The Central Limit Theorem
• Consider a sequence Xk of Bernoulli (p) trials. • By the (strong) LLN we know that ∑n 1 Xk n will converge to p. • In particular, the limit is deterministic, there is nothing random about it anymore. • What is the limit of ∑n 1 Xk−np n ? • This makes sense in light of what we discovered last time: ∑n 1 Xk is concentrated in an interval of size c √ n about its mean np. • A different type of limit is encountered if we normalize by √ n instead of n. • The following graphs depict the pmf of