Question: 9. Let X1, X2, . . . be positive, i.i.d. random variables with mean / # 0 and finite variance 02. Let Sn = >

9. Let X1, X2, . . . be positive, i.i.d. random variables with mean / # 0 and finite variance 02. Let Sn = > Xk, n 2 1. k=1 (a) Show that Sn - All V converges in distribution as n - co to a random variable Sn + nul with distribution N(0, a2) and determine a2. (b) Show that Sn - nul converges in probability as n - co, and determine the limit. Sn + nut

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