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Joint Probability Distribution Function

10. Annie and Alvie have agreed to meet between 5:00 pm and 6:00 pm for dinner at a local health food restaurant. Let X=Annie's arrival time and Y=Alvie's arrival time. Suppose X and Y are independent with each uniformly distributed on the interval [5, 6].

a. What is the joint pdf of X and Y?
b. What is the probability that they both arrive between 5:15 and 5:45?
c. If the first one to arrive will wait only 10 minutes before leaving to eat elsewhere, what is the probability that they have dinner at the health-food restaurant? [Hint: The event of interest is A={(x,y): | x-y | < 1/6}.] (Please use the given hint. Thanks.)

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I suggest you also check out*:
http://mathworld.wolfram.com/UniformDistribution.html
http://mathworld.wolfram.com/JointDistributionFunction.html
http://www.ccl.rutgers.edu/~ssi/thesis/thesis-node53.html

10. Annie and Alvie have agreed to meet between 5:00 pm and 6:00 pm for dinner at a local health food restaurant. Let X=Annie's arrival time and Y=Alvie's arrival time. Suppose X and Y are independent with each uniformly distributed on the interval ...

Solution Summary

The 4 pages solution shows how to find the pdf and how to set and solve the integrals that will give the required answers.

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