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A difficult homework problem I received:
Two people meet between 1:00 and 2:00. The person that arrives first will wait for 15 minutes and then leave. Find the probability that the two actually meet, if arrival times are random.
Thanks.
Here is an outline of one possible solution:
~ and ~ .
Get the pdf for .
Calculate .
For other solutions read this thread: http://www.mathhelpforum.com/math-he...obability.html
The question only asked to find the probability of this event.
So, I wouldn't find the density of .
Instead I would just integrate the region in , where
. Naturally, one must assume that these rvs are independent.
But we must becareful that if one person arrives at 1:05, then the other person must arrive between 1 and 1:20.
So drawing this region in is quite important.