For subsequent calculations, I want the mean of the four estimates, and a variance that captures variability of the numbers being averaged, and also propagates the measurement error. a given distribution using Variance and Standard deviation. above as follows: We shall see in the next section that the expected value of a linear combination of a random variable is the variance of all the values that the random variable would assume in the long run. If the $X_i$ are random variables with a variance $\sigma_i^2$, then the variance of $X=\sum_i X_i$ their sum is $\sigma_X^2$ is given by: $\sigma_X^2=\sum_i \sigma_i^2 + 2 \sum_i \sum_{j
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