设X1,X2,…,Xn平均数为X均
则S^2=1/n((X1-X均)^2+(X2-X均)^2.(Xn-X均)^2)
ax1+b,ax2+b,…,axn+b的平均数为
1/n(ax1+b+ax2+b+…+axn+b)=a(1/n(X1+X2+…+Xn))+b=ax均+b
ax1+b,ax2+b,…,axn+b的方差为
1/n((ax1+b-(ax均+b))^2+(ax2+b-(ax均+b))^2+...(axn+b-(ax均+b))^2)=a^2*(1/n((X1-X均)^2+(X2-X均)^2.(Xn-X均)^2)=a^2*s^2