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How to calculate the average x-coordinate of a region?
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I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation infinitely many times, what is the average of the x-coordinate?
Thanks for your help!
calculus probability integration improper-integrals average
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
$endgroup$
add a comment |
$begingroup$
I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation infinitely many times, what is the average of the x-coordinate?
Thanks for your help!
calculus probability integration improper-integrals average
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
$endgroup$
add a comment |
$begingroup$
I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation infinitely many times, what is the average of the x-coordinate?
Thanks for your help!
calculus probability integration improper-integrals average
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
$endgroup$
I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation infinitely many times, what is the average of the x-coordinate?
Thanks for your help!
calculus probability integration improper-integrals average
calculus probability integration improper-integrals average
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
asked Sep 9 '15 at 0:56
John SmithJohn Smith
674514
674514
add a comment |
add a comment |
1 Answer
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$E[x] = int_{cal R} x dA$ where ${cal R}$ is the two-dimensional region (assumed uniform density) and $dA$ is a differential area, such as $dx dy$ or $2 pi r dr dtheta$.
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
$E[x] = int_{cal R} x dA$ where ${cal R}$ is the two-dimensional region (assumed uniform density) and $dA$ is a differential area, such as $dx dy$ or $2 pi r dr dtheta$.
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
add a comment |
$begingroup$
$E[x] = int_{cal R} x dA$ where ${cal R}$ is the two-dimensional region (assumed uniform density) and $dA$ is a differential area, such as $dx dy$ or $2 pi r dr dtheta$.
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
add a comment |
$begingroup$
$E[x] = int_{cal R} x dA$ where ${cal R}$ is the two-dimensional region (assumed uniform density) and $dA$ is a differential area, such as $dx dy$ or $2 pi r dr dtheta$.
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$E[x] = int_{cal R} x dA$ where ${cal R}$ is the two-dimensional region (assumed uniform density) and $dA$ is a differential area, such as $dx dy$ or $2 pi r dr dtheta$.
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
answered Sep 9 '15 at 1:02
David G. StorkDavid G. Stork
11.1k41432
11.1k41432
add a comment |
add a comment |
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