# 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.)

#### Solution Preview

Hello and thank you for posting your question to Brainmass!

The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

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.