Let be a Poisson process with intensity λ and denote by T1 the time of the first event. Then, Show that, for Let be an inhomogeneous Poisson process with time dependent intensity Find, with...

Let

be a Poisson process with intensity λ and denote by T₁
the time of the first event. Then,

Show that, for

Let

be an inhomogeneous Poisson process with time dependent intensity

Find, with T₁
as in the previous problem, the probabilities