Let (Y, Z) be the typical cycle of an alternating renewal process, where Y and Z have an Erlang distribution with joint parameter λ and parameters n = 2 and n = 1, respectively. For t → ∞, determine...

Let (Y, Z) be the typical cycle of an alternating renewal process, where Y and Z have an Erlang distribution with joint parameter λ and parameters n = 2 and n = 1, respectively.

For t → ∞, determine the probability that the system is in state 1 at time t and that it stays in this state over the entire interval [t, t + x], x > 0.

Hint Process states as introduced in section 3.3.6.