Originally Posted by
shogunhd Hi
I've been looking at this problem for awhile now.
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}.
For [A]
I set the pdf of x & y = (1/60) for 5 hr, 0 min <= x,y <= 5 hr, 60 min / 0 otherwise
for the pdf of f(x,y) = (1/3600) for 5 hr, 0 min <= x,y <= 5 hr, 60 min / 0 otherwise
Is this correct? If not, please explain.
Can you also show me how I can set up parts [b] & [C]