121. 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 X  the number of start-ups 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)? [Hint:

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. Qual. Tech., 1983: 103—106.)