In Exercise 11-8, suppose that both sides receive random-sized re-enforcements that increase their numbers, and that these re-enforcements arrive at random times. Re-enforcements to x ( t ) arrive with interarrival times that have an exponential distribution with mean 8 hours, and the f rst re-enforcement arrives not at time 0, but after one of kel01315_ch11_479-518.indd 517 05/12/13 3:19 PM 518 Chapter 11 these interarrival times. The size of the re-enforcement to x ( t ) has a Poisson distribution with mean 20. Similarly, y ( t ) is re-enforced at interarrival times exponentially distributed with mean 4 hours (the f rst re-enforcement arrives after one of these interarrival times past time 0), and with re-enforcement sizes distributed as Poisson random with mean 30. Run the model until one side or the other is completely depleted, with the same animation elements as in Exercise 11-8. Do ten replications and make entries in the Statistic data module that will produce an estimate of the probability that x wins (that is, y ( t ) is depleted to zero f rst), the expected duration of the f ght, and the expected f nal value of x ( t ) 2 y ( t ), which could be positive or negative. Depending on the probability distributions involved, this model does require simulation, since no analytical solution is available, unlike in Exercise 11-8.