Let (Xn)n>1 be a sequence of independent and identically distributed (i.i.d.) random -Xn for N≥ 1. Assume that Xn, takes

[answerhappygod]

Let Xn N 1 Be A Sequence Of Independent And Identically Distributed I I D Random Xn For N 1 Assume That Xn Takes 1 (45.86 KiB) Viewed 25 times

Let (Xn)n>1 be a sequence of independent and identically distributed (i.i.d.) random -Xn for N≥ 1. Assume that Xn, takes the three values 1,-1,0, each with probability 1/3. variables. Define SN = [10] [5] (a) Prove that, almost surely, Sy is unbounded (as N → ∞). (b) Explain why, almost surely, SN=0 for infinitely many N. (c) We know that converges in distribution to a mean-zero, normally dis- tributed, random variable Y, say. Define convergence in distribution. [5] (d) Give (without proof) an example of a set ACR for which P(YE A) = 0 but for which P(SN/VNE A) = 1/2 for all positive odd integers N. [5]