12. Events occur according to a Poisson process with rate . Any event that occurs within a...

12. Events occur according to a Poisson process with rate λ. Any event that occurs within a time d of the event that immediately preceded it is called a d-event. For instance, if d = 1 and events occur at times 2, 2.8, 4, 6, 6.6, . . . , then the events at times 2.8 and 6.6 would be d-events.

(a) At what rate do d-events occur?

(b) What proportion of all events are d-events?