T_1,T_2-T_1T_3 - T_2,... are iid Exponential(lambda) rvs., that is, each has pdf

Question

T_1,T_2-T_1T_3 - T_2,... are iid Exponential(lambda) rvs., that is, each has pdf lambdae^-lambdat. In paritikmlar, E(T_i -t_i-1) = 1/lambda, which reflects the intuitive fact that the expected maiting time to the next success is inversely proportional to the intensity naite lambda. Partial Proof. P[T_1 > t] = p[no successes occur in (0, t] ] = P[Y_t = 0] = e^-lambdat, since Y_t ~ Poisson(lambdat)).. (Completion of the proof of Proposition 1.9). Show that T_1 and T_2 - T_1 me independent exponential(A) rvs. Show that T_1, T_2 - T_1 T_m - T_n_1 are iid exponential (lambda) rvs.

Explanation / Answer

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http://wwwf.imperial.ac.uk/~bin06/Stochastic-Processes/spl24.pdf

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