Question: Let F(t)=0 for t < 0, F(t) = p for 0 t < 1, and F(t)=1 otherwise. Use the central limit theorem to evaluate

Let F(t)=0 for t < 0, F(t) = p for 0 ≤ t < 1, and F(t)=1 otherwise. Use the central limit theorem to evaluate directly the distribution of supt|Fn(t) − F(t)|, and show that Fn(t) tends to F(t) almost surely and uniformly in t.

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