

    en.wikipedia.org/wiki/Binomial_distribution

    This is because for k > n/2, the probability can be calculated by its complement as (,,) = (,,). Looking at the expression f(k, n, p) as a function of k, there is a k value that maximizes it. This k value can be found by calculating

  8. Order statistic - Wikipedia

    en.wikipedia.org/wiki/Order_statistic

    Using the above formulas, one can derive the distribution of the range of the order statistics, that is the distribution of () (), i.e. maximum minus the minimum.

  9. Q-function - Wikipedia

    en.wikipedia.org/wiki/Q-function

    In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.