problemset29

problemset29 - STAT/MA 416 November 4, 2011 Problem Set 29...

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STAT/MA 416 November 4, 2011 Problem Set 29 Name: 1. Let X 1 ,X 2 ,X 3 be independent exponential waiting times, each with an average of 30 minutes. Let Y = X 1 + X 2 + X 3 . a. What is the average (in minutes) of Y ? b. What is the standard deviation (in minutes) of Y ? 1

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2. A chef working in a kitchen believes that the waiting time until the next dessert order is exponential, with an average of 3 minutes. The times between dessert orders are assumed to be independent exponentials, also with 3 minutes on average. Let Y be the time until the next dessert order, and let Z be the subsequent time (afterwards) until the following dessert order. [E.g., if it is 12 noon right now, and the next order arrives at 12:04 PM, and the order after that arrives at 12:11 PM, then Y = 4 and Z = 7.] Let X = Y + Z . Find the density of X . 2
Suppose that the times until Hector, Ivan, and Jacob’s pizzas arrive are independent exponential random variables, each with average of 20 minutes. Let X be the

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problemset29 - STAT/MA 416 November 4, 2011 Problem Set 29...

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