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In particular, m is a sample median if and only if m minimizes the arithmetic mean of the absolute deviations. [ 7 ] More generally, a median is defined as a minimum of E ( | X − c | − | X | ) , {\displaystyle E(|X-c|-|X|),} as discussed at Multivariate median (and specifically at Spatial median ).
The rule can then be derived [2] either from the Poisson approximation to the binomial distribution, or from the formula (1−p) n for the probability of zero events in the binomial distribution. In the latter case, the edge of the confidence interval is given by Pr(X = 0) = 0.05 and hence (1−p) n = .05 so n ln(1–p) = ln .05 ≈ −2
For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . ...
Trimethyl borate is the organoboron compound with the formula B(OCH 3) 3 and a metal alkoxide. It is a colourless liquid that burns with a green flame. [1] It is an intermediate in the preparation of sodium borohydride and is a popular reagent in organic chemistry. It is a weak Lewis acid (AN = 23, Gutmann-Beckett method). [2]
Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters). [3]A tilde (~) denotes "has the probability distribution of". Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator of it, e.g., ^ is an estimator for .
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Tetramethyl orthosilicate (TMOS) is the chemical compound with the formula Si(OCH 3) 4.This molecule consists of four methoxy groups bonded to a silicon atom. The basic properties are similar to the more popular tetraethyl orthosilicate, which is usually preferred because the product of hydrolysis, ethanol, is less toxic than methanol.
More precisely, if n = 2m+1 for some integer m, then the sample median is (+) and so is an order statistic. On the other hand, when n is even , n = 2 m and there are two middle values, X ( m ) {\displaystyle X_{(m)}} and X ( m + 1 ) {\displaystyle X_{(m+1)}} , and the sample median is some function of the two (usually the average) and hence not ...