Uniform Distribution Problem on Efficiency
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A bus travels between two cities $A$ and $B$ which are $100$ miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a Uniform Distribution over $(0,100)$. There is a bus service station in city $A$, city $B$ and in the center of the route between $A$ and $B$. It is suggested that it would be more efficient to have the three stations at $25,50$ and $75$ miles, respectively, from $A$.
The question asks if the second arrangement is more efficient, I know how to calculate the probabilities, my intuition tells me that the second system is better, but can’t seem to come up with a way to conclusively state that either one will be better, can anyone help?
probability probability-distributions uniform-distribution
asked Nov 27 '18 at 15:01
user601297user601297
31019
$endgroup$
add a comment |
$begingroup$
A bus travels between two cities $A$ and $B$ which are $100$ miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a Uniform Distribution over $(0,100)$. There is a bus service station in city $A$, city $B$ and in the center of the route between $A$ and $B$. It is suggested that it would be more efficient to have the three stations at $25,50$ and $75$ miles, respectively, from $A$.
The question asks if the second arrangement is more efficient, I know how to calculate the probabilities, my intuition tells me that the second system is better, but can’t seem to come up with a way to conclusively state that either one will be better, can anyone help?
probability probability-distributions uniform-distribution
asked Nov 27 '18 at 15:01
user601297user601297
31019
$endgroup$
$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43
add a comment |
$begingroup$
A bus travels between two cities $A$ and $B$ which are $100$ miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a Uniform Distribution over $(0,100)$. There is a bus service station in city $A$, city $B$ and in the center of the route between $A$ and $B$. It is suggested that it would be more efficient to have the three stations at $25,50$ and $75$ miles, respectively, from $A$.
The question asks if the second arrangement is more efficient, I know how to calculate the probabilities, my intuition tells me that the second system is better, but can’t seem to come up with a way to conclusively state that either one will be better, can anyone help?
probability probability-distributions uniform-distribution
asked Nov 27 '18 at 15:01
user601297user601297
31019
$endgroup$
A bus travels between two cities $A$ and $B$ which are $100$ miles apart. If the bus has a breakdown, the distance from the breakdown to city A has a Uniform Distribution over $(0,100)$. There is a bus service station in city $A$, city $B$ and in the center of the route between $A$ and $B$. It is suggested that it would be more efficient to have the three stations at $25,50$ and $75$ miles, respectively, from $A$.
The question asks if the second arrangement is more efficient, I know how to calculate the probabilities, my intuition tells me that the second system is better, but can’t seem to come up with a way to conclusively state that either one will be better, can anyone help?
probability probability-distributions uniform-distribution
probability probability-distributions uniform-distribution
asked Nov 27 '18 at 15:01
user601297user601297
31019
asked Nov 27 '18 at 15:01
user601297user601297
31019
asked Nov 27 '18 at 15:01
user601297user601297
31019
asked Nov 27 '18 at 15:01
user601297user601297
31019
asked Nov 27 '18 at 15:01
user601297user601297
31019
31019
$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43
add a comment |
$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43
$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43
$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43
add a comment |
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$begingroup$
Perhaps you should try to calculate the expected value for the distance between the disabled bus and the nearest service station for the two cases.
$endgroup$
– Dean
Nov 27 '18 at 16:43