(New page: 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? x= time I arrive y= wait tim...) |
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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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3 |_____ | 3 |_____ | ||
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1 | 1 | ||
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Revision as of 18:03, 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?
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
