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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Expected values can also be used to compute the variance, by means of the computational formula for the variance = [] ( []). A very important application of the expectation value is in the field of quantum mechanics .
Sample variance can also be applied to the estimation of the variance of a continuous distribution from a sample of that distribution. We take a sample with replacement of n values Y 1, ..., Y n from the population of size , where n < N, and estimate the variance on the basis of this sample. [15] Directly taking the variance of the sample data ...
In statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean.The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling.
which is an unbiased estimator of the variance of the mean in terms of the observed sample variance and known quantities. If the autocorrelations are identically zero, this expression reduces to the well-known result for the variance of the mean for independent data. The effect of the expectation operator in these expressions is that the ...
In words: the variance of Y is the sum of the expected conditional variance of Y given X and the variance of the conditional expectation of Y given X. The first term captures the variation left after "using X to predict Y", while the second term captures the variation due to the mean of the prediction of Y due to the randomness of X.
The probability density function is (,) = ((+)) (),where I 0 (z) is the modified Bessel function of the first kind with order zero.. In the context of Rician fading, the distribution is often also rewritten using the Shape Parameter =, defined as the ratio of the power contributions by line-of-sight path to the remaining multipaths, and the Scale parameter = +, defined as the total power ...
In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then