where Theorem 2 Under M. 1 − M. 5 , and CPQD, sharp bounds on F$_{0}$ ( y$_{0}$ ) , F$_{1}$ ( y$_{1}$ ) , and F$_{Δ}$ ( δ ) are identical to those given in Theorem 1. Sharp bounds on F ( y$_{0}$, y$_{1}$ ) are obtained as follows: for ( y$_{0}$, y$_{1}$ ) ∈$_{R}$ ×$_{R}$ , where 39 F$_{d}$ ( y ) ∈ $^{[}$F L d ( y ) , F U d ( y ) $^{]}$, F ( y$_{0}$, y$_{1}$ ) ∈ $^{[}$F $^{L}$( y$_{0}$, y$_{1}$ ) , F U ( y$_{0}$, y$_{1}$ ) $^{]}$, F$_{Δ}$ ( δ ) ∈ $^{[}$F L Δ ( δ ) , F U Δ ( δ ) $^{]}$, F ( y$_{0}$, y$_{1}$ ) ∈ $^{[}$F $^{L}$( y$_{0}$, y$_{1}$ ) , F U ( y$_{0}$, y$_{1}$ ) $^{]}$, Theorem 2 F L 0 ( y ) = sup z ∈ Ξ $^{[}$P ( y | 0 , z ) (1 − p ( z )) + L wst 01 ( y, z ) $^{]}$, F U 0 ( y ) = inf z ∈ $_{Ξ}$[ P ( y | 0 , z ) (1 − p ( z )) + U sm 01 ( y, z )] , F L 1 ( y ) = sup z ∈ Ξ $^{[}$P ( y | 1 , z ) p ( z ) + L wst 10 ( y, z ) $^{]}$, F U 1 ( y ) = inf z ∈ $_{Ξ}$[ P ( y | 1 , z ) p ( z ) + U sm 10 ( y, z )] , F $^{L}$( y$_{0}$, y$_{1}$ ) = sup z ∈ Ξ    max $^{{}$( P ( y$_{0}$ | 0 , z ) − 1) (1 − p ( z )) + L wst 10 ( y$_{1}$, z ) , 0 } + max $^{{}$L wst 01 ( y$_{0}$, z ) + ( P ( y$_{1}$ | 1 , z ) − 1) p ( z ) , 0 }   $_{}$, F U ( y$_{0}$, y$_{1}$ ) = inf z ∈ Ξ    min { P ( y$_{0}$ | 0 , z ) (1 − p ( z )) , U sm 10 ( y$_{1}$, z ) } + min { U sm 01 ( y$_{0}$, z ) , P ( y$_{1}$ | 1 , z ) p ( z ) }   $_{}$, F L Δ ( δ ) = sup z ∈ Ξ    sup max y ∈$_{R}$ { P ( y | 1 , z ) p ( z ) − U sm 01 ( y − δ, z ) , 0 } +sup max y ∈$_{R}$ $^{{}$L wst 10 ( y, z ) − P ( y − δ | 0 , z ) (1 − p ( z )) , 0 }    , F U Δ ( δ ) = 1 + inf z ∈ Ξ    inf min y ∈$_{R}$ $^{{}$P ( y | 1 , z ) p ( z ) − L wst 01 ( y − δ, z ) , 0 } +inf min y ∈$_{R}$ { U sm 10 ( y, z ) − P ( y − δ | 0 , z ) (1 − p ( z )) , 0 }   $_{}$.