The Central Limit Theorem(CLT) .The Central Limit Theorem The CDF ofn=n o√m converges to standard normal CDF in the sense that limP(Zn≤z)=Φ(z) n→0∞ The distribution of the r.v.Znapproaches a normal distribution.The Central Limit Theorem (CLT) • The Central Limit Theorem The CDF of 𝑍𝑛 = 𝑋1+⋯+𝑋𝑛−𝑛𝜇 𝜎 𝑛 converges to standard normal CDF Φ 𝑧 = 1 2𝜋 න −∞ 𝑧 𝑒 −𝑥 2/2𝑑𝑥 in the sense that lim 𝑛→∞ P 𝑍𝑛 ≤ 𝑧 = Φ(𝑧) The distribution of the r.v.𝑍𝑛approaches a normal distribution