Question

容量分别是n1,n2.组成一个联合样本n1+n2,组合样本的方差是?

Answer 1

组合样本的方差是 S1^2 + S2^2

This problem is not as simple as the answer suggests here. When combining m random variables: n1, n2, ..., nm each with an average value of X1, X2, ..., Xm and a standard deviation S1, S2, ..., Sm, the average of the new random variable N = n1 + n2 + ... + nm will have an average value of X = X1 + X2 + ... + Xm, this is expected. The standard deviation of the new random variable, though, is S = (S1^2 + S2^2 + ... + Sm^2)^(1/2). So the variance of the new random variable or Var(N) = S1^2 + S2^2 + ... + Sm^2