Given that a train arrives at a train station every hour (1:20, 2:20, 3:20 etc.) and that I go to the train station from 1:00 to 2:00 how much time do I wait? <BR><BR> If you go to the edit page you can see this better. I am not sure how to get wiki to show this the way I want it to. If you know how please feel free to fix it.<BR><BR> x= time I arrive<BR> y= wait time<BR><BR> A={x<=1:20} P[A]=1/3<BR> B={X>=1:20} P[B]=2/3<BR><BR> Theorem of Total Probability<BR> fY(y)=fY/A(y)*P[A] + fY/B(y)*P[B]<BR><BR> fY/A<BR> |<BR> 3 |_____<BR> | |<BR> |_____|______<BR> 1/3<BR><BR> fY/B<BR> |<BR> 2/3 | ______<BR> | | |<BR> |____|______|______<BR> 1/3 1<BR><BR> FY(y) | 1 |___________ | | |___________|______ 1<BR><BR> <nowiki>
