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Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables (multivariate), rather than just one. [1]
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.
Formally, a function of n variables is a function whose domain is a set of n-tuples. [note 3] For example, multiplication of integers is a function of two variables, or bivariate function, whose domain is the set of all ordered pairs (2-tuples) of integers, and whose codomain is the set of
The MA plot puts the variable M on the y-axis and A on the x-axis and gives a quick overview of the distribution of the data. In many microarray gene expression experiments, an underlying assumption is that most of the genes would not see any change in their expression; therefore, the majority of the points on the y -axis ( M ) would be located ...
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density f {\displaystyle f} , mean μ {\displaystyle \mu } and variance σ 2 {\textstyle \sigma ^{2}} , the moment generating function exists and is equal to
Welch showed that the first confidence procedure dominates the second, according to desiderata from confidence interval theory; for every , the probability that the first procedure contains is less than or equal to the probability that the second procedure contains . The average width of the intervals from the first procedure is less than that ...
If X is a random variable taking values in the d-dimensional Euclidean space, X has finite expectation, X ' is an independent identically distributed copy of X, and ‖ ‖ denotes the norm in the Euclidean space, then a simple measure of asymmetry with respect to location parameter θ is ():= ‖ ′ ‖ ‖ + ′ ‖ (=) and dSkew ...