Hi I don't know if this question makes sense but I hope someone could help me out.
The equations for exponential distribution in a poisson process is given as:
$P(T> \tau) = e^{-\lambda\tau}$ for $ \tau\geq0$
and $P(T\leq\tau) = 1 - P(T<\tau) = F(\tau)$
For all I know I use these two equations when solving for 'waiting times' kinda question but I am not clear about when to use which. I would assume $T$ to be the total time span. Can anyone help me clear my doubts?