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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? | + | [[Category:ECE302Fall2008_ProfSanghavi]] |
| + | [[Category:probabilities]] | ||
| + | [[Category:ECE302]] | ||
| + | [[Category:problem solving]] | ||
| + | =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? <BR><BR> | ||
| − | + | =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.<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> | |
| − | < | + | |
| − | fY/A | + | Theorem of Total Probability<BR> |
| − | + | fY(y)=fY/A(y)*P[A] + fY/B(y)*P[B]<BR><BR> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | fY/B | + | |
| − | | | + | fY/A<BR> |
| − | 2/3 | ______ | + | |<BR> |
| − | | | | | + | 3 |_____<BR> |
| − | |____|______|______ | + | | |<BR> |
| − | 1/3 1 | + | |_____|______<BR> |
| + | 1/3<BR><BR> | ||
| + | |||
| + | fY/B<BR> | ||
| + | |<BR> | ||
| + | 2/3 | ______<BR> | ||
| + | | | |<BR> | ||
| + | |____|______|______<BR> | ||
| + | 1/3 1<BR><BR> | ||
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|___________|______ | |___________|______ | ||
| − | 1 | + | 1<BR><BR> |
| − | < | + | |
| + | ---- | ||
| + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
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
