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The general formula for the variance of the outcome, X, ... This expression can be used to calculate the variance in ... The same proof is also applicable for samples ...
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.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The conditional variance tells us how much variance is left if we use to "predict" Y. Here, as usual, E ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} stands for the conditional expectation of Y given X , which we may recall, is a random variable itself (a function of X , determined up to probability one).
In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written ) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same. The numerical estimate resulting from ...
Then the first, "unexplained" term on the right-hand side of the above formula is the weighted average of the variances, hσ h 2 + (1 − h)σ t 2, and the second, "explained" term is the variance of the distribution that gives μ h with probability h and gives μ t with probability 1 − h.
Note in the later section “Maximum likelihood” we show that under the additional assumption that errors are distributed normally, the estimator ^ is proportional to a chi-squared distribution with n – p degrees of freedom, from which the formula for expected value would immediately follow. However the result we have shown in this section ...
Small range can be achieved when approximating the function around the mean, when the variance is "small enough". When g is applied to a random variable such as the mean, the delta method would tend to work better as the sample size increases, since it would help reduce the variance, and thus the taylor approximation would be applied to a ...