(*) Show that it is possible for the KS distance between the CDF of two cumulative distribution functions F x( ) and F x * ( ) with domain [0,1] can be made arbitrarily close to 1 while at the same time making their corresponding exposure curves G x( )

and G x * ( ) arbitrarily close.

Hint: Assume that F x * ( ) is related to F x( ) as below and ensure that ε is as small possible while k is as close as possible to 1.

F x k F x x k k F x x

* ( ) = ( − ) ( ) ≤ <

+ − ( ) ( ) ≤ ≤







1 0 1 1

ε

ε