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homework_6_2005

# homework_6_2005 - Homework Set#6 Problem 1 In planning a...

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Homework Set #6 Problem 1 In planning a building, the number of elevators is chosen on the basis of balancing initial costs versus the expected delay times of the users. These delays are closely related to the number of stops the elevator makes on a trip. If an elevator runs full (n people) and there are k floors, we want to find the expected number of stops R the elevator makes on any trip. Assuming that the passengers act independently and that any passenger chooses a floor with equal probability k 1 . Show that: 1 1 k n E[R] = 1 k Hint: It is often useful to define “indicator random variables” as follows: Let X i = 1 if k the elevator stops at floor i, and X i = 0 if it does not. Then observe that R = X i . Find = 1 the expected value of X i after finding the probability that X i = 0. Problem 2 In the very preliminary planning of some harbor island developments, there was discussion regarding the cost estimates of building four bridges. There had as yet not

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