5.1.12 Consider the mixed Poisson process of Section 5.1.4, and suppose that the mixing parameter 2 has the exponential density f ./ D e???? for > 0.

(a) Show that equation (5.3) becomes

(b) Show that

so that X0.t/ and the increment X0.tCs/????X0.t/ are not independent random variables, in contrast to the simple Poisson process as defined in Section 5.1.2.

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( Pr{X' (t) = j} = 1= (1+1) (1+1) for j=0,1,....