RUN PROBABILITIES IN SEQUENCES OF MARKOV-DEPENDENT TRIALS * Steven J. Schwager Biometrics Unit, Cornell University, Ithaca, New York 14853 BU-765-M Rev. August 1982 ABSTRACT The probability of the occurrence of a run R is obtained as a function of the composition of R, the number n of trials, and the probabilities of the v :l!: 2 possible outcomes at each trial. The run R can consist of any spe- cified sequence of outcomes, and the probability that one or more of a given collection of runs occurs is also evaluated. The probabilities of the v possible outcomes can vary arbitrarily from trial to trial, and can be L-order Markov dependent on the L preceding outcomes. The practical application of these results is discussed. KEY WORDS: Runs tests; Runs distributions; Multiple Markov dependence; Time-dependent trials.