Let X₁, ...,X_n be independent standard exponential r.v.’s, and

Prove that

grows as lnn; more precisely,

where V_n is a r.v. whose d.f. P(V_n ≤ x) → G(x) = exp{−e^−x}. This distribution is called the double exponential distribution. Graph the d.f. G(x). Is it the d.f. of a positive r.v.? Compare the order of the growth and the type of normalization with these in Proposition 3. Give some heuristic comments on it.