Suppose we have 3 independent observations X1, X2, X3 from a distribution with mean µ and standard deviation σ. What is the variance of the mean of these 3 values: (X1 + X2 + X3)/3?
Added by John D.
Step 1
So, the variance of (X1 + X2 + X3) is Var(X1) + Var(X2) + Var(X3). Since X1, X2, and X3 are from the same distribution, they have the same variance, which is σ^2. So, Var(X1 + X2 + X3) = σ^2 + σ^2 + σ^2 = 3σ^2. Show more…
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