Question: . Consider a Poisson process with parameter X. Given that n events happen by time t, show that the PDF of the time of occurrence

. Consider a Poisson process with parameter X. Given that n events happen by time t, show that the PDF of the time of occurrence Th of the kth event

(k < n) is given by n!

f (x) =

-KI F (1 -* ) **

=(k-1)!(n - k)! tk 0 < x < t,

=0, x≥ t.

Show that E(Tk) = kt/(n+ 1).

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