The purchaser of a power-generating unit requires c consecutive successful start-ups before the unit will be accepted. Assume that the outcomes of individual start-ups are independent of one another. Let p denote the probability that any particular start-up is successful. The random variable of interest is of start-ups that must be made prior to acceptance. Give the pmf of X for the case . If , what is ? [Hint: For

, express p(x) “recursively” in terms of the pmf evaluated at the smaller values .] (This problem was suggested by the article “Evaluation of a Start-Up Demonstration Test,” J. Quality Technology, 1983: 103–106.)