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I'm looking to find an expected mean and standard deviation from summing across the elements of a sample from a normal distribution.

Say we have a normally distributed population with mean of 1000 and standard deviation of 10, of which I am taking a sample of 100.

Intuition tells me that my expected value would be n*μ = 100 * 1000 = 100000; but I'm not sure how to construct any statistic for expected variance around that value.

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The expected mean of the sum of 100 samples drawn from this distribution is 100 * 1000 = 100,000.

The expected variance of the sum of 100 samples drawn from this distribution is 100 * (10^2) = 10,000.

This wiki page https://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9_formula.29 gives the general formula for the sum of uncorrelated random variables.

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