No. 3 Let X1, X2, ..., Xn, ... be R-valued IID random variables with mean u...

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No. 3 Let X1, X2, ..., Xn, ... be R-valued IID random variables with mean u and vari- ance o2. Moreover, let S, = Di-1 Xk, and Fn(x) = P(Sn < x). %3D k=1 (1) Show that {Fn}n€N Converges to a function uniformly on R. (2) Give the uniform limit in (1). No. 3 Let X1, X2, ..., Xn, ... be R-valued IID random variables with mean u and vari- ance o2. Moreover, let S, = Di-1 Xk, and Fn(x) = P(Sn < x). %3D k=1 (1) Show that {Fn}n€N Converges to a function uniformly on R. (2) Give the uniform limit in (1).