Positive random variables X and Y satisfy a scale model with parameters > 0 if P(Y

t) = P(X t) for all t > 0, or equivalently, G(t) = F(t/)

(a) Show that in this case, log X and log Y satisfy a shift model with parameter log .

(b) Show that if X and Y satisfy a shift model with parameter , then e^Xand e^Ysatisfy a

scale model with parameter e.

(c) Suppose a scale model holds for X, Y . Let c > 0 be a constant. Does X' = X^c, Y' = Y^c

satisfy a scale model? Does log X', log Y' satisfy a shift model?