Let w1, w2, ... be the waiting times in a Poisson process {x(t); t >= 0} of rate lambda. Independent of the process, let Z1, Z2, ... be independent and identically distributed random variables with common probability density function f(x), 0 < x < inf.

What is Pr(Z > z) where Z = min(w1 + Z1, w2 + Z2, ...)?