Joe and Laura have aggreed to meet for dinner between 5PM and 6PM. Let X= Joe\'s
ID: 3384010 • Letter: J
Question
Joe and Laura have aggreed to meet for dinner between 5PM and 6PM. Let X= Joe's arrival time and Y= Laura's arrival time. Assume X and Y are independent with each uniformly distributed on the interval from 5PM to 6PM.
A.) What is the joint probability density function for X and Y? Draw a sketch in the x,y plane showing where the density function is nonzero.
B.) Suppose the first one to arrive will only wait 10 minutes before leaving. If you were going to evaluate the probability that Joe and Laura eat together, the first thing that you would need to do is identify where in the X,Y plane that this event is true. Draw a sketch in the X,Y plane showing where this event is true. Hint: The event of interest is A = ((x,y): |x-y| <= 1/6).
Explanation / Answer
Joe and Laura have aggreed to meet for dinner between 5PM and 6PM. Let X= Joe's
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