Suppose that {N (t) : t 0} is a Poisson process with rate > 0. (a) If
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Suppose that {N (t) : t 0} is a Poisson process with rate > 0.
(a) If t > s provide an expression for P ( N(t) = n | N(s) = m ) , consider the cases n m and n < m separately.
(b) Again assume that t > s, provide an expression for cov ( N(t) , N(s) ) = E ( N(t) N(s) ) E ( N (t) ) * E ( N (s) ).
Tip: E( N(t) ) = t and Var ( N(t) ) = E( N(t)^2 ) (E( N(t) ))^2 = t.
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