Positive random variables X and Y satisfy a scale model with parameters δ > 0 if P(Y ≤
t) = P(δX ≤ t) for all t > 0, or equivalently, G(t) = F(t/δ)
(a) Show that in this case, log X and log Y satisfy a shift model with parameter log δ.
(b) Show that if X and Y satisfy a shift model with parameter ∆, then eX and eY satisfy a
scale model with parameter e∆.
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