For a conditional Poisson process.

(a) Explain why a conditional Poisson process has stationary but not independent increments.

(b) Compute the conditional distribution of A given {N(s), 0 st}, the history of the process up to time t, and show that it depends on the history only through N(t). Explain why this is true.

(c) Compute the conditional distribution of the time of the first event after given that N(t) = n.

(d) Compute lim P{N(h) 1} h-0 h

(e) Let X, X2,... denote the interarrival times. Are they independent? Are they identically distributed?