- Expectation of the Sample Mean: E[Xn]
- Variance of the Sample Mean: V[Xn]
Sample Mean θ^n is converging to Population Mean θ: n→∞limE[(θ^n−θ)2]=0
n→∞limV[θ^n]+(E[θ^n]−θ)2)=0
n→∞limnσx2+(μx−μx)2=0
θ^n→θ
∀ϵ>0, n→∞limP(∣θ^n−θ)∣>ϵ)=0
n→∞limP(∣xn−μx∣>ϵ)≤n→∞limnϵ2σx2
MI