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 startups are independent of one another. Let p denote the probability that any particular start-up is successful. The random variable of interest is X = the number of startups that must be made prior to acceptance. Give the pmf of X for the case c = 2. If p = .9, what is P(X < 8)? [For x > 5, express p(x) "recursively" in terms of the pmf evaluated at the smaller values x - 3, x - 4, ..., 2.] (This problem was suggested by the article "Evaluation of a Start-Up Demonstration Test," J. Quality Technology, 1983: 103-106.)