样本X1,X2,……Xn平均数为5,方差为3,
则,
5 = [X1 + X2 + ...+ Xn]/n
3 = [(X1 - 5)^2 + (X2 - 5)^2 + ...+ (Xn - 5)^2]/n
因此,
[3(X1 - 1) + 3(X2 - 1) + ...+ 3(Xn - 1)]/n
= 3[X1 + X2 + ...+ Xn]/n - 3
= 15 - 3 = 12
{[3(X1 - 1) - 12]^2 + [3(X2 - 1) - 12]^2 + ...+ [3(Xn - 1) - 12]^2]/n
= {[3X1 - 15]^2 + [3X2 - 15]^2 + ...+ [3Xn - 15]^2]/n
= {9[X1 - 5]^2 + 9[X2 - 5]^2 + ...+ 9[Xn - 5]^2]/n
= 9[(X1 - 5)^2 + (X2 - 5)^2 + ...+ (Xn - 5)^2]/n
= 9*3 = 27.
则3（X1-1）,3（X2-1）,……,3（Xn-1)标准差为
(27)^(1/2) = 3*(3)^(1/2)