6.7.10 Consider a stationary .0;/ Cox process.

(a) Show that

whence

(b) Establish the limit

where

(c) We interpret the limit in

(b) as the conditional probability PrfN..0; t]/ D 0jEvent occurs at time 0g:
Show that

where

(d) Let be the time to the first event in .0;1/ in a stationary .0;/ Cox process with D D 1 and D 2. Show that E[ jEvent at time 0] D 1:

Why does this differ from the result in Problem 6.7.4?

Transcribed Image Text:

Pr{N((0,h]) > 0, N((h,h+t])=0} = f(t;)-f(t+h;),