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In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite. A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
The ratio estimator is a statistical estimator for the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals
where σ ij represents the covariance of two variables x i and x j. The double sum is taken over all combinations of i and j, with the understanding that the covariance of a variable with itself is the variance of that variable, that is, σ ii = σ i 2. Also, the covariances are symmetric, so that σ ij = σ ji. Again, as was the case with the ...
In a message that appeared to be intended as a private communication to Elon Musk, President-elect Donald Trump said in a social media post Friday that Microsoft founder Bill Gates had asked to ...
John "Pondoro" Taylor, an ivory hunter who over his career shot over 1,000 elephants along with a variety of other African game and who is renowned for writing two books about rifles and cartridges for African hunting, devised the Taylor KO factor to place a mathematical value on the concussive effects a cartridge and bullet would have on an ...
Detroit Lions wide receiver Jameson Williams has been fined $19,697 by the NFL for "Unsportsmanlike Conduct (obscene gestures)" for his dive into the end zone last week against the Jacksonville ...