23 Matching Annotations
  1. Apr 2024
    1. view the annotations

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    1. lly inspect the empirical PDF and compute the sample coefficient of skewness from a set of observations as g1=∑i=1n(xi−x―)3nσ3 where xi

      why g? maybe we use q, to allign with the arbitrary function of random variables from uncertainty propagation?

    1. Some simple examples are:

      I am going to use q for generic functions in the risk and reliability part. check with Sandra if this will cause issues for observation theory. This reserves g for the specific case where g<0 is defined as failure. will use X for the parameters of q, though (so if a situation with both, could use q1 and q2, or q and h or...?)

    1. Xi in the random vector X=[X1X2…Xm]T are normally distributed, then X will have the multivariate normal distribution,

      make sure random vector is also included in the fundamental concepts page

    1. We use a capital letter to denote a random variable and realizations of that random variable are described with a lower case letter.

      add vectors of random variables

    1. Textbook

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    1. solved analytically (linear functions and Gaussian random variables). Random variables are limited to continuous parametric distributions and linear measures of dependence (correlation coefficient, multivariate Gaussian). If these requirements are relaxed, we will use simulation to calculate the failure probability numerically (i.e., Monte Carlo simulation).

      correct this paragraph if copulas are used

  2. Mar 2024
    1. Discrete Fourier Transform (DFT)

      I am looking through this page for a ppt and notice there are no figures that illustrate the DFT/fft in Python. We should add something (prepare for PA and WS for the week).