The zinc-phosphate coating on the threads of steel tubes used in oil and gas wells is critical to their performance. To monitor the coating process, an uncoated metal sample with known outside area is weighed and treated along with the lot of tubing. This sample is then stripped and reweighed. From this it is possible to determine whether or not the proper amount of coating was applied to the tubing. Assume that the probability that a given lot is unacceptable is .05. Let X denote the number of runs conducted to produce an unacceptable lot. Assume that the runs are independent in the sense that the outcome of one run has no effect on that of any other. (Based on a report in American Machinist, November 1982, p. 81.)
(a) Verify that X is geometric. What is "success" in this experiment? What is the numerical value of p?
(b) What is the exact expression for the density for X?
(c) What is the exact expression for the moment generating function for X?
(d) What are the numerical values of E[X], E[X2], a2, and a?