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[8] [9] [verification needed] Cramer's rule can also be numerically unstable even for 2×2 systems. [10] However, Cramer's rule can be implemented with the same complexity as Gaussian elimination, [11] [12] (consistently requires twice as many arithmetic operations and has the same numerical stability when the same permutation matrices are ...
The number of distinct terms (including those with a zero coefficient) in an n-th degree equation in two variables is (n + 1)(n + 2) / 2.This is because the n-th degree terms are ,, …,, numbering n + 1 in total; the (n − 1) degree terms are ,, …,, numbering n in total; and so on through the first degree terms and , numbering 2 in total, and the single zero degree term (the constant).
The logarithmic moment generating function (which is the cumulant-generating function) of a random variable is defined as: = [ ()].Let ,, … be a sequence of iid real random variables with finite logarithmic moment generating function, i.e. () < for all .
Cramér’s decomposition theorem, a statement about the sum of normal distributed random variable; Cramér's theorem (large deviations), a fundamental result in the theory of large deviations; Cramer's theorem (algebraic curves), a result regarding the necessary number of points to determine a curve
As a result of the work of H. Maier on gaps between consecutive primes, the exact formulation of Cramér's conjecture has been called into question [...] It is still probably true that for every constant c > 2 {\displaystyle c>2} , there is a constant d > 0 {\displaystyle d>0} such that there is a prime between x {\displaystyle x} and x + d ...
The result is named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, [1] [2] [3] but has also been derived independently by Maurice Fréchet, [4] Georges Darmois, [5] and by Alexander Aitken and Harold Silverstone. [6] [7] It is also known as Fréchet-Cramér–Rao
In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φ c) is a measure of association between two nominal variables, giving a value between 0 and +1 (inclusive). It is based on Pearson's chi-squared statistic and was published by Harald Cramér in 1946. [1]
A natural question to ask, given the somewhat abstract setting of the general framework above, is whether the rate function is unique. This turns out to be the case: given a sequence of probability measures (μ δ) δ>0 on X satisfying the large deviation principle for two rate functions I and J, it follows that I(x) = J(x) for all x ∈ X.