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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 appliedto the tubing.Assume that the probability that a given lot is unacceptable is0.05.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.

（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],σ²,and σ？

（E）Find the probability that the number of runs required to produce an unacceptable lot is at least 3.

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在把油和瓦斯被用於得很好的鋼管的線上的鋅－磷酸鹽的塗料是重要的對他們的表現。為了要監視塗料程序，一個不塗上一層的金屬製的樣本與在區域以外知道連同裝管的運氣一起被秤重而且對待。這一個樣本然後被除去而且再秤重。從這，決定是可能的，是否適當量的塗料是 appliedto 裝管。假定，可能性一個給定的運氣是無法接受的是 0.05.讓 X 指示奔跑 co 的數字

（一）查證， X 是幾何學的。這實驗的 " 成功 " 是什麼？p 的數字價值是什麼？

（B）什麼為 X 為密度是精確的表達？

（C）什麼為 X 為片刻母函數是精確的表達？

（D）什麼是 E 〔X〕、 E 〔X2] 、σ 2 和σ的數字價值？

（E）發現可能性奔跑的數字必需的生產一個無法接受的運氣是至少 3.