# Joint CDF of a word problem

##### New member
So I have this word problem as seen below:

Joy and Ethan have agreed to meet for dinner between 8:00 PM and 9:00 PM. Suppose that Ethan may
arrive at any time between the set meeting. Joy on the other hand will arrive at the set meeting under the
following conditions:
• Joy will always arrive earlier than Ethan.
• Joy will never arrive later than 20 minutes.
• Joy’s arrival time added to Ethan’s arrival time will never exceed an hour.
Let X be the arrival time (in minutes) of Ethan and Y be the arrival time (in minutes) of Joy after 8:00
PM. Assume that all possible arrival times under the specified conditions are equally likely to occur.

I need to find the joint PDF of X and Y, which is easy enough as all that requires is differentiating the joint CDF with respect to both x and y. However, I'm not entirely sure how I would go about finding the joint CDF from the word problem above.
So far, I've gotten the bounds of the two variables as 0<X< 20 and X<Y<60 and X+Y <=60.
However, I do not know what to do next. I would appreciate any help on how to go about solving this problem. Thank you.

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