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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? | 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? | ||
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| + | 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 | x= time I arrive | ||
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Theorem of Total Probability | Theorem of Total Probability | ||
fY(y)=fY/A(y)*P[A] + fY/B(y)*P[B] | fY(y)=fY/A(y)*P[A] + fY/B(y)*P[B] | ||
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fY/A | fY/A | ||
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|___________|______ | |___________|______ | ||
1 | 1 | ||
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Revision as of 18:06, 5 October 2008
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?
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
