Concept explainers
Ref erring to the previous exercise, 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
- a. Verify that the total area under the density curve is equal to 1.
(Hint: Area of a triangle =
- b. What is the
probability that w is less than 20? - c. What is the probability that w is less than 10?
- d. What is the probability that w is greater than 30?
7.30 Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a train. Suppose that the density curve is as pictured (a uniform distribution):
- a. What is the probability that x is less than 10 minutes? more than 15 minutes?
- b. What is the probability that x is between 7 and 12 minutes?
- c. Find the value c for which P(x < c) = 0.9.
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Chapter 7 Solutions
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