Consider a man and a woman who arrive at a certain location; whoever arrives first will wait for the other to arrive. If X and Y denote (respectively) the arrival times of the man and the woman after noon, in minutes, assume that X and Y are independent and each Uniformly distributed on [0, 60]. (In other words, the man and woman arrive independently, at Uniform times between noon and 1 PM.)
If the woman arrives at 12:35 PM, find the expected time spent waiting, i.e., find
E (|X - Y| |Y = 35).
Since we know that Y = 35, we may as well just substitute "35" for Y. so that we only have X's in our lives. So we just need to find
E (|X-35|)