Define a functional space of functions of the form $F(t)=p_1 exp^{-\mu_1(\delta-t)}+p'_1 (1-exp^{-\mu_1(\delta-t)}))$. $p_1,p'_1,\delta,\mu$ are parameters in [0,1] and trivially, variation of these parameters builds the instances of our functional space. The goal is to solve the following optimization problem tractably:

$max_{F_1,F_2\in F(t)} \int_0^\delta \lambda exp^{-\lambda t} (F_1(t)-F_2(t))dt$.