Let X1, X2, be sequence of independent nonnegative random variables having a common distribution function F such that P(X₁ = 0) < 1, E[X₁] = a < ∞, Var[X₁]=0² <00. Denote So = 0, Sn = X1 + + Xn₁ n = 1, 2,..., and = Nt sup{n Sn ≤t}, : for any t≥ 0. 1. (10pts) Can we write N₁ = max{n: Sn <t} for any t > 0? Why? 2. (10pts) Show that Nto almost everywhere as t→ ∞.