Referring to Exercise 7.25, let x and y be waiting times

Chapter 0, Problem 7.26

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Referring to Exercise 7.25, let x and y be waiting times on two independently selected days. Define a new random variable w by w x y, the sum of the two waiting times. The set of possible values for w is the interval from 0 to 40 (because both x and y can range from 0 to 20). It can be shown that the density curve of w is as pictured (this curve is called a triangular distribution, for obvious reasons!): a. Verify that the total area under the density curve is equal to 1. (Hint: The area of a triangle is .) b. What is the probability that w is less than 20? less than 10? greater than 30? c. What is the probability that w is between 10 and 30? (Hint: It might be easier first to find the probability that w is not between 10 and 30.)

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