93.

a. In a Poisson process, what has to happen in both the time interval (0, t) and the interval (t, t t) so that no events occur in the entire interval (0, t t)? Use this and Assumptions 1–3 to write a relationship between P0(t t) and P0(t).

b. Use the result of part

(a) to write an expression for the difference P0(t t)  P0(t). Then divide by t and let

t 0 0 to obtain an equation involving (d/dt)P0(t), the derivative of P0(t) with respect to t.

c. Verify that P0(t)
et satisfies the equation of part (b).

d. It can be shown in a manner similar to parts

(a) and (b)

that the Pk?