=+9, show that E(Tn) = n Var(Tn) = n 2 E eTn =

=+9, show that E(Tn) = n

λ

Var(Tn) = n

λ2 E



e−βTn

=

 λ

λ + β

n for β > 0. These results agree with our earlier findings concerning the mean, variance, and Laplace transform of Tn. (Hints: Use NTn = n and set β = −λ(1 − e−θ) for the third equality.)

268 10. Martingales