1. Suppose you and your partner each roll two dice. Each of you computes the average of your two rolls. The summary statistic is the difference between your average and your partner’s average. Describe the sampling distribution of these differences.

2. Two different pumping systems on levees have pumps numbered 1, 2, 3 and 4, configured as in Display 6.32. In System I, water will flow from A to B only if both pumps are working. In System II, water will flow from A to B if either pump is working. Assume that each pump has this lifelength distribution: 1 month with probability 0.1, 2 months with probability 0.3, and 3 months with probability 0.6. Lifelength refers to the length of time the pump will work continuously without repair. Assume that the pumps operate independently of each other. (You are interested only in whether water will flow, not the amount of water flowing.).

a. Find the distribution of the length of time water will flow for System I.

b. Find the distribution of the length of time water will flow for System II.

c. Find the expected time that water will flow for each system and compare. Which system would you recommend?

 

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