Continuation. The Poisson distribution of long runs. 12 If the number k of trials and the length of runs both tend to infinity, so that kqp" , then the probability of having exactly n runs of length r tends to e-/n!. Hint: Using the preceding problem, show that the generating function is asymptotically {1+qp'(1-x)}* ~e-(1-r). Use the continuity theorem of XI, 6.