8.2 CHEBYSHEV'S INEQUALITY AND THE WEAK LAW 8.3 The Central Limit Theorem Theorem 2.1 The weak law of large numbers Let X1,...,Xn be a sequence of independent and identically distributed random variables.Each having finite mean E(Xi)u,D(Xi)-2.Then,for any c>0, P+,+X-川≥)→0 asn→∞ 4口5,42手·3000 Xiaohan Yang Chapter 8 Limit Theoremslogo 8.2 CHEBYSHEV’S INEQUALITY AND THE WEAK LAW OF LARGE NUMBERS 8.3 The Central Limit Theorem Theorem 2.1 The weak law of large numbers Let X1, · · · , Xn be a sequence of independent and identically distributed random variables. Each having finite mean E(Xi) ˆ=µßD(Xi) ˆ=σ 2 . Then, for any  > 0, P(| X1 + · · · + Xn n − µ| ≥ ) → 0 as n → ∞ Xiaohan Yang Chapter 8 Limit Theorems