Consider a linear birth process with birth rates and state space Z = {0, 1, 2, ...}. (1) Given X(0) = 1, determine the distribution function of the random time point T 3 at which the process enters...

Consider a linear birth process with birth rates

and state space Z = {0, 1, 2, ...}.

(1) Given X(0) = 1, determine the distribution function of the random time point T₃
at which the process enters state 3.

(2) Given X(0) = 1, determine the mean value of the random time point T_n
at which the process enters state n, n > 1.