The first raw moment and the second and third " unnormalized central " moments are additive in the sense that if " X " and " Y " are independent random variables then
42.
In digital image processing, the pixels of a " white noise image " are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval.
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:where the independent random variables " X " " n " are each equal to 0 or 1 with equal probabilities this is a Bernoulli trial of each digit of the binary expansion.
44.
If I know the standard deviations of two independent random variables, how do I calculate the standard deviation of their difference ? 151.152.101.44 17 : 50, 16 August 2007 ( UTC)
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The probability density function of the sum of two independent random variables " U " and " V ", each of which has a probability density function, is the convolution of their separate density functions:
46.
It is very useful in stochastics where the log-likelihood ( i . e . the logarithm of a product integral of independent random variables ) equals the integral of the log of these ( infinitesimally many ) random variables:
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The mean field particle interpretation of this Feynman-Kac model is defined by sampling sequentially " N " conditionally independent random variables \ xi ^ { ( N, i ) } _ { n + 1 } with probability distribution
48.
Consider \ textstyle n independent random variables \ textstyle X _ 1, \ dots, X _ n each of which follows an arbitrary distribution with support \ textstyle \ { 0, 1, \ dots, k-1 \ }.
49.
This distribution is sometimes confused with the Bates distribution, which is the "'mean "'( not "'sum "') of " n " independent random variables uniformly distributed from 0 to 1.
50.
This distribution is sometimes confused with the Irwin Hall distribution, which is the distribution of the "'sum "'( not "'mean "') of n independent random variables uniformly distributed from 0 to 1.
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