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If we draw a graph of the logistic map (), we can observe that the slope of the tangent at the fixed point exceeds 1 at the boundary = and becomes unstable. At the same time, two new intersections appear, which are the periodic points x f 1 ( 2 ) {\displaystyle x_{f1}^{(2)}} and x f 2 ( 2 ) {\displaystyle x_{f2}^{(2)}} .
1/52! chance of a specific shuffle Mathematics: The chances of shuffling a standard 52-card deck in any specific order is around 1.24 × 10 −68 (or exactly 1 ⁄ 52!) [4] Computing: The number 1.4 × 10 −45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.For example, a 2,1 represents the element at the second row and first column of the matrix.
Hasler's temperature scale showing degrees of body temperature based on an individual's latitude. The Roman Greek physician Galen is given credit for introducing two concepts important to the development of a scale of temperature and the eventual invention of the thermometer. First, he had the idea that hotness or coldness may be measured by ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
Thus Earth's circumference in nautical miles would be 21 600 (viz., 60 minutes of arc × 360 degrees in four 90-degree quadrants; a quadrant being the length of the quarter-circle from the North Pole to the equator). In 1669, Jean Picard, a French astronomer, was the first person to measure the Earth accurately.