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  2. Taylor expansions for the moments of functions of random ...

    en.wikipedia.org/wiki/Taylor_expansions_for_the...

    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.

  3. First-order second-moment method - Wikipedia

    en.wikipedia.org/wiki/First-order_second-moment...

    In probability theory, the first-order second-moment (FOSM) method, also referenced as mean value first-order second-moment (MVFOSM) method, is a probabilistic method to determine the stochastic moments of a function with random input variables

  4. Algebra of random variables - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_random_variables

    List of convolutions of probability distributions – the probability measure of the sum of independent random variables is the convolution of their probability measures. Law of total expectation; Law of total variance; Law of total covariance; Law of total cumulance; Taylor expansions for the moments of functions of random variables; Delta method

  5. Experimental uncertainty analysis - Wikipedia

    en.wikipedia.org/wiki/Experimental_uncertainty...

    Even if the PDF can be found, finding the moments (above) can be difficult. 4. The solution is to expand the function z in a second-order Taylor series; the expansion is done around the mean values of the several variables x. (Usually the expansion is done to first order; the second-order terms are needed to find the bias in the mean.

  6. Ratio estimator - Wikipedia

    en.wikipedia.org/wiki/Ratio_estimator

    Another estimator based on the Taylor expansion is [3] = where n is the sample size, N is the population size, m x is the mean of the x variate and s x 2 and s y 2 are the sample variances of the x and y variates respectively.

  7. Euler Mathematical Toolbox - Wikipedia

    en.wikipedia.org/wiki/Euler_Mathematical_Toolbox

    Euler handles symbolic computations via Maxima, which is loaded as a separate process, communicating with Euler through pipes. The two programs can exchange variables and values. Indeed, Maxima is used in various Euler functions (e.g. Newton's method) to assist in the computation of derivatives, Taylor expansions and integrals. Moreover, Maxima ...

  8. Today's Wordle Hint, Answer for #1258 on Thursday, November ...

    www.aol.com/todays-wordle-hint-answer-1258...

    If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1258 ahead. Let's start with a few hints.

  9. Linear approximation - Wikipedia

    en.wikipedia.org/wiki/Linear_approximation

    Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case = states that = + ′ () + where is the remainder term. The linear approximation is obtained by dropping the remainder: f ( x ) ≈ f ( a ) + f ′ ( a ) ( x − a ) . {\displaystyle f(x)\approx f(a)+f'(a)(x-a).}

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