Let's say I have points $T_i$ forming Poisson point process. I need to find $\lambda$ - Poisson intensity and $F$ - distribution of i.i.d. variables $X_i$ (or maybe some general rules for them) such that with probability $1$ at some time $i$ we will have $T_i < X_i$. I have no other constants.
The thing is with that information I don't even know when to start. Any hint will be appreciated. Thank you.