Latest revision as of 13:20, 22 November 2011

Question

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?

Answer

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.

x= time I arrive
y= wait time

A={x<=1:20} P[A]=1/3
B={X>=1:20} P[B]=2/3

Theorem of Total Probability
fY(y)=fY/A(y)*P[A] + fY/B(y)*P[B]

fY/A

 |

3 |_____

 |     |

 |_____|______

      1/3

fY/B

   |

2/3 | ______

   |    |      |

   |____|______|______

       1/3     1

FY(y)

   |
1  |___________
   |           |
   |___________|______
               1

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