help please

3. In a Poisson process with rate A, dene Pn(t) : P{N(t) : n}, where N(t) is the number of events which have occurred by time t, and suppose that N (0) 0. (a) Using the axioms of the Poissorn process and by expressing Po(t + 5d) = P{N(t + (R) = D} in terms of the number of events up to time t and the number between times t and t + 6t Show that PM) = 413w). Hence show that Pg(t) = Ke'\