Zero mean and unit variance An easy calculation yields E[X1+…+XnJ-n E[Zn] ovn 2二0 。For variance,we have var(X1+…+Xn) no2 var(Zn)= (ovn)2 n21Zero mean and unit variance • An easy calculation yields E[𝑍𝑛] = E 𝑋1 + ⋯ + 𝑋𝑛 − 𝑛𝜇 𝜎 𝑛 = 0 • For variance, we have var 𝑍𝑛 = var 𝑋1 + ⋯ + 𝑋𝑛 𝜎 𝑛 2 = 𝑛𝜎 2 𝑛𝜎 2 = 1