For the regenerative method, show that v = E(Z)/E(N). [Hint: Observe thatwhere n′ is the n...

For the regenerative method, show that v = E(Z)/E(N). [Hint: Observe that

where n′ is the number of regeneration cycles and M(n′) is the total number of observations (a random variable) in the n′ cycles. Let n′ → ∞ and apply the strong law of large numbers (see Sec. 4.6) to both sides of the above equation.] Also conclude that  as n′ → ∞ (w.p. 1), so that  is a strongly consistent estimator of v. (See the definitions of v in Sec. 9.5.3.)