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. Quality Technology, 1983: 103–106.)
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